Piaget’s Theory of Intellectual Development · 2016-10-14 · Preface Since the early 1950s,...

Piaget’s Theory of Intellectual Development

Third Edition

Herbert P. Ginsburg and Sylvia Opper

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Table of Contents

1 Biography and Basic Ideas

2 Infancy

3 The Years 2 through 11: The Semiotic Function and Piaget’s Early Work

4 The Years 2 through 11: Piaget’s Later Work

5 Adolescence

6 Learning, Development, and Education


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Foreword

TodayPiagetseemstobethechildpsychologistintheeyesoftheAmericanpublic.Hisnamecrops

up in countless publications, and his ideas are discussed in many different circles—psychological,

educational,philosophical,psychiatric.Inspiteofhispopularity,however,heremainsadifficultauthor,

especiallyforanEnglish-speakingreader.Piaget’sTheoryofIntellectualDevelopment is thereforevery

welcome.Thanks to the joint effortsof aPiagetian-trainedpsychologist andanAmericanprofessorof

developmentalpsychology,wenowhave abook thatbringsout andexplains thedifficulties sooften

encounteredbystudentsofPiaget.Nottofeeldisturbedatanymisinterpretationofhisthoughtisarare

pleasurewhenreadingabookaboutPiaget,andIwasdelightedtofindthattheauthorshavenotfallen

intothetwomostcommonpitfalls:theyhavenotoversimplified,norhavetheybeencontenttoadoptthe

difficultPiagetianterminologywithoutadequateexplanation.

The undergraduate students of Piagetian theory, for whom this book is intended, are really

fortunate to have this book to help them understand some of the more abstruse concepts; even our

Genevanstudentsdonotfindhistheoryeasytograsp.EachtimePiagetcomesacrossabehavior,however

trivial itmay seem, he seeks to explain itwith reference to his theoretical framework,which is thus

continuously being refined and enriched; with Piaget, the empirical is never separated from the

theoretical.Itisthiscontinuingdevelopmentthatstudentsfinddifficult,andthatissoclearlybroughtto

light in thisbook.The authors in fact adopt this technique, passing from theory to example, andvice

versa,inawaywhichisbothclearandcomprehensible.Theirexamplesofchildren’sbehaviorhavebeen

most carefully selected, and I particularly like the use of various aspects of one example to illustrate

differenttheoreticalpoints.Ialsothinkitusefulthattheauthorshaveincludedotherinterpretationsof

somePiagetianconcepts,thusgivingthereaderanideaofPiaget’spositionincontemporarypsychology.

Infact,althoughthiswell-writtenbookisprimarilydestinedforstudents,itisquiteclearthatitwill

enablemanyreadersalreadywellacquaintedwithPiaget’stheorytoexplorehisreasoningmoredeeply.

It is not concernedwith lengthydiscussionor criticism,butprovides, as itwas intended to, a concise

descriptionandclearanalysisofPiaget’sthoughtandwork.


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BärbelInhelder

Geneva,Switzerland

ProfessorofDevelopmentalPsychology


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Preface

Sincetheearly1950s,Piaget’stheoryhasdominatedthefieldof intellectualdevelopment.From

1920until his death in1980, Piaget andhis collaboratorsproducedmoreworthwhile research and

theory than any other individual or group of investigators in child psychology. The sheer volume of

Piaget’soutputisstaggering.Hepublishedmorethanfortyfull-lengthbooksandmorethanahundred

articlesinthefieldofchildpsychology.

Butnumbersalonedonottellthestory.Piagetcapturedtheinterestofmodernpsychologistsand

educators for several important reasons.First,he introduceda scoreofnewand interestingproblems

whichpreviouslywentunnoticed.Forexample,itwasPiagetwhodiscoveredtheprofoundlycomplex

problemofconservation,whichhascaughttheimaginationofmanyinvestigators.Thisproblemtapsone

aspectofthechild’sabilitytoconstructarealitywhichtranscendsthemereappearanceofthings.Second,

Piaget’s theorieshave reorientedcurrent conceptionsof the child’sdevelopment.His ideasarenovel,

imaginative,andcomprehensive.Theyhavesubstantiallysupplantedthestimulus-responsebehaviorist

theoryasthemostinfluentialpointofviewindevelopmentalpsychology.Andfinally,ofalltheoriesof

development, Piaget’s is the one most securely founded upon the study of the child. None of the

investigatorswhose theories have beenused to explain the development of children—Freud, Lewin,

Hull,Miller andDollard, Skinner,Werner—has studied childrenas extensively ashasPiaget. In fact,

someof these figures— for example, Freud,Hull, Skinner—hardly studied children at all. Gesell did

studychildren,butdidnotproduceaviabletheory.Bycontrast,fornearlysixtyyearsPiagetobserved,

interviewed,andtestedchildrenofallages,andthisenormoussetofempiricaldataisthefoundationof

histheory.

Clearly, then, persons interested in human development should at the least be familiar with

Piaget’swork.Unfortunately, this is no simple task. For themost part, Piaget is an extremely difficult

writer:hisideasarenovelandhardtoassimilate;hisstyleofwritingisnottheultimateinlucidity;many

of his theoretical terms sound strange to the ears of the professional psychologist or educator, and

certainlytothenovice;andhislatercontributionsarestatedintermsofsymboliclogicandmathematics.

Thesedifficultieshaveseveralunfortunateconsequences.OneisthatthejoboflearningaboutPiagetis


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veryonerousindeed.TheinterestedreaderseemstorequireatextintroducingPiaget’sideasbeforehe

orsheisabletoprofitfromtheprimarysourcesthemselves.

Wehavewritten this book in the hope of assisting the beginning student of Piaget. It is a brief

introductiontohisbasic ideasand findingsconcerningthechild’s intellectualdevelopment.Wehope

that the book will be useful to students, particularly undergraduates, in psychology, education, and

alliedfields.Thebookmaybeusedassupplementaryreading, inwholeorinpart, incoursesdealing

withchildpsychology,cognition,educationalpsychology,andsoon.Wehope,too,thatthebookmaybe

readwithprofitbythegeneralreader.

Despitethefactthatthebookisanintroduction,andabriefoneatthat,wehavetriedtopresentthe

material in some depth. That is, we have assumed that the reader, although knowing little about

psychologyandPiaget,isintelligentandwillingtoworkabittounderstandPiaget’sideas.Second,we

haveassumedthatthereadershouldnotbeshieldedfromdifficultaspectsofPiaget’stheory,liketheuse

ofsymboliclogic.

Naturally,inabookofthistype,wehavehadtobeselective.NodoubtreadersfamiliarwithPiaget

willnoticethatwehaveomittedanumberofimportanttopics.Forexample,wedonotdescribethework

on perception, or the research on concepts of geometry. We make no pretense at offering a

comprehensive treatment of Piaget’s work. Rather, we have tried to present, as lucidly as possible,

Piaget’smajortheoreticalnotionsconcerningintellectualdevelopment,aswellassomeoftheresearch

onwhichtheyarebased.SincetheaimofthisbookistopresentclearlythebasicsofPiaget’sideas,we

havekeptourowncritiquetoaminimum.Forthesamereason,andalsotoavoidavery longbook,we

havenot referredextensively to independent investigators’ researchonPiaget’s ideas. So thisbook is

neitheracritiquenorareviewoftheliterature;itisanintroductiontoPiaget.

Theaimofthisthirdeditionistoupdatethesecond.Sincethewritingofthesecondedition,Piaget

and his collaborators produced new research and theory on a variety of topics, mainly concerning

developmentandlearning.Itisquiteremarkablethatduringthelasttenyearsofhislife—whenhewas

inhisseventiesandearlyeighties—Piagetwasengagedinamajorexpansionandevenrevisionofhis

theory. In this edition,we outline thesemajor changes and thereby complete our account of Piaget’s


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theory.(ForadetailedexpositionoflatedevelopmentsinPiaget’stheory,seeGallagherandReid,1981.)

Whileintroducingthisnewmaterial,wehaveattemptedtoretainfeaturesthatwethinkmadethebook

valuabletomanyreaders,namely,anexpositionwhichissimpleandclearandyetfaithfultothedepth

ofPiaget’sideas.

Chapter1beginswithabriefbiographyofPiagetandoutlinessomeofhisbasicideas.Chapter2

dealswithhisaccountofdevelopmentininfancy.Thefocusisonanaspectofthetheorywhichhasnot

beensufficientlystressed,namely,theaccountoflearningandmotivation.Chapter3describesPiaget’s

earlyresearchandtheoryconcerningthechildfromabout2to11yearsofage.Amongthetopicscovered

arethedevelopmentofsymbolism,thechild’smethodsofcommunication,andmoraljudgment.Chapter

4presentsPiaget’sresearchonchildrenfromabout2or3to11or12yearsofageandcoverstheclassic

workonclasses,relations,number,andconservation,aswellasnewerresearchonfunctions,imagery,

andmemory.Weincludecross-culturalwork,wherepertinent.Chapter5discussesadolescentthought,

describing Piaget’s use of logic as a model for adolescent thought and his notion of adolescent

competence.Chapter6presentsadiscussionof learninganddevelopmentandcoversmaterials from

Piaget’slastworks,publishedduringtheperiodfromthemid-1970sonward.Itincludesdescriptionsof

hisrevisedmodelof theequilibrationprocess, theroleofdisturbancesanddisequilibria, thespiralof

knowing, and possibility and necessity. We have followed this with an expanded discussion of the

implicationsofPiaget’sworkforeducation.Wehopethatbytheendofthebookstudentswillhavesome

insightintoPiaget’sviewsandwillappreciatethemagnitudeofhiscontribution.

Finally, we have employed several bibliographic conventions. If a book of Piaget’s has been

translatedintoEnglish,weuseitsEnglishtitleandpublicationdate;otherwise,weusetheFrench.Ifa

bookisfrequentlycited,werefertoitbyitsinitials.Thus,foreasyreference,TheOriginsofIntelligencein

Childrenbecomes01.


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Acknowledgments

Theauthorswishtothankthefollowingpublishersforpermissiontoreprintinthisbookcopyrighted

materialsbyPiaget:

Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique et Phénocopie (Paris:

Hermann,1974),Figureofthespiralofknowing,reprintedbypermissionofHermann.

The Child’s Conception of Number (with Alina Szeminska), translated by C. Gattegno and F. M.

Hodgson(London:Routledge&KeganPaulLtd.,1952),pp.45,50,75,79,82,124-125,reprintedby

permissionofRoutledge&KeganPaulLtd.andW.W.Norton&Co.,Inc.

TheChild’sConceptionoftheWorld,translatedbyJ.andA.Tomlinson(NewYork:Harcourt,Brace&

World, Inc., 1929), pp. 258-259, 274, reprinted by permission of Routledge & Kegan Paul Ltd. and

HumanitiesPress,Inc.

The Construction of Reality in the Child, translated by M. Cook (New York: Basic Books, Inc.,

Publishers,1954),pp.14,25,51,76,77,79-80,reprintedbypermissionofRoutledge&KeganPaulLtd.

andBasicBooks,Inc.,Publishers.

TheEarlyGrowthofLogicintheChild,translatedbyE.A.LunzerandD.Papert(London:Routledge

&KeganPaulLtd.,1964),pp.21,102,109,reprintedbypermissionofRoutledge&KeganPaulLtd.and

Harper&Row,Publishers.

“EquilibrationandtheDevelopmentofLogicalStructures,”inDiscussionsonChildDevelopment:The

FourthMeetingoftheWorldHealthOrganization,StudyGrouponthePsychobiologicalDevelopmentofthe

Child, edited by J. M. Tanner and B. Inhelder (London: Tavistock Publications Ltd., 1956), p. 102,

reprintedbypermissionoftheWorldHealthOrganization.TheGrowthofLogical

ThinkingfromChildhoodtoAdolescence, translatedbyA.ParsonsandS.Seagrin(NewYork:Basic

Books,Inc.,Publishers,1958),pp.56,60,70-71,75,103,116-17,129,130,reprintedbypermissionof

Routledge&KeganPaulLtd.andBasicBooks,Inc.,Publishers.


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JudgmentandReasoningintheChild,translatedbyM.Warden(NewYork:Harcourt,Brace&World,

Inc., 1926), pp. 17-18, 87, 88, 123, reprinted by permission of Routledge & Kegan Paul Ltd. and


TheLanguageandThoughtoftheChild,translatedbyM.Gabain(London:Routledge&KeganPaul

Ltd.,1926),pp.35,37,41,126,130,149,reprintedbypermissionofRoutledge&KeganPaulLtd.and


TheMoralJudgmentoftheChild,translatedbyM.Gabain(NewYork:Harcourt,Brace&World,Inc.,

1932),pp.55,60,122,126,141,reprintedbypermissionofRoutledge&KeganPaulLtd.andCrowell-

Collier,Inc.

TheOriginsof Intelligence inChildren, translatedbyM.Cook (NewYork: InternationalUniversity

Press,1952),reprintedbypermissionofDelachaux&Niestlé.

Play,Dreams,andImitationinChildhood,translatedbyC.GattegnoandF.M.Hodgson(NewYork:W.

W.Norton&Co.,Inc.,1951,1962),pp.10,30,31,46-47,55-56,63,65,96,218,222,224,225,231,

232,bypermissionofRoutledge&KeganPaulLtd.andW.W.Norton&Co.,Inc.

The Psychology of Intelligence, translated by M. Percy and D. E. Berlyne (London: Routledge &

KeganPaulLtd.,1950),pp.6,7,reprintedbypermissionofRoutledge&KeganPaulLtd.andHumanities

Press,Inc.


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Biography and Basic Ideas

WeshallbeginbyreviewingJeanPiaget’slifetogivethereaderanideaoftheinfluencesaffecting

hisworkandofthewidescopeofhisactivities;thenweshalldiscussinapreliminarywaysomebasic

ideasandthemesthatunderliehistheoryofintellectualdevelopment.

BIOGRAPHY1

JeanPiagetwasbornonAugust9,1896,inthesmalluniversitytownofNeuchatel,Switzerland.

His father was a historian who specialized in medieval literature, and his mother was a dynamic,

intelligent,andreligiouswoman.Piagetshowedanearlyinterestinnature;heenjoyedobservingbirds,

fish,andanimalsintheirnaturalhabitat.Atschool,too,hisleaningsweretowardthebiologicalsciences.

But his was no ordinary schoolboy enthusiasm: when he was only 10 years old, a natural history

magazinepublishedhisfirstarticle,describinganalbinosparrowseeninthepark.Soonhewasableto

help the director of the natural history museum of Neuchatel, where his task was to assist in the

classificationofthemuseum’szoologycollection.Atthistime,hebegantostudymollusksand,from15to

18yearsofage,publishedaseriesofarticlesontheseshellfish.Oneofthepapers,writtenwhenPiaget

wasonly15yearsold,resultedintheofferofthepostofcuratorofthemolluskcollectionattheGeneva

naturalhistorymuseum.Piagethadtodeclinethepositiontocompletehishighschoolstudies.

Asanadolescenthespentavacationwithhisgodfather,SamuelCornut,aSwissscholar,whowasto

haveaconsiderableinfluenceonhisintellectualdevelopment.CornutfeltthatPiaget’shorizonswere

too restricted in the direction of the biological sciences and decided to introduce the young man to

philosophy,particularlytotheworkofBergson.Consequently,Piaget,whountilthenhadgivenhismain

attentiontothestudyofbiologyandthenaturalbehavioroforganisms,nowturnedhisthoughtstoother

pursuits.Hisreadingsbroadenedtoincludephilosophy,religion,andlogic.Contactwiththesesubjects

ledeventuallytoaspecialinterestinepistemology,thebranchofphilosophyconcernedwiththestudyof

knowledge.Hebecamecurioustodiscovertheanswerstosomeofthebasicquestionsofthediscipline:

Whatisknowledge?Howisitacquired?Canonegainanobjectiveunderstandingofexternalreality,oris


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one’sknowledgeof theworld coloredanddistortedby internal factors?Although fascinatedby these

issues, Piaget felt that their solution could not be provided solely by philosophy. In comparing the

attributesofphilosophyandscience,Piaget’sconclusionwasthat“anideaisonlyanidea,whileafactis

only a fact” (Insights and Illusions in Philosophy, 1971b). In other words, he was convinced that the

philosophicalapproachistoospeculative,andthescientificapproachissometimestoofactual.Whatis

neededisalinkagebetweenthetwo:anexperimentalphilosophy,asitwere.

Wesee,then,thatduringhisadolescencePiagetconcentratedontwomajorintellectualpursuits:

biologyandepistemology.Thereis,ofcourse,agreatgapbetweenthetwodisciplines.Oneisconcerned

with life and the other with knowledge. One employs scientific methods and the other relies on

speculation.Piagetbegantowonderwhetheritmightnotbepossibletobridgethisgapbetweenthetwo

disciplinesandtofindsomewayofintegratinghisbiologicalandepistemologicalinterests.Howcould

oneinvestigatetheveryfascinatingproblemsofknowledge,andatthesametimeutilizethescientific

frameworkofbiology?

Although interested in epistemological questions, Piaget put his major efforts into the study of

biology. In 1916he completedhis undergraduate studies in natural sciences at theuniversity of his

hometown,Neuchatel.Only twoyears later, at theageof21,he submitted to the sameuniversityhis

dissertationon themollusksof theValais regionof Switzerlandand received thedegreeofDoctorof

Philosophy.

After finishing his formal studies, Piaget decided to explore psychology. He left Neuchatel for

ZurichtoworkintwopsychologicallaboratoriesandatBleuler’spsychiatricclinic.Hethendiscovered

psychoanalysisandtheideasofFreud,Jung,andothersandlaterpublishedanarticleontherelations

betweenpsychoanalysisandchildpsychology.In1919heleftZurichforParis,wherehespenttwoyears

at the Sorbonne University, studying clinical psychology as well as logic, epistemology, and the

philosophyofscience.Hisencounterwithphilosophyoncemoreconvincedhimthat it isnecessaryto

supplementpurespeculationwiththescientificapproach.

ItwasduringhisstayinParisthatanopportunityarosewhichwastoshapethedirectionofhis

futurework.In1920heacceptedapostwithDr.TheophileSimonintheBinetLaboratoryinParis.(With


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Alfred Binet, Simon had earlier constructed the first successful intelligence test.) Piaget’s taskwas to

develop a standardized French version of certain English reasoning tests. In a standardized test the

wordingofthequestionsandtheirorderofpresentationarepreciselydefined,andtheexaminermust

notdeviatefromthepre-establishedprocedure.Theaimofastandardizedtestistopresenteachsubject

with the same problems so that the subsequent differences in performance can be attributed not to

variations in the questions, but to differences in the subjects’ intelligence (or other traits being

measured).

Attheoutset,Piagetwasnotveryenthusiasticaboutthework.Standardizingatestcanbeavery

mechanical and tedious process. But then three major events occurred. First, although intelligence

testingusuallyfocusesonthechild’sabilitytoproducecorrectresponses,Piagetfeltthat,onthecontrary,

thechild’sincorrectanswerswerefarmorefascinating.Whenquestioningthechildren,Piagetfoundthat

thesamewronganswersoccurredfrequentlyinchildrenofaboutthesameage.Moreover,therewere

different kinds of commonwrong answers at different ages. Piaget puzzled on themeaning of these

mistakes. He came to the conclusion that older children are not just “brighter” than younger ones;

instead,thethoughtofyoungerchildrenisqualitativelydifferentfromthatofolderones.Inotherwords,

Piaget came to reject a quantitative definition of intelligence—a definition based on the number of

correct responseson a test. The real problemof intelligence, Piaget felt,was todiscover thedifferent

methodsofthinkingusedbychildrenofvariousages.

Second,Piagetsoughtadifferentmethodforthestudyofintelligence.Heimmediatelyrejectedthe

standardized testprocedure. Suchanapproach,he felt,was too rigid: for example, itmight lead toa

considerablelossofinformationifthechilddidnotunderstandthequestions.Consequently,hesoughta

lessstructuredmethodwhichwouldgivehimmorefreedomtoquestionthechild.Hissolutionwasto

apply to the task his previous experience in clinical psychology: he modified psychiatric interview

techniquestomakethemsuitable for thestudyofchildren’s thought.Thenewmethodwasextremely

flexible.Itinvolvedlettingthechild’sanswers(andnotsomepreconceivedplan)determinethecourseof

questioning. If the child said something interesting, then it would immediately be pursued, without

regardforastandardizedprocedure.Theaimofthis“clinicalmethod”wastofollowthechild’sownline

of thought,without imposing anydirectionon it, to comprehend theunderlying causesof the child’s

responses.


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At about the same time as hiswork in theBinet Laboratory, Piagetwas also studying abnormal

childrenattheSalpetrièreHospitalinParis.Hefelt,likeFreud,thatknowledgeofabnormalfunctioning

might provide insight into the normal working of the mind. Piaget therefore applied the “clinical

method”developedattheBinetLaboratorytohisstudyofabnormalchildren.However,hefoundthatthe

methodwasnot adequate since abnormal children’s verbal abilitiesweredeficient. Consequently, for

thesechildrenheaddedanimportantprocedure:thechildwasrequirednotonlytoanswerquestions,

but also to manipulate certain materials. Unfortunately, Piaget did not immediately apply the

supplementedclinicalmethod—freeverbalquestioningplusmaterialsformanipulation—tothetesting

ofnormalchildren.ItwasonlyaftertheexclusivelyverbalprocedureprovedinadequatethatPiagetlater

madeuseofhisexperienceatSalpetrière.

Third,whileusingtheclinicalmethodtostudychildren’sthought,Piagetwasreadingextensively

inlogic.Itoccurredtohimthatabstractlogicmightberelevantinseveralwaystochildren’sthinking.He

noticed, for instance, that children younger than about 11 years were unable to carry out certain

elementary logical operations. The possibility of extensively investigating this apparent deficiency

immediatelypresenteditself.Also,Piagetfeltthatthoughtprocessesformanintegratedstructure(nota

conglomerationofisolatedunits)whosebasicpropertiescanbedescribedinlogicalterms.Forexample,

thelogicaloperationsinvolvedindeductionseemedtocorrespondtocertainmentalstructuresinolder

children. He set himself the goal of discovering how closely thought approximates logic. This was a

distinctiveconceptionofthepsychologyofintelligence.

The years at the Binet Laboratory were very fruitful. Piaget published several accounts of his

psychologicalresearchonchildren.But,moreimportant,thestayinParistaughtPiagetthattheproblem

of intelligencemust be defined in terms of discovering children’s ways of thinking, that the clinical

method isuseful for the studyof thought, and that logic, rather than the imprecisenatural language,

mightbeanefficientwayofdescribingthought.Furthermore,Piagethadnowdiscoveredawayinwhich

hemightintegratehisbiologicalandepistemologicalinterests.Ashesawit,thefirststepwastopursue

thepsychologyofhumanintelligence.Asapsychologist,hecouldstudytheinpidual’sknowledgeofthe

world,hisattemptstocomprehendreality.Thiskindofpsychology,inotherwords,wouldbedirectedat

epistemologicalissues.Also,itwouldbebiologicallyoriented.ForPiaget,thismeantseveralthings.First,

psychologicaltheorymightmakeuseofbiologicalconcepts.Forinstance,intelligencecouldbeviewedin


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termsofanorganism’sadaptationtoitsenvironment.Second,psychologymightfocusontheprocessof

intellectualgrowthintheinpidual.Hebelievedthatafullunderstandingofhumanknowledgecouldbe

gainedonlythroughthestudyofitsformationandevolutioninchildhood.Howcouldonecomprehend

thefinalproductwithoutknowinghowitdeveloped?Forthesereasons,then,Piagetdecidedtoengage

firstinthepsychologicalstudyofthechild’sunderstandingofreality.Hisinitialintentionwastospenda

fewyearsinexperimentedstudiesofthechild’sintelligenceandthenturntoasecondproject,namely,

theapplicationofhispsychologicaldiscoveriestothetheoreticalproblemsofepistemology.Hefeltthat

hecouldclarifyepistemologicalissuesonlyafterhehaddevelopedanunderstandingoftheinpidual’s

cognitivegrowth.Asweshallsee,Piagetspentmorethana“fewyears”athisfirsttask.Itwasonlyafter

somethirtyyearsofpsychologicalstudythatPiagetwasabletoturnhisattentiontotheoreticalquestions

ofepistemology.

In1921, thedirectorof theJean-JacquesRousseauInstitute inGeneva,EdouardClaparède,who

hadbeenimpressedbyPiaget’searlyarticlesonchildren,offeredhimthepostofdirectorofresearchat

theInstitute.Piagetacceptedtheoffer,whichgavehimanexcellentopportunitytocarryonhisstudyof

child thought.Theoutcomeofhis researchwas a seriesof articles and thepublication, from1923 to

1932, of his first five books on children. The first one, Language and Thought in the Child (1926b),

provides naturalistic and experimental observations on the child’s use of language. Piaget found, for

instance, that the young child’s speech is substantially egocentric and that this tendency decreases

graduallyasthechildgrowsolder.JudgmentandReasoningintheChild(1926a)dealswiththechanges

incertaintypesofreasoningfromearlytolatechildhood.TheChild’sConceptionoftheWorld(1929)uses

theexclusivelyverbalclinicalmethodtoprovidedataonhowthechildviewsthesurroundingworld,

and onwhat he believes to be the origins of dreams, of trees, the sun, and themoon. InThe Child’s

Conception of Physical Causality (1960a), Piaget describes the child’s ideas on the causes of certain

naturalphenomena,suchasthemovementofthecloudsandofrivers,theproblemofshadows,orthe

displacement ofwaterwhen an object is immersed. Finally,The Moral Judgment of the Child (1932)

providesinformationonthedevelopmentofmoralbehaviorandjudgment.HerePiagetmaintainsthat

children show two typesofmoral judgment: theyoung childholds to apredominantly authoritarian

moralcode,whereastheolderchilddevelopsamoralityofsocialconcernandcooperation.

Contactwithpsychoanalysisisevidentintheearlyworks:Piaget’stheoriesmakeuseofFreudian


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ideasandaresometimesevenstatedinFreudianterms.Thebooksalsogiveabrief indicationofwhat

Piagetwaslatertoexpandupon:aviewofintellectualdevelopmentasconsistingofaseriesofstages.

Throughhis research,Piagetwasbecoming increasinglyawareof thedifferencesbetween the child’s

and the adult’s thoughtprocesses.He realized that the child isnotmerely aminiature replicaof the

adult:notonlydoesthechildthinklessefficientlythantheadult,buthealsothinksdifferently.Thus,

Piagetbecame convinced that itwasnecessary to conceiveof intellectualdevelopment in termsof an

evolutionthroughqualitativelydifferentstagesofthought.

Piagetalsoattemptedtodiscover thecausesof this intellectualevolution.His first interpretation

was that intellectual development resulted particularly from social factors, like language and contact

withparentsandpeers.Later, afterhis studyof infancy,where the roleof language isnegligiblebut

whereonthecontrarythechild’sownactivityisparamount,hechangedhisinterpretationofthenature

ofintellectualdevelopment:hedeemphasizedtheinfluenceofsocialfactorsandstressedactionasthe

sourceofthought.

MuchtoPiaget’sastonishment,thefirstfivebooks,whichhehimselfcallshis“adolescent”works,

gainedhimconsiderablefame,particularlyamongchildpsychologists.Piaget,whohadneverinhislife

passedanexaminationinpsychology,suddenlybecameanauthorityonthesubject.Thestircausedby

thebooksdisturbedhimsomewhatsinceheconsideredthemtobeonlypreliminaryandtentative,and

notanexpressionofhisdefinitiveviewsonthenatureofintelligence.Hewaswellawareofthebooks’

deficiencies. Nevertheless, he agreed to publish the volumes,mainly because he felt theymight lead

otherstofurtherresearcheventuallyresultinginafullerunderstandingofchildthought.

IntheUnitedStates, thebookswereat firstreceivedenthusiastically,andduringthe1920sand

1930s, Piaget’sworkwas highly regarded in this country. Then followed a period, lasting until the

middle 1950s, when his views, as expressed in the early books, came under much criticism. Some

investigators felt that Piaget’s findings could not be replicated. Butwith the publication in the early

1950sofEnglishtranslationsofseveralofPiaget’slaterbooks,interestinhisworkrevived.

Duringtheperiodfrom1920to1930,Piaget’stimewasfullyoccupied.Heperformedagreatdeal

of research and at the same time also taught various courses in psychology, sociology, and scientific


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thoughtatGenevaandNeuchatel.Histhreechildrenwerebornduringtheseyears:adaughterin1925,

aseconddaughterin1927,andasonin1931.Piagetandhiswife,oneofhisformerstudents,became

closeobserversoftheirchildren’sbehavior.Theresultsoftheirstudy,whichcoveredthe“sensorimotor

period”frombirthuntilabouttheageof2,werepublishedintwovolumes:TheOriginsofIntelligencein

Children(1952c)andTheConstructionofRealityintheChild(1954).Piaget’sstudyofinfancyconvinced

himthatthoughtderivedfromthechild’saction,andnotfromhislanguage.Thisincreasedemphasison

actionledPiagettomodifyhistestingtechniqueforolderchildren.Herememberedhispastexperience

at the Salpetrière Hospital and his solution to the difficulties encountered in trying to apply an

exclusivelyverbalmethodtoabnormalchildren.Consequently,hemadethemanipulationofconcrete

materialsanessentialaspectoftheclinicalmethodforchildrenofallages.Theemphasiswasnolonger

onlanguagealone,butonmanipulationsupplementedbylanguage.

From1929to1939Piaget’sprofessionallifebecameevenmoreactive.Hewasappointedprofessor

ofhistoryofscientificthoughtatGenevaUniversity.Hebecameassistantdirector,andshortlyafterward

co-director, of the Jean-Jacques Rousseau Institute, which he helped to reorganize when it became

attachedtoGenevaUniversity.HetaughtexperimentalpsychologyatLausanneUniversity.Also,Piaget

becameinvolvedininternationalaffairsandacceptedthechairmanshipoftheInternationalBureauof

Education,latertobecomeaffiliatedwithUNESCO.

Piaget’sexperiencesledtoseveralchangesinhisthinking.Thestudiesofinfancyinfluencedhimto

modifyhistechniquesofresearch,andtoplacegreateremphasisontheroleofthechild’sactivityinthe

formationofthought.Also,histeachingopenedupnewareasforresearchandexperiment.Thecourse

onthehistoryofscientificthoughtdirectedhimtowardthestudyofthechild’sunderstandingofcertain

scientificnotions.Withtwoimportantcollaborators,BärbelInhelderandAlinaSzeminska,hesetoutto

explorethisfield,andin1941publishedtwobooksontheirresearch.Thefirst,writtenwithB.Inhelder

wasTheChild’sConstructionofQuantities (1974). Itshowshowthechildgraduallycomestorecognize

that certain physical attributes of an object, like its substance orweight, do not varywhen the object

merelychangesshape.Surprisingly,youngchildrenfailtoconservetheseinvariants.Thesecondbook,

written with A. Szeminska was The Child’s Conception of Number (1952). Here Piaget describes the

evolutionofthechild’seffortstomasterthenotionofnumber.

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Thenextbook,publishedin1942,Classes,Relations,etNombres,dealswith thecorrespondence

betweencertainoperationsofformallogicandmentaloperations.Piagetuseslogictodescribethemental

operationsavailabletothechild from7to11 inthestageof“concreteoperations.”Thebookis thusa

fulfillment of Piaget’s early intention at the Binet Laboratory in Paris to use a formal language for

psychologicalpurposes.

Piagetthenbecameinterestedintheperceptualresearchofthe“Gestalt”psychologists.Hislackof

agreementwith some of their theories, however, led him and his collaborators to a lengthy series of

experiments into the nature of perception. At first Piaget replicated the experiments of the Gestalt

psychologists.Laterhisstudieswereextendedtocoverperceptionnotonlyasanisolatedprocess,but

also its relation to intelligence. For some twenty years, from 1943 onward, Piaget and his associates

producedanumberofarticlesandmonographsonperception.Theculminationwasthepublicationin

1961 of his book, The Mechanisms of Perception (1969), which describes perceptual structures and

processesandrelatesthemtointellectualones.

Intheearly1940s,AlbertEinsteinsuggestedtoPiagetthatitmightbeofinteresttoepistemologyif

hewere to investigate thechild’sunderstandingof time,velocity,andmovement.Piaget followedthe

suggestionandin1946publishedtwobooksonthesematters:TheChild’sConceptionofTime(1970b)

andTheChild’sConceptionofMovementandSpeed(1970a).Inthesameyear,1946,Piagetalsopublished

hisbookon symbolic thought,Play,Dreams,and Imitation (1951),which contains observationsonhis

ownchildren,from2to4yearsofage.

AftertheSecondWorldWar,appreciationofPiaget’sworkbegantospreadthroughouttheworld.

He received honorary degrees from several universities, including Harvard, the Sorbonne in Paris,

Brussels,andtheUniversityofBrazil. In theUnitedStates,however,Piagetwashonoredbutnot fully

understood;onlyhisfirstfivebookshadbeentranslated.Duringthe1940s,hecontinuedhisactivitiesin

theInternationalBureauofEducationandwasappointedheadoftheSwissdelegationtoUNESCO.In

1947PiagetpublishedasmallvolumeentitledThePsychologyof Intelligence (1950b). The book is a

collectionoflecturesPiagethadgivenin1942totheCollegedeFranceinParisandsetsout,forthefirst

timeatanylength,anoverviewofPiaget’stheoryofmentaldevelopment.


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During this time, Piaget continued his research into various aspects of cognition. From the

experimentsonperceptiongrewthestudyoftwocloselyalliedfields:thechild’sunderstandingofspace

and of geometry. In collaboration with Inhelder and Szeminska, he published in 1948 The Child’s

ConceptionofSpace(1956)andTheChild’sConceptionofGeometry(1960).In1949PiagetwroteTraité

deLogique,abookdealingwiththebasicoperationsinvolvedinlogic.Thebookisthefirstfullsummary

of his logical system: it expands upon the logical models already used in previous research and

introducesadditionallogicalmodelswhichhewaslatertoapplytoadolescentthought.

Fromabout1920 to1950,Piagethadbeenengaged in experimentalworkwith children in an

attempttounderstandtheevolutionofhumanintelligence.Nowhefeltpreparedtoapplytheresultsof

hispsychologicalresearchtotheepistemologicalproblemswhichhadoriginallymotivatedhisinterestin

psychology.In1950hepublishedathree-volumeserieson“geneticepistemology”entitledIntroductiona

l’Epistémologie Génétique (1950a). The books are a synthesis of his thinking on various aspects of

knowledge, includingmathematics, physics, psychology, sociology, biology, and logic. Piaget analyzes

thesefacetsofknowledgeintermsoftherelationbetweentheinpidualandhisenvironment—between

theknowerand theknown.He tries todeterminewhether this relationship isaffectedby the typeof

knowledge involved, for instance, whether mathematical knowledge involves a different kind of

interactionwiththeenvironmentfromthatofphysicalknowledge.Piagetalsodrawsaparallelbetween

the historical and inpidual development of knowledge, and he finds that the evolution of inpidual

thoughtsometimesfollowsthesameprogressionasthehistoryofscientificthought.

NextPiagetturnedtothestudyofchanceandtheelementaryconceptsofprobability.In1951,he

andInhelderpublishedabookentitledTheOriginoftheIdeaofChanceintheChild(1975),whichdeals

with the child’s understandingof randomevents inhis environment. In1952Piagetwas appointed

ProfessorofGeneticPsychologyattheUniversityofParis(Sorbonne),whereheremaineduntil1962.At

the same time he continued to teach at Geneva University and to head the Jean-Jacques Rousseau

Institute.Healsopursuedhisresearchintobothperceptionandlogicalthought.In1952hepublisheda

bookcalledEssai sur lesTransformationsdesOpérationsLogiques (1952b), dealingwithprepositional

logicandvariouslogicalstructures,likethegroupandlattice,whichheusedasmodelsforadolescent

andadultthought.Afterhavingstudiedtheperiodofearlyandmiddlechildhood,Piagetturnedtothe

nextphaseofintellectualdevelopment:thethoughtoftheadolescentandtheadult.In1955Piagetand


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Inhelderpublishedabookonthissubject,TheGrowthofLogicalThinkingfromChildhoodtoAdolescence

(1958),whichcompared,againinlogicalterms,thethoughtprocessesoftheadolescentwiththoseofthe

youngerchild.

The year 1956was important for Piaget, for hewas able to initiate a project that he had been

contemplating for some time. With his broad scope of interests, including biology, zoology, logic,

mathematics,psychology,philosophy,andepistemology,Piagethadalwaysdreamedofthepossibilityof

an interdisciplinary approach to basic problems of cognition. The idea had initially encountered a

certain amount of skepticism, but Piaget finally managed to establish an institution where such

interdisciplinary cooperation was possible. An international Center for Genetic Epistemology was

createdwithintheFacultyofScienceofGenevaUniversity.TheaimoftheCenterwastogathertogether

eachyearanumberofeminentscholarsinvariousfields—biologists,psychologists,mathematicians,and

others—whowouldcombinetheireffortstostudyagivenproblem.Eachpersonwouldtreattheproblem

from the point of view of his specialty, but the research was to be coordinated through regular

discussions. At the end of the year, a symposiumwould be held,where the researchers’ conclusions

wouldbediscussed.Thedeliberationsofeachsymposiumwouldbepublishedinaseriesofmonographs,

entitledStudiesinGeneticEpistemology.Overthepastthirtyyears,approximatelyfortyofthesevolumes

havealreadybeenpublished,andhavedealtwithavarietyofsubjectssuchasthenotionofcausality,the

learningprocesses,andmathematicalthinking.

In1959PiagetpublishedwithInhelderTheEarlyGrowthofLogic intheChild (1964).Thebook

againuseslogicalmodelstodescribethementaloperationsofthechildfrom7to11years.Ittreatsin

particularthechild’smethodofclassifyingandoforderingobjects.In1964asmallbookcontainingsix

short essays on various psychological topicswas published (Six Psychological Studies, 1967) and the

following year, 1965, Piaget published Insights and Illusions of Philosophy (1971b). In this book he

discussestheessentialdifferencesbetweenphilosophy,whichleadstosubjective“wisdom,”andscience,

whichleadstoobjectiveknowledge.Healsoexplainswhyheturnedawayfromhisearlypreferencefor

theformertowardthelatter.Inthesameyear,1965,healsopublishedabookoffoursociologicalstudies

entitledEtudesSociologiques,whichisacollectionofsomeofthelectureshehadgiveninhiscourseson

sociology.

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ThetitlesofPiaget’sbooksindicatethatthecontentsdealingeneralwithhighlyspecializedaspects

ofthinkingorcognition.Eachbooktreatsaparticulartopic,likegeometryornumber,inasimilarmanner.

That is, the notion is studied from its origins in the child to the point, usually in late childhood or

adolescence,whereitreachesamaturestatus.Althoughsuchanapproachisofinteresttopsychologists

andeducators,difficultiesarepresentedforthepersonwhowishesonlytogetageneralunderstanding

ofPiaget’soverallsystem.In1966,therefore,recognizingtheneedforashortintroductoryworkonhis

system,PiagetandInhelderpublishedashortbookentitledThePsychologyoftheChild(1969),which

was intended for thegeneralpublic.Thebookgivesabrief summaryofPiaget’s theoryof intellectual

developmentandalsodealswithrelatedmatterssuchasperception.Inthesameyear,1966,thesetwo

authorsalsopublishedabookonmentalimagery,MentalImageryintheChild(1971),whichdescribes

thedevelopmentofmental imagesand relates it to thegrowthof intelligence. In1967hepublished

Biology and Knowledge (1971a), which deals with the relations between biological factors and the

cognitive processes. He then turned his interests in another direction and in 1968 with Inhelder

publishedMemoryandIntelligence(1973).Inthisbook,Piagetintroducesanewapproachtothestudyof

memory:heexaminestherelationsbetweenmemoryandthedevelopmentof intellectualfunctioning.

He finds, forexample, thatmemorydoesnotalwaysdeteriorateovertime;paradoxically,memorycan

improveasaresultofthedevelopmentofcertainrelatedintellectualskills.Anotherbookpublishedin

1968,Structuralism(1970d),reflectsPiaget’scontinuinginterestintheapplicationofstructuralmodels

tomanydifferentdisciplines,andinparticulartotheoperationsofintelligence.

In the1960s and1970sPiaget’s fame continued to spread, andhis bookswere translated into

many languages. In America, where his work had at first been received with a certain amount of

skepticism,hewasnowrecognizedasa leader inhis field. In1969hewashonoredbytheAmerican

PsychologicalAssociation.In1971,attheageof75,PiagetretiredasdirectoroftheRousseauInstitute,

althoughhestillactivelypursuedhisresearchactivitiesasheadoftheCenterforGeneticEpistemology.

Hecontinuedtobeprolificinhiswritingsandpublications.Agreatmanynewbooksandarticles,aswell

asreeditionsofearlierworks,werepublishedinthe1970s.Someofthemajortitlesincludetwobooks

dealingwitheducation,ScienceofEducationandthePsychologyoftheChild(1970c)andToUnderstandIs

to Invent: The Future of Education (1973b) and two books on genetic psychology, Psychology and

Epistemology:TowardsaTheoryofKnowledge(1972b)andTheChildandReality:ProblemsofGenetic

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Psychology (1973a). In Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique et

Phénocopie(1974a),Piagetreturnedtohisearlyinterestinbiologyandtriedtorelateabiologicalmodel

ofdevelopmenttotheintellectualprocesses.

Piaget also conducted studies with Garcia into the notion of causality (Understanding Causality,

1974). Stemming from this research has been Piaget’swork on the child’s growing awareness of his

actions.Studiesinthisareahavebeenpublishedinthreebooks,TheGraspofConsciousness:Actionand

Concept in theYoungChild (1976b),Réussir et Comprendre (1974b), andLe Comportement, Moteur de

I’Evolution(1976a).Attheendofhislife,Piagetpublishedseveralimportantbooksdealingwithissues

ofdevelopmentandlearning.TheseincludeTheEquilibrationofCognitiveStructures(1985),Successand

Understanding(1978),Experiments in Contradiction (1981a),andLePossible et leNecessaire (1981b,

1983).

TheevolutionofPiaget’sinterestsisclearlyillustratedbythetitlesandcontentsofhisbooksand

other publications. From his early work in biology, particularly the study of mollusks, he gradually

turned to the psychological development of the child. His intention was to find a link between the

biological study of life and the philosophical study of knowledge. His first few books on children’s

thought were exploratory, setting forth his preliminary theory of intellectual development. Later,

however,hebegan tostatehis theories in termsofa formal language: logic.Thesubjectmatterofhis

booksalsobegantochange;hebecameattractedtothestudyofthechild’sunderstandingofscientificand

mathematicalnotions,aswellastootheraspectsofthecognitiveprocesses:perception,mentalimagery,

memory, consciousness. Once he had achieved a good measure of understanding of the child’s

intellectualprocesses,Piagetthenwishedtoplacehispsychologicaltheorieswithinalargerframework.

Hereturned,aftermorethanfortyyearsofpsychologicalresearch,tohisoriginalinterests—theoretical

problemsinepistemologyandbiology—andattemptedtoviewthedevelopmentof intelligenceasthe

linkbetweenthetwo.Towardtheendofhislife,Piagetbecameinvolvedintheproblemoftherelations

among reality, necessity, and possibility and in the issues of development and learning. It is quite

remarkable that, intohis eighties, Piaget pursuedhis professionalworkwith great vigor.Hedied on

September16,1980.


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BASIC IDEAS

Inthepresentsection,wewillintroduceseveralbasicideasthathaveshapedPiaget’sapproachto

the study of intellectual development. A scientist usually employs a theoretical framework to guide

experimentationandtheorizing.Theframeworkisnotadetailedtheorybutapointofvieworasetof

attitudeswhichorientsthescientist’sactivities.Apsychologist,forexample,maybebasicallycommitted

bothtoFreudian ideasandtothepersonalitytestapproach,whicharethen likelytogivedirectionto

researchandanalysis.Forexample, this frameworkmay influence thescientist tochoose tostudy the

familialcausesofneurosisratherthanpossiblephysicalbasesofthedisorder.Further,thisorientation

mightleadthescientisttoinvestigatethematterbygivingpaper-and-penciltests,whichmightproduce

resultsdifferentfromthosewhichcouldbeobtainedbythedirectobservationofthechildinthehome.

Thisisnottodeny,ofcourse,thatscientistsdochangetheiropinionsasaresultofconflictingresearch

evidence.Itisneverthelesstruethatorientingattitudescanbeinfluential;thescientistdoesnotbegin

workwithoutpreconceptions,andthesethenorganizetheinterpretationofresearchdata.2

Piaget’sorientingattitudes, statedquiteexplicitly, areconcernedwith thenatureof intelligence

andwithitsstructureandfunctions.

Intelligence

First,howdoesPiagetdefinethenatureof intelligence?ThereadershouldbeawarethatPiaget

hadalmostcompletefreedominthisregard.Previoustothe1920s,whenhebeganhisinvestigations,

there had been little research or theorizing on intelligence. The mental testing approach was in

evidence, as exemplified by the Binet-Simon IQ test, and there were also scattered experimental

investigationsofintellectualprocesseslikememoryintheadult.However,neitheroftheseapproaches

hadbeendevelopedextensively,andpsychologistshadhardlyagreed,anddonotconcureventoday,on

thepropersubjectmatterforthepsychologyofintelligence.3Doesintelligencerefertorotememory,to

creativity,toIQtestperformance,tothechild’sreasoning,ortoothermatters?BecausePiagetbeganhis

studies during a pioneering era, he was free to conceive of intelligence in terms of his unique

perspective.Hewascarefulnot tobeginbyproposing too rigidorpreciseadefinitionof intelligence.

Piagetdidnotwanttofallintothetrapoftoonarrowlycircumscribingthesubjectmatterwhensolittle


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wasknownaboutit.Tolaydownanoverlyrestrictivedefinitionattheoutsetwouldhavebeentocurtail

investigation and impede discovery. In fact, themajor aim of Piaget’s researchwas to discoverwhat

actuallyconstitutesintelligence.

Desiring to avoid premature restrictions, Piaget offered several definitions of intelligence, all

couched in general terms. These definitions reflect Piaget’s biological orientation. For example,

“intelligenceisaparticularinstanceofbiologicaladaptation. . .”(OriginsofIntelligence,pp.3-4).This

states quite clearly that human intelligence is one kind of biological achievement, which allows the

inpidualtointeracteffectivelywiththeenvironmentatapsychologicallevel.Anotherdefinitionstates

that intelligence “is the formofequilibriumtowardswhich thesuccessiveadaptationsandexchanges

betweentheorganismandhisenvironmentaredirected”{PsychologyofIntelligence,p.6).Theuseofthe

term “equilibrium,” borrowed fromphysics, suggests a balance, a harmonious adjustment between at

least two factors—in this case between the person or his cognitive structures and his environment.

Althoughthebalancemaybedisturbed,theinpidualcanperformactionstorestoreit.Intelligenceisthe

“instrument”which enables the inpidual to achieve this equilibriumor to adapt bymeans of certain

actionscarriedoutontheenvironment.Thedefinitionalsoimpliesthatequilibriumisnotimmediately

achieved:asthechilddevelops,thetypeofactionsthatheisabletocarryoutontheenvironmentwill

change and so, too, will the resulting equilibrium. Thus, for Piaget, there is no single and final

intelligence,butratherasuccessionof intellectualstages. It isofspecial interest to thepsychologist to

studytheevolutionofattemptsatequilibriumandthedynamicprocessesunderlyingit.Piaget’sprimary

goal,then,couldbedefinedasthestudyofchildren’sgradualattainmentofintellectualstructureswhich

allowforincreasinglyeffectiveinteractionswiththeenvironment.

Another definition stresses that intelligence is “a system of living and acting operations”

(PsychologyofIntelligence,1950b,p.7).Piagetisinterestedinmentalactivity,inwhattheinpidualdoes

in his interactionwith theworld. Piaget believes that knowledge is not given to a passive observer;

rather,knowledgeofrealitymustbediscoveredandconstructedbytheactivityofthechild.Asweshall

seelater,thispositionisatoddswiththebehavioristviewwhichforalongtimedominatedAmerican

psychology.

Finally,Piaget’sdefinitionofintelligenceinvolvesintellectualcompetence.Heisinterestedinthe


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inpidual’soptimumleveloffunctioningathiscurrentdevelopmentalstage.ForPiaget,intelligencedoes

notnecessarilyrefertotheinpidual’sordinaryorhabitualactivities,buttothebestthathecando.This

competencemayofcoursebeobscuredbyallkindsofconditions,bothtemporaryandlong-lasting—for

example,fatigue,boredom,illness.Factorslikethesemayproduceperformancethatfallsshortofpossible

competence.Whileitisimportanttounderstandhowandwhythishappens,Piaget’smaininterestisin

whattheinpidualcando,whetherornotthisiswhatheordinarilydoes.

Thusfar,wehaveseenthat intelligence involvesbiologicaladaptation,equilibriumbetweenthe

inpidualandtheenvironment,gradualevolution,mentalactivity,andcompetence.Thesedefinitionsare

intentionallyquitegeneral.Itisalsoinstructivetotakenoteofwhatthedefinitionsdonotstress.Theydo

notemphasizeinpidualdifferencesinintelligence.Whilesuchanemphasiswouldbequiteconsonant

withabiologicalapproach,Piagetisnotconcernedwithwhetheronepersonismoreintelligentormore

cleverthananother,orwhy.Piaget,ofcourse,recognizesthatdifferencesinintellectualabilitydoexist,

but he is not particularly interested in their analysis; instead, he seeks to abstract from the various

idiosyncraticmanifestationsofbehavioradescriptionofthegeneralformofthought.Thus,forPiaget,the

issueisnotwhyonebabystartstotalkat18monthsandanotherat22months;theissueisratherwhat

wordsmeantobothbabiesoncetheydotalk.Similarly,forPiaget,thequestionisnotwhyonechildcan

rememberthenamesoftwenty-fourstateswhileanotherchildrememberstwenty-eight;itisratherwhat

mental processes allow each child to remember whatever he does. So Piaget is less concerned with

explainingintellectualdifferencesthanunderstandingthementalprocesseswhichweallshare.

Itisimportanttonotethatthedefinitionsplacelittleemphasisontheemotions.Piaget,ofcourse,

recognizes that the emotions influence thought, and in fact, he repeatedly states that no act of

intelligence is complete without emotions. They represent the energetic or motivational aspect of

intellectual activity.Nevertheless,Piaget’s empirical investigationsanddetailed theories substantially

ignoretheemotionsinfavorofthestructureofintellect.

Piagethaschosenoneofseveralavailablestrategieswithwhichto investigate thepsychologyof

intelligence.Hedeemphasizesinpidualdifferencesandtheeffectsofemotionsonthoughtand,instead,

focusesontheoptimumleveloffunctioning.Manypsychologists,particularlyBritishandAmerican,have

concentratedon inpidualdifferencesbymeansof the testapproachto investigate intellectualactivity.


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Othershaveattemptedfromtheoutsettoconsidertheinfluenceoftheemotions,especiallyanxiety,on

intellectualperformance.Whichstrategyisbest?Theanswerseemstobethatallareofinterest.Allview

theproblemof intelligence fromdifferent angles anddealwith somewhatdifferent issues.Unable to

studyeverything,thescientistusuallysettlesononeapproachtoaccomplishanythingatall.Asweshall

seeinthepagesthatfollow,Piaget’sapproachseemstohaveamplydemonstrateditsmerits.

Inadditiontoproposinggeneraldefinitions,Piagethasstructuredthepsychologyofintelligenceby

theselectionoftheparticularsubjectmatterhehasinvestigated.Aswesawinthebiographicalreview,

Piaget’searlyworkswereconcernedwithsuchmattersasverbalcommunicationandmoral judgment.

With thepassageof timePiagethas come to stress thechild’sunderstandingofvarious scientific and

mathematical ideaslikevelocityandone-to-onecorrespondence.TounderstandPiaget’sconceptionof

intelligence,therefore,wemustnotonlyconsiderhisdefinitions,butthenatureofhisresearchactivities.

Thelatter,especiallyinrecentyears,revealratheruniquescientificandepistemologicalconcerns.

Inconclusion,wehaveseenhowPiaget’s twomajor interests—biologyandepistemology—have

shapedhisapproachtothepsychologyofintelligence.Thebiologicalconcernresultedindefinitionsof

intelligence in general terms of growth, stages, adaptation, equilibrium, and similar factors. The

epistemologicalfocushasresultedintheempiricalinvestigationofthechild’sunderstandingofspace,

time, causality, and similar notions. Piaget looks at intelligence in terms of content, structure, and

function.Wewillconsideraspectsoftheseinthefollowingsections.

Content

Onesimpleaspectofthought is itsmanifestcontent.Thisreferstowhattheinpidual isthinking

about,what interestshimat themoment,or the terms inwhichhecontemplatesagivenproblem.For

instance,whenaskedwhatmakesacargo,themechanicgivesananswerintermsoftheexplosionofgas,

themovementofpistons,thetransferofpowerfromonepointtoanother.Thesestatementsreflectthe

contentsof his thought. If a young childwereposed the samequestion, the responsewouldbequite

different.Ignorantoftheworkingsofthemotor,hemightsupposethatthecar’smovementresultsfrom

allthehorsesinside.Obviously,thecontentofhisthoughtisquitedifferentfromthatoftheadult.


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During the early portion of his career, Piaget’s research focused on the contents of the child’s

thought.TheChild’sConceptionoftheWorldandTheChild’sConceptionofPhysicalCausality,bothwritten

inthe1920s,paidparticularattentiontothechild’sviewsofthephysicalworld.Theclinicalmethodwas

used to obtain the child’s answers to such questions as:Where do shadows come from?What causes

rivers to flow or the clouds tomove?Despite these initial investigations, Piaget felt that the study of

contentwasonlyaminorgoalforthepsychologyofintelligence.Whiledescriptionsofcontentmayhave

someinterest,theydonotgetattheheartofthematter;theydonotexplainwhythoughttakestheformit

does.ForPiaget,therefore,theprimarygoalofthepsychologyofintelligenceisnotthemeredescription

of the content of thought but the understanding of basic processes underlying and determining the

content. Piaget has therefore devoted the greater part of his career in psychology to the study of the

structuresandfunctionsofintelligence.

Specific Heredity

ItshouldcomeasnosurprisethatPiaget’stheoreticalframeworkdealswiththeroleofbiological

factorsinthedevelopmentofintelligence.Thesefactorsoperateinseveralways:oneofthemisdefined

asthehereditarytransmissionofphysicalstructures,orspecificheredity.Differentspeciesare,ofcourse,

endowed by heredity with different physical structures. The nervous system, for example, varies

considerablyfromwormtohuman,andtheeffectsofthisvariationareobvious.Theinheritedphysical

structuresbothpermitcertainintellectualachievementsandprohibitothers.Theeyeisoneexampleof

suchastructure.Gibson(1966)pointsoutthatpredatoryanimalsaregenerallyendowedbyheredity

with frontal eyeswhichallow them to see clearlywhat is aheadand thereforewhat canbepounced

upon. By contrast, preyed-upon animals are generally endowed by hereditywith lateral eyeswhich

allowwideperipheralvisionsothatpotentialenemiescanbeidentified.Indeed,therabbitcanevensee

behinditsownhead.Thephysicalstructureoftheorganismquiteliterallydeterminesitsbasicviewofthe

world.

Another form of specific heredity is theautomatic behavioral reaction.For example, members of

manyspeciespossessvariousreflexesfrombirth.Whenaspecifiedeventintheenvironment(astimulus)

occurs,theorganismautomaticallyrespondswithaparticularbehavior.Nolearningortrainingorother

experiencewith the environment is usually necessary for the reflex response to occur.Moreover, all


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members of the species, unless they are in someway defective, possess the reflex. The basis for this

automatic behavior is an inherited physical mechanism. When the stimulus occurs it activates this

mechanism which produces the response. One example of automatic behavior is the sucking reflex,

whichisnecessaryforsurvival.Whenanyobject(thestimulus)touchesaninfant’s lips, theautomatic

responseistosuck.Thenewborndoesnotneedtobetaughttomakeanelementarysuckingresponse.A

furtherexampleistheabilitytocry.

Thenewborn’s physical structure is such thatwhenhungryhe automatically signalsdiscomfort

with a wail. Often the reflexes are adaptive: they help the organism in its interaction with the

environment.

Piaget feels that in the case of human intelligence, reflexes and other automatic patterns of

behaviorplayonlyaminorrole.Itisonlytheinfant,andmorespecificallythenewborn,whosebehavior

isheavilydependentontheelementarybehavioralreactionsofthetypedescribed.Piaget’sresearchhas

shownthatafterthefirstfewdaysof life,thereflexesaremodifiedbytheinfant’sexperienceandare

transformed into a new type of mechanism—the psychological structure—which is not directly and

simply provided by heredity. Aswe shall see, psychological structures form the basis for intellectual

activityandaretheproductofacomplexinteractionbetweenbiologicalandexperientialfactors.

Athirdaspectofspecificheredityisphysicalmaturation.Thegeneticcodeprovidesthebasisforthe

growthofphysicalstructuresalongcertainpaths.Forexample,asthechildgrowsolder,thebraingrows

larger,andthemusclesof the legsbecomestronger.Suchphysicalmaturation isoftenassociatedwith

various psychological activities: as the brain grows, speech emerges; as the leg muscles strengthen,

permitting greatermobility, the child expands his exploration of the world. Maturation alone is not

sufficienttocausethedevelopmentoftheseandotheractivities,butappearstobenecessaryformany,if

not all, of them. We shall see shortly that, in Piaget’s view, experience and other factors are also

necessary.

General Heredity

We have seen that specific heredity affects intelligence in three ways: (1) inherited physical


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structures set broad limits on intellectual functioning, (2) inherited behavioral reactions have an

influenceduringthefirstfewdaysofhumanlifebutafterwardareextensivelymodifiedastheinfant

interactswithhisenvironment,and(3) thematurationofphysical structuresmayhavepsychological

correlates.Piaget’stheoreticalframeworkpostulatesthatbiologicalfactorsaffectintelligenceinafourth

way:allspeciesinherittwobasictendenciesor“invariantfunctions”:organizationandadaptation.Thisis

generalheredity.

Letusfirstconsiderorganization.Thistermreferstothetendencyforallspeciestosystematizeor

organize their processes into coherent systemswhichmay be either physical or psychological. In the

formercase,fishpossessanumberofstructureswhichallowfunctioninginthewater,forexample,gills,a

particular circulatory system, and temperature mechanisms. All these structures interact and are

coordinated into an efficient system. This coordination is the result of the organization tendency. It

shouldbeemphasizedthatorganizationrefersnottogillsorthecirculatorystructureinparticular,butto

thetendencyobservedinall lifeto integratetheirstructures intoacompositesystem(orhigher-order

structure).

Atapsychologicallevel,too,thetendencytoorganizeispresent.Inhisinteractionwiththeworld,

theinpidualtendstointegratehispsychologicalstructuresintocoherentsystems.Forexample,thevery

younginfanthasavailabletheseparatebehavioralstructuresofeitherlookingatobjectsorofgrasping

them. He does not initially combine the two. After a period of development, he organizes these two

separatestructuresintoahigher-orderstructurewhichenableshimtograspsomethingwhilelookingat

it.Organization,then, isthetendencycommontoall formsof lifeto integratestructures,bothphysical

andpsychological,intohigher-ordersystemsorstructures.

Thesecondgeneralprincipleoffunctioningisadaptation.Allorganismsarebornwithatendencyto

adapt to the environment. Theways in which adaptation occurs differ from species to species, from

inpidualtoinpidualwithinaspecies,orfromstagetostagewithinanyoneinpidual.Nevertheless,the

tendencytoadaptinsomewayoranotherisaninvariantfunctionandthereforeconsideredanaspectof

biology. Adaptation may be considered in terms of two complementary processes: assimilation and

accommodation.


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We will illustrate these processes first by means of a simple physiological example, namely,

digestion.Whenapersoneatssomethinghisdigestivesystemreactstothesubstancesincorporated.To

dealwith the foreign substance, themuscles of the stomach contract in variousways, certain organs

release acids, and so on. Putting thematter in general terms,wemay say that the person’s physical

structures(thestomachandrelatedorgans)accommodatetotheenvironmentalevent(thefood).Inother

words, the process of accommodation describes the inpidual’s tendency to change in response to

environmentaldemands.Thefunctionalinvariantofassimilationisthecomplementaryprocessbywhich

theinpidualdealswithanenvironmentaleventintermsofcurrentstructures.Inthecaseofdigestion,

theacidstransformthefood intoa formwhichthebodycanuse.Thusthe inpidualnotonlymodifies

structuresinreactiontoexternaldemands(accommodation),healsouseshisstructurestoincorporate

elementsoftheexternalworld(assimilation).

ForPiaget,intellectualadaptationisalsoaninteraction,oranexchange,betweenapersonandhis

environmentandinvolvesthesametwoprocesses—assimilationandaccommodation—asarefoundin

biology.Ontheonehand,thepersonincorporatesorassimilatesfeaturesofexternalrealityintohisown

psychologicalstructures;ontheotherhand,hemodifiesoraccommodateshispsychologicalstructuresto

meetthepressuresoftheenvironment.Consideranexampleofadaptationininfancy.Supposeaninfant

of4monthsispresentedwitharattle.Hehasneverbeforehadtheopportunitytoplaywithrattlesor

similartoys.Therattle,then,isafeatureoftheenvironmenttowhichheneedstoadapt.Hissubsequent

behaviorrevealsthetendenciesofassimilationandaccommodation.Theinfanttriestograsptherattle.

Todothissuccessfullyhemustaccommodateinmorewaysthanareimmediatelyapparent.First,hemust

accommodatehisvisualactivitiestoperceivetherattlecorrectly,forexample,bylocatingitinspace.Then

he must reach out, adjusting his armmovements to the distance between himself and the rattle. In

graspingtherattle,hemustmoldhisfingerstoitsshape;inliftingtherattlehemustaccommodatehis

muscular exertion to its weight. In sum, the grasping of the rattle involves a series of acts of

accommodation, or modifications of the infant’s behavioral structures, to suit the demands of the

environment.

Atthesametime,graspingtherattlealsoinvolvesassimilation.Inthepasttheinfanthasalready

graspedthings;forhim,graspingisawell-formedstructureofbehavior.Whenheseestherattleforthe

firsttime,hetriestodealwiththenovelobjectbyincorporatingitintoahabitualpatternofbehavior.Ina


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sensehetriestotransformthenovelobjecttosomethingwithwhichheisfamiliar,namely,athingtobe

grasped.Wecansay,therefore,thatheassimilatestheobjectintohisframeworkandtherebyassignsthe

objecta“meaning.”

Adaptation, then, is a basic tendency of the organism and consists of the two processes of

assimilationandaccommodation.Howdo the tworelate tooneanother?First, it is clear that theyare

complementaryprocesses.Assimilationinvolvestheperson’sdealingwiththeenvironmentintermsof

his structures, while accommodation involves the transformation of his structures in response to the

environment.Moreover,theprocessesaresimultaneouslypresentineveryact.Whentheinfantgrasps

the rattle,his fingersaccommodate to its shape; at the same timehe is assimilating the rattle intohis

framework,thegraspingstructure.

In sum, Piaget postulates that there are two general principles of functioning which affect

intelligence: organization and adaptation (assimilation and accommodation). These biological factors,

aspectsofgeneralheredity,arecommontoallspecies.Whileorganizationandadaptationareinherited,

theyarenotstructures(likereflexes)buttendencies.Theparticularwaysinwhichanorganismadapts

andorganizes itsprocessesdependalsoon itsenvironmentand its learninghistory. InPiaget’sview,

humanbeingsinheritfewparticularintellectualreactions;rather,theyinheritatendencytoorganize

theirintellectualprocessesandtodevelopparticularadaptationstotheirenvironment.

Psychological Structures

Wehaveseen that the inpidual tends toorganizehisbehaviorand thoughtand toadapt to the

environment.Thesetendenciesresultinanumberofpsychologicalstructureswhichtakedifferentforms

at different ages. The child progresses through a series of stages, each characterized by different

psychological structures, before attaining adult intelligence. Frombirth to about 2 years, the infant is

unabletothinkandcanonlyperformovertaction.Forexample,ifatoyfallsaparthecannotfirstthink

how it might best be put together again; instead, he might immediately act on the toy and try to

reassemble it. His activities, however, are not random, but display order and coherence. Almost

immediatelyafterbirththeinfantshowsorganizedbehavior.As-wehaveseen,someofthesepatternsof

action,likethereflex,areduemainlytohereditaryfactors.However,specifichereditycannotexplainall


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theorderlinessintheinfant’sbehavior.Forexample,the2-month-oldinfantusuallysuckshisthumbora

finger.Whenputinthecribheregularlybringshishandtothemouthinarelativelyquickandefficient

way.Inthecommonlanguagewewouldprobablysaythattheinfanthasacquiredthe“habit”ofthumb-

sucking.Theword“habit”impliesaregularity,acoherence,intheinfant’sactions.Itisclearthatthumb-

suckingisnotbasedentirelyoninheritedphysicalstructures.Whilethereisareflextosuckanyobject

touching the lips, there is no innate tendency to bring the hand to themouth; this activitymust be

learned.InPiaget’stheory,suchanorganizedpatternofbehavioristermedascheme,4Theconceptof

schemeisusedinaverybroadway.Itcanrefertothereflexesandotherkindsofinnatebehavioralready

discussed.ItisinthiswaythatPiagetspeaksofthe“suckingscheme.”Butthevastmajorityofschemesare

not innate; instead, they are in someway based on experience, as in the case of the thumb-sucking

scheme.

Thusfarwehavespokenoftheschemeonlyasapatternofbehavior,orasanactionwhichdisplays

coherenceandorder.However,thereareanumberofadditionalaspectsofthescheme.First,itinvolves

activityonthepartofthechild;theconceptisusedtodescribethingshedoes.Mostoften,useoftheterm

inthiswaypresentsnodifficulties.Occasionally,however,schemeisusedtodescribeactionswhichare

notimmediatelyobvious.Forexample,Piagetspeaksofthe“lookingscheme.”Theuseof“scheme”hereis

quitedeliberatesincehemeanstoimplythatvisionisanactiveprocess;thechild’seyesmoveasthey

activelysearchtheenvironment.Second,schemereferstothebasicstructureunderlyingthechild’sovert

actions.Schemeisusedtodesignatetheessenceofthechild’sbehavior.Letustakethumb-suckingasan

example. Ifweexamine the infant’sbehavior indetail,wewill see thatno twoactsof thumb-sucking

performedbyonechildarepreciselythesame.Ononeoccasiontheactivitystartswhenthethumbis10

inchesfromthemouth,onanotherwhenitis11inchesaway.Atonetimethethumbtravelsinalmosta

straightlinetothemouth;atanothertimeitstrajectoryisquiteirregular.Inshort,ifwedescribebehavior

insufficientdetail,wefindthattherearenotwoidenticalactions.Thereisnooneactofthumb-sucking,

butmany;infactthereareasmanyasthenumberoftimesthechildbringsthethumbtothemouth.At

firstglancethissituationmightseemtoposeinsurmountabledifficultiesforthepsychologist.Howcan

shedescribeandexplainbehaviorifeachactisdifferentfromeveryother?Fortunately,thedifficultyis

onlyapparent,sincemostpsychologistsarenotreallyinterestedinthefinedetailsofbehavior.Whatis

important,especiallyforPiaget,isthestructureofbehavior,thatis,anabstractionofthefeaturescommon


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toawidevarietyofactswhichdifferindetail.Inthecaseofthumb-sucking,whetherornottheactstarts

fromadistanceof10or11inchesisofnosignificance.Whatiscrucialisthattheinfanthasacquireda

regularwayofgettingthethumbintothemouth.This“regularway”isanabstractionfurnishedbythe

psychologist.Theinfantputsthehandintohismouthinmanyparticularways,notwobeingidentical,

andthepsychologistdetectsinthesespecificactionsacertainregularitywhichshethencallsascheme.

Letusnowconsideranothertypeofpsychologicalstructure:thatoftheclassifyingoperationsofthe

olderchildfromabout7to11years.Supposeanexaminerpresentsthechildwithacollectionofredand

bluebeadsmixed together.Confrontedwith this situation theolderchild first thinksof theobjectsas

beingmembersofclasses.Thereistheclassofredbeadsandtheclassofblueones.Further,unlikethe

youngerchild,herealizesthattheclassofredbeadsisincludedinalargerclass,thatofbeadsingeneral.

Anotherwayofputtingthematteristosaythathegroupstheredbeadsintooneclassandconceivesofit

asbeingapartofahierarchyofclasses.Theclassimmediately“above”theredbeads(thatis,themore

inclusiveclass)isthatofbeads-in-general.Ofcourse,theclassofbeads-in-generalmayalsobelocatedin

aclassificationhierarchy.Theclassofsolidobjectscontainstheclassofbeads.

Obviously, theolder child’s operational schemes arequitedifferent from the infant’s behavioral

schemes.Thelatterinvolvepatternsofbehavior;theinfantactsovertlyontheworld.Althoughtheolder

child’sschemesalsoinvolveactingontheworld,thisisdoneintellectually.Heconsiders,forexample,the

relativelyabstractproblemofwhethergivenclassesarecontainedinothers.Piagetdescribesthisaspect

oftheolderchild’sthoughtintermsoftheoperationsofclassification.WhatisimportantforPiagetisnot

thatthechildcananswerquestionsaboutbeads(that,ofcourse,istrivial),butthathisactivitiesreveal

theexistenceofabasicthoughtstructure,namely,theoperationsofputtingthingstogether,ofplacing

theminclasses,offorminghierarchiesofclasses,andsoon.Classification,then,iscomposedofaseriesof

intellectualactivitieswhichconstituteapsychologicalstructure.Ofcourse,thechilddoesnotrealizethat

hehassuchastructureandmaynotevenknowwhattheword“classification”means.Theclassification

structure and “schemes”bothdescribe anobserver’s conceptionof thebasicprocessesunderlying the

child’sactivities;thechildhimselfiscertainlynotawareofthesestructures.


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The Description of Structures

HowcanwedescribethepsychologicalstructuressobasictoPiaget’stheory?Onewayisbyusing

commonlanguage.Wecansaythatthechildclassifiesobjectsorthathismoraljudgmentis“objective,”

andsoforth.Sometimesthecommonlanguageadequatelyconveysmeaning,butsometimesitdoesnot.

Unfortunately, thereareoccasionswhenanordinarywordmeansdifferentthingstodifferentpeople.

When this occurs the scientist is in danger of beingmisunderstood. Consequently, the sciences have

tendedtodevelopvariousformallanguagestoguaranteeprecisecommunication.Thephysicistdoesnot

saythatobjects“fallveryfast”or“pickupspeedastheygoalong.”Instead,hewritesaformulainwhich

eachtermispreciselydefinedandinwhichtherelationsamongthetermsarecompletelyspecifiedby

the formal language of mathematics. If the reader of the formula knows what the terms mean and

understands the requisite mathematics, then the physicist’s meaning can be accurately transmitted

withoutthedangerofmisinterpretation.

Piaget feels that psychology, too, should attempt to use formal languages in describing the

structuresunderlyingthought.Psychologicalwordsinparticulararequiteambiguous.Whilethetheorist

mayintendaparticularmeaningforwordslike“habit,”or“thought,”or“classification,”itisextremely

probable that these terms will signify to others a wide variety of alternative interpretations.

Consequently, Piaget has attempted to use formal languages—particularly aspects of logic and of

mathematics—to describe the structures underlying the child’s activities. In later chapters we shall

considerindetailboththeformaldescriptionofthestructuresandPiaget’srationaleforusingit.

Functions, Structures, and Equilibrium

WecannotemphasizesufficientlytheextenttowhichPiagetbelievesthatthefunctionalinvariants

—organizationandadaptation(assimilationandaccommodation)—andthepsychologicalstructuresare

inextricablyintertwined.Aswehaveseen,assimilationandaccommodation,althoughcomplementary,

nevertheless occur simultaneously. A balance between the two is necessary for adaptation.Moreover,

adaptation is not separate from organization. In the process of organizing his activities the inpidual

assimilates novel events into preexisting structures, and at the same time accommodates preexisting

structurestomeetthedemandsofthenewsituation.


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Furthermore, the functional invariants (organization and adaptation) are closely related to the

structures of intelligence. As a result of the tendencies toward adaptation and organization, new

structuresarecontinuallybeingcreatedoutoftheoldonesandareemployedtoassisttheinpidualin

interactionwiththeworld.Lookingatthematteranotherway,structuresarenecessaryforadaptation

andorganization.Onecouldneitheradapttotheenvironmentnororganizeone’sprocessesiftherewere

nobasicstructuresavailableattheoutset.Ontheotherhand,theveryexistenceofastructure,whichby

Piaget’sdefinitionisanorganizedtotality,entailsthenecessityfororganizationandadaptation.

Thereare,however,importantdifferencesbetweentheinvariantfunctionsandthestructures.As

theinpidualprogressesthroughthelifespan,thefunctionsremainthesamebutthestructuresvary,and

appearinafairlyregularsequence.Anotherwayofsayingthisisthatintellectualdevelopmentproceeds

throughaseriesofstageswitheachstagecharacterizedbyadifferentkindofpsychologicalstructureand

adifferenttypeofinteractionbetweentheinpidualandtheenvironment.Aninpidualofanyagemust

adapttotheenvironmentandmustorganizehisresponsescontinually,buttheinstrumentsbywhichthe

personaccomplishesthis—thepsychologicalstructures—changefromoneageleveltoanother.Boththe

infantandadultorganizeandadapt,buttheresultingpsychologicalstructuresarequitedifferentforthe

twoperiods.

Piaget further proposes that organisms tend toward equilibrium with the environment. The

organism—whether a human being or some other form of life—tends to organize structures into

coherentandstablepatterns.Thesewaysofdealingwiththeworldtendtowardacertainbalance.The

organismtriestodevelopstructureswhichareeffectiveininteractionwithreality.Thismeansthatwhen

aneweventoccurs theorganismcanapply to it the lessonsof thepast (or assimilate theevents into

already existing structures) and easily modify current patterns of behavior to respond to the

requirementsof thenewsituation.With increasingexperience theorganismacquiresmoreandmore

structuresandthereforeadaptsmorereadilytoanincreasingnumberofsituations.

SUMMARY AND CONCLUSIONS

Early inhis lifePiagetdeveloped twomajor intellectual interests:biology, thestudyof life, and

epistemology, the study of knowledge. After devoting a number of years to each of these disciplines,


Page 36

Piagetsoughtawaytointegratethem.InthecourseofhisworkattheBinetLaboratoryinParis,hecame

to the conclusion that psychology might provide the link between biology and epistemology. Piaget

decidedtospendafewyearsstudyingtheevolutionofknowledgeinthechildandthenapplythefruits

ofthisresearchtothesolutionofthetheoreticalproblemswhichinitiallymotivatedhim.Fortunatelyfor

child psychology, the few years became many, and in their course Piaget has produced over forty

volumes reporting his investigations into such matters as the child’s moral judgment, the infant’s

patternsofbehavior,andtheadolescent’ssolutionofscientificproblems.Onlyinthe1950swasPiaget

able to return to theoretical issues in epistemology. Late in life, Piaget continued his contributions to

psychology,andpublishedworksoncausality,consciousness,anddevelopmentandlearning.Hediedin

1980.

Piaget’sresearchandtheoryhavebeenguidedbya frameworkwhichcanbedefinedasasetof

orientingattitudes.Hisdefinitionof intelligence isnot restrictive,but states that intelligence involves

biological adaptation, equilibrium between the inpidual and his environment, and a set of mental

operationswhichpermitthisbalance.Piaget’sresearchactivitiesalsohaveincreasinglycometofocuson

the growth of the child’s understanding of the basic concepts of science, mathematics, and similar

disciplines. Piaget is less interested in studying the contents of the child’s thought than the basic

organizationunderlyingit.

Theinpidualinheritsphysicalstructureswhichsetbroadlimitsonintellectualfunctioning.Many

of theseare influencedbyphysicalmaturation.The inpidualalso inheritsa fewautomaticbehavioral

reactionsorreflexeswhichhavetheirgreatestinfluenceonfunctioninginthefirstfewdaysoflife.These

reflexes are rapidly transformed into structureswhich incorporate the results of experience.Another

aspectofinheritanceinvolvesthegeneralprinciplesoffunctioning.Onegeneralprincipleoffunctioning

isorganization;allspecieshavethetendencytoorganizetheirprocesses.

A second aspect of general functioning is adaptation, which may be further subpided into

assimilation and accommodation. Accommodation refers to the organism’s tendency to modify its

structures according to the pressures of the environment, while assimilation involves using current

structures to deal with the environment. The result of the principles of functioning is a series of

psychologicalstructureswhichdifferqualitativelyfromoneanotherthroughoutaperson’slifetime.For


Page 37

example,theinfantemploysbehavioralschemesorpatternsofaction,whilethechildfromabout7to11

usesmentaloperations.WhatisimportantforPiagetisnotthechild’sbehaviorinall itsdetailbutthe

structureunderlyinghis activities. For thepurposeof clarity, Piagethasmadean attempt todescribe

these structures in terms of formal languages—logic and mathematics. The general tendencies—

adaptationandorganization—andthestructuresareallrelatedtooneanother.

Assimilation and accommodation are complementary,whereas organization and adaptation are

interwoven. For instance, one assimilates an environmental event into a structure, and one

accommodatesa structure to thedemandsof theenvironment.Eventually theorganism tends toward

equilibrium,aimingatabalancebetweenexistingstructuresandtherequirementsoftheworld.Inthis

balance thestructuresaresufficientlydevelopedso that theorganismneedexert littleefforteither to

accommodatethemtorealityortoassimilateeventsintothem.

Piaget’sframeworkisquitegeneral,andatthispointthereadermustfindithardtoevaluate.Inthe

followingpageswewillseethefruitfulnessofPiaget’sorientingattitudes.Wewillreview,forexample,

the evolutionof thepsychological structuresunderlying the child’s intelligence,wewill examine the

waysinwhichassimilationandaccommodationaffectthechild’sinteractionwiththeworld,andwewill

considerPiaget’stheoryofequilibration.

Notes

1Piagethaswrittenshortautobiographiesinseveralvolumes.One,althoughoutdated,appearsinEnglish:J.Piaget,“Autobiography,”inE.G.Boring et al., eds.,HistoryofPsychology inAutobiography, Vol. IV (Worcester,Mass.: ClarkUniversity Press, 1952), pp.237-56.SeealsoChapter1inJ.Piaget,InsightsandIllusionsinPhilosophy,trans.W.Mays(NewYork:WorldPublishingCo.,1971).

2For a discussion of these and related matters, see T. S. Kuhn, The Structure of Scientific Revolutions, 2nd ed. (Chicago: University ofChicagoPress,1970).

3In this connection, it is interesting to compare two sources. One is a 1921 symposium inwhich leading psychologists attempted,withconsiderabledifficulty, todefine intelligence:L.E.Tyler, ed., Intelligence:SomeRecurring Issues (New York: VanNostrandReinhold Company, 1969). A second is a similar symposium, held in 1974: L. B. Resnick, ed., The Nature of Intelligence(Hillsdale, N.J.: L. Erlbaum Associates, 1976). Howmuch progress in defining intelligence has beenmade in the past fiftyyears?

4Piaget’sFrench termschemehasusuallybeen translated intoEnglishasschema (plural,schemata).Wedonot follow this practice sincePiagethadbeenusingtheFrenchwordschema foranotherpurpose.Also,thereadershouldbeawarethatschemeneednotreferonlytobehavior;therearementalschemestoo.


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Infancy

Piaget’s theorypides intellectual development into fourmajorperiods: sensorimotor (birth to2

years), preoperational (2 years to 7 years), concrete operational (7 years to 11 years), and formal

operational(11yearsandabove).(Asweshallseeshortly,theseagesareonlyroughestimates;theyvary

frominpidualtoinpidual,andfromculturetoculture.)Thischaptertreatsthefirstoftheseperiods,the

sensorimotor,whichoccursduringinfancy.

Theaccountof infancyisnovelandsometimessurprising.Thesurprisesusuallytakeoneoftwo

forms:caseswhere,accordingtoPiaget,theinfantiscapableofmuchmoresophisticatedandelaborate

forms of behavior than we would have expected and, conversely, cases where the infant shows

unexpecteddeficiencies.Consideranexampleofthefirstcase.

The untrained observer of an infant in the first few months of life usually reports several

impressions. The baby, who is much smaller than anticipated, appears weak and fragile, and

extraordinarilypassive.Hedoesnotseemtodomuchofanything.Thenewbornspendsmostofthetime

insleep,andusuallywakesonlytobefed.Evenduringthefeeding,hedoesnotseemveryalert,and

sometimes,infact,fallsasleepduringthemeal.Sincetheinfantseemstoshowlittlereactiontopeopleor

things, our observer may even suspect that the newborn does not see the world clearly, if at all.

Apparentlysuchaninfantiscapableoflearningalmostnothing.

Piaget’sviewoffersastrongcontrasttothisconceptionofthenewbornasapredominantlyhelpless

and inactive creature, forhe characterizes thenewbornas active andas an initiatorofbehavior.The

infantquicklylearnstodistinguishamongvariousfeaturesoftheimmediateenvironmentandtomodify

hisbehaviorinaccordancewiththeirdemands.Infact,hisactivityrevealstheoriginsofintelligence.

One of the first questions we should ask about these surprising findings (or indeed about any

findings) is, how does he know?What are themethodswhich allow Piaget to penetrate beyond the

commonly held assumptions and to propose a new and startling view of infancy? The question is

particularly germane in the case of Piaget since he ismethodologically unorthodox, at least by some


Page 40

standards.

METHOD

In the courseofhispsychological investigations,Piagethasemployedavarietyofmethods.The

assumptionhasbeenthatmethodsmustbetailoredtomeettherequirementsofdifferentproblemsand

agegroups.Inthecaseofinfancy,themethodologyemployedispartlynaturalisticandpartlyinformal-

experimental.

Formuchofthetime,Piagetcarefullyobservedthebehaviorofhisownthreeinfants—Lucienne,

Laurent,andJacqueline—asitoccurrednaturally.Forinstance,hewouldsitbythecribandmakecareful

notes of the infant’s play, or he would direct his attention to the infant’s eyemovements and try to

determine the direction of the infant’s gaze. In these instances Piaget did not make use of special

scientificinstrumentsorexperimentalapparatus.Hedidnotuseanotherobservertocheckthereliability

of the observations. In general, the intention was to employ careful observation, unaided by

instrumentation,tolearnasmuchaspossibleaboutthebehavioroftheinfantinthenaturalhabitat.The

procedureisobviouslydifferentfromtheusualexperimentalapproachinwhichthechild’sbehavioror

physiological reactions are observed, often with special instruments, under carefully controlled

conditionsinthelaboratory.ButPiaget’sapproachishardlyuniqueorscientificallytaboo.Naturalistic

methodsareusedinzoology,forexample,byethologistsinterestedinthebehaviorofanimalsintheir

naturalsurroundings.Ithasbeenused,too,inchildpsychology,bythe“babybiographers”whoobserved

theirownchildrenandwhoincludedsuchnotablefiguresasCharlesDarwin.

Piaget’s procedure has its unique advantages and disadvantages. The latter have often been

stressedattheexpenseoftheformer.Forexample,Piagetbasedhisconclusionsonasampleofonlythree

children,hardlyasufficientnumbertoensurethegeneralityoftheresults.Piagetandhiswifemadeall

the observations themselves. Although both Piaget and his wife were trained psychologists, it is the

generalfeelingthatparentsarenotoriouslypoorevaluatorsoftheirownchildren’sperformance.Also,

when naturalistic observation is used, it is impossible to identify cause-and-effect relations with

certainty.Whilesomeeventmayhaveseemedtobethecause,otheruncontrolledeventsmayinfacthave

beeninvolvedtoo.Further,thestandardstatisticaltestswerenotused,althoughtodaytheyareusually


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seenasindispensabletoolsofresearch.

Despite these apparent deficiencies, Piaget’s methods offer a number of advantages. First and

foremost,Piaget is anexceedingly sensitiveobserverof children. Somepeople,probably regardlessof

formaltraining,havethisabilityandsomepeopledonot;Piagetdoes.TheacuityofPiaget’sobservations

is confirmed by their generally successful replication by independent investigators.1 Second, Piaget’s

intimate contact with his subjects allowed him to discover phenomena which might have gone

unobservedorunnoticedinthelaboratory.Thecontrolledexperimenttendstofocustheinvestigator’s

attentiononthelimitedclassofbehaviorofinterest,andindeed,oftenmakesitimpossibleforotherkinds

ofbehavior tooccurorbenoticed.Theseotherevents,ofcourse,maybeofgreater interest thanthose

whichtheexperimenterisstudying.Third,Piaget’sgreatfamiliaritywithhischildrenoftengavehimthe

insighttoresolvecertaindelicateissuesofinterpretation.If,forexample,oneofhischildrenwasunable

towindupatoy,Piaget’sextensiveknowledgeofthechildwaslikelytogivegoodgroundsfordeciding

whetherthefailurewasduetolackofinterest,orfatigue,orrealinability.Anexperimenter,ontheother

hand,notknowingthesubjectswell,oftenisunabletomakesuchreasonabledecisions.

Fourth,Piagetwasabletoobservehissubjectsoveralongperiodoftime.Suchlongitudinalstudies

are rare in psychology and provide a perspective which is notably absent from most experimental

designs. Fifth, Piaget feels that at the initial stagesof research theuseof statisticsmaybepremature.

One’saimattheoutsetistoexploreanddescribe.Theintentionistodiscoverandidentifythesignificant

processesandproblemswhichatalaterstageofinvestigationmaybesubjecttorigorousstatisticaltest.

Sixth, Piaget attempted to compensate for the obvious deficiencies of the naturalistic procedure by

performinginformalexperiments.If,forexample,observationsuggeststhatthechildcannotdeedwith

certain kinds of obstacles, Piaget may intervene in the natural course of events by imposing these

obstaclesonthechildandthenobservetheresults.Theseexperimentsare,ofcourse,informal,sincea

verysmallnumberofsubjects—threeatmost—isinvolved,andsincethecontrolsareoftenincomplete.

Nevertheless,Piagetissensitivetothelimitationsofnaturalisticobservationandwheneverpossibletries

to supplement itwith experimental techniques.We see then that Piaget’s unorthodox procedure for

studyinginfantshasagooddealtorecommenditandcannotbesummarilydismissed.2

Theresultoftheseinvestigationsisanaccountof infancyintermsofsix“sensorimotor”stages.It


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should be emphasized that the age limits of each stage are only approximate, and subject to wide

inpidual variations. Piaget stresses the flexibility of the age normswhich are probably influenced by

inpidual differences in physical and social environment, physiological factors, and so on. What is

importantistheregularorderofsuccessionofthestages,regardlessoftheparticularagesatwhichthey

appear.

STAGE 1: BIRTH TO 1 MONTH

Thenewbornisnotacompletelyhelplesscreature,butarrivesintheworldwithcertainabilities

which are provided by heredity. (In fact, over the past several years research has shown that the

newbornisfarmoreskilled,visually,forexample,thanwaseversupposed.3)Oneinnateskillthatthe

newbornpossessesisthesuckingreflex.Whenthelipsaretouched,thenewborninallculturesresponds

automaticallywithunlearnedsuckingmovements.Indescribingthenewborn’sbehavior,Piaget’scentral

themes are, first, that the sucking reflex, and others too, are not simply activated by external stimuli;

instead,thenewbornofteninitiatesactivityhimself.Second,althoughthephysicalstructureoftheinfant

provides ready-mademechanisms, like the sucking reflexwhich functions frombirthandwhich isof

obvious utility, these furnish only a basis for future development. Even in the first month of life

experienceplaysanimportantroleinmodifyingandsupplementingtheinheritedmechanisms.

Considerthefollowingobservation.

DuringtheseconddayalsoLaurentagainbeginstomakesucking-movementsbetweenmeals....Hislipsopenand close as if to receive a real nippleful butwithout having an object. This behavior subsequently became

morefrequent....(OriginsofIntelligence,OI,pp.25-26)4

The observationmay at first seem quite pedestrian. But let us review it.Why did Laurent suck

betweenmeals?Thereareseveralpossibleinterpretations.Sometimesreflexactivitymaybesaidtobe

involved.Thatis,an“externalexcitant”or“unconditionedstimulus,”likeafinger,mayautomaticallyset

off thereflexof suckingby touching the lips.But in thecaseofLaurent, a reflex interpretationseems

untenable, since no external excitant appears to have been involved. Another explanation might

attribute Laurent’s sucking to hunger, but this interpretation too seems implausible, since Laurent’s

suckingsometimesoccurredsoonafterhislastfeeding(when,presumably,hewasnothungry)andnot


Page 43

just immediatelyprecedingthenext feeding(whenheprobablywashungry).Athirdpossibility,also

rejectedbyPiaget,involvestwosteps:(1)Weassumethatinthepastthechild’snutritivesuckinghad

beenassociatedwithpleasure;thatis,whenhesuckshegetsmilk,whichreduceshishungerpangsand

is therefore pleasurable. (2) Because of this previous association between sucking and pleasure, it

graduallyoccursthatsuckingaloneintheabsenceofmilkacquiresthepowertoelicitfeelingsofpleasure

intheinfant.Consequently,itmaybethatintheobservationcited,Laurentsuckedbecausesuckingitself

had become rewarding through its past association with pleasure. But this explanation also seems

implausiblesincetheextentoftheassociationbetweenpleasureandsuckingwaslimitedtosuchashort

periodoftime.

Since thesevarious explanations—external excitant, hunger, andassociationwithpleasure—do

notseemabletoaccountfornonnutritivesucking,Piagetinvokesoneformofassimilationtoexplainthe

results.RecallthatinChapter1wedefinedassimilationasafunctionalinvariant,atendencycommonto

all forms of life. In itsmost general form assimilation involves the organism’s tendency to deal with

environmentaleventsintermsofcurrentstructures.Piagethasfurtherproposedthatassimilationtakes

threeparticularforms.Inthepresentinstance,theprincipleoffunctionalassimilationapplies.(Theother

twotypesarerecognitoryassimilationandgeneralizingassimilation,whichwewill discuss later.) The

principleof functionalassimilationassertsthatwhenanorganismhasastructureavailable, there isa

basictendencytoexercisethestructure,tomakeitfunction.Thisisparticularlytruewhenthestructureis

notwellformedorisincompleteinsomeway.Also,theprincipleapplieswhetherthestructureisinnate,

asinthecaseofthesuckingreflex,orlearned,asinotherinstanceswewillreviewshortly.Whenapplied

to thepresentobservation, theprincipleof functionedassimilationasserts thatLaurent’snonnutritive

suckingsimplyrepresentsthetendencyofthesuckingreflextoexerciseitselfortofunction.Thissimple

behavioral scheme is not yetwell formed and requires exercise to consolidate itself. In otherwords,

Laurentdidnotsuckbecausehewashungry,orbecauseanexternalexcitantsetoffthereflex,orbecause

he had associated the sucking with pleasure. He sucked because there is a tendency for available

schemeslikesuckingtofunction.

Acloselyrelatedtendencyisgeneralizingassimilation.Sinceschemesneedexerciseandrepetition,

theyalsorequireobjectstobeusedinsatisfyingthisneed.Thesuckingscheme,therefore,tendstoextend

itself,togeneralize,toavarietyofobjects.Whilethenewbornatfirstsucksonlythenipple,orperhapsa


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fingerthataccidentallycomesintocontactwiththelips,theinfantlaterexercisessuckingonnewobjects

likeablanketorvarioustoys.Thus,Piagetstressesactivityonthepartoftheinfant.Thesuckingreflexis

not simply activated by a series of excitants; rather, the infant, in seeking to exercise this scheme

(functionalassimilation),activelysearchesoutobjectswhichwillallowittofunction.Theobjectsserveas

nourishment,or“aliments,”fortheneedtosuck.

The first two principles—functional and generalizing assimilation—are energetic: they get the

newborn’sbehaviorstarted.Inthecourseofhisactivities,thenewbornhastheoccasiontolearnaboutthe

environment. The reflex of sucking becomes “differentiated.” Consider this observation concerning

Laurent:

At0;0(20)[zeroyears,zeromonths,and20days]hebitesthebreastwhichisgivenhim5cm.fromthenipple.Foramomenthesuckstheskinwhichhethenletsgoinordertomovehismouthabout2cm.Assoonashebeginssuckingagainhestops. . . .Whenhissearchsubsequentlyleadshimaccidentlytotouchthenipplewiththemucosaoftheupperlip(hismouthbeingwideopen),heatonceadjustshislipsandbeginstosuck.(OI, p.26)

Fromthisandothersimilarobservations,Piagetconcludesthattheinfantinthefirstmonthoflife

showsaprimitiverecognitioncalledrecognitoryassimilation.Whentheinfantisnottoohungry,hemay

suckanything—thefingers,theblanket,whatever—toexercisehisscheme.Butwhenhungerisstrong,

the infant shows selectivity or discrimination in choosing objects to suck. While rejecting the skin

surroundingthenipple, the infantseizes immediatelyuponthenipple itselfanddoesthissorapidly

thatwemayreasonablycallthebehavioracrudeformofrecognition.Onecautionhere:Piagetdoesnot

proposethattheinfant“recognizes”thenippleinthesamesensethatanadultdoes.(Wewillseelater

thattheinfant’sconceptofobjectsisimmature.)Inthepresentcasetheinfantmerelyshowsthatwhenit

isnecessaryhecanperceivethedifferencebetweenthenippleandotherthings.

Howdoestheinfantlearntorecognizethenipple?Learningmustbeinvolvedsincethenewborn

doesnotimmediatelydisplaythiskindofrecognition;experienceiscertainlyrequiredforittodevelop.

Piaget’spositionisthatinthecourseofexercisingandgeneralizingthesuckingscheme,theinfantcomes

intocontactwithavarietyofstimulation.Someofthestimulationisvisual(thesightofthebreast,etc.).

Some is tactual-kinesthetic (touches on the lips, the feeling of swallowing milk, etc.). And some

stimulationispostural(theinfantisgenerallylyingdowninacertainposition).Whileaccumulatingthis


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experience,theinfantcomestodifferentiateamongmanyaspects.Hefindsthatsomeareasofthebreast

lookdifferentfromothers;somefeeldifferentfromothers;andthatoneareayieldsmilkwhileothersdo

not.Theinfantcomestomakethesediscriminationsthroughrepetitiousexperiencewhichistheresultof

functional and generalizing assimilation. Then,when hungry the infant shows evidence of previous

perceptuallearning5bychoosingthatareawhichhasproducedmilkinthepastandbyrejectingother

areas. To put the matter in another way, the infant learns about the world in the course of many

explorations; when properly motivated, he manifests this learning by the performance of certain

distinctivereactions.

Finally,anevenmorecomplicatedkindoflearningoccursduringthefirststage.Theprincipleof

accommodation—of modification of the scheme to suit the demands of the environment—is also

operative,andoneresult is that the infant learns tosearch for thenipple inan increasinglyeffective

manner.Considertheseobservations:

At first, when put to the breast, Laurent does not show a particularly systematic search for the

nipple.Heobviouslyhasnothadsufficientexperienceeithertorecognizethenippleorlocateit.Buton

thethirddayLaurentmakesnewprogressinhisadjustmenttothebreast.Allheneedsinordertogropewithopenmouthtowardfinedsuccessistohavetouchedthebreastorthesurroundingtegumentswithhislips.Buthehuntsonthewrongsideaswellasontherightside. . . .Assoonashischeekcomes intocontactwiththebreast, Laurent at 0;0(12) applies himself to seeking until he finds drink. His search takes its bearings:immediately from the correct side, that is to say, the side where he experienced contact. . . . At 0;0(26)Laurent. . . feelsthenippleinthemiddleofhisrightcheek.Butashetriestograspit, it iswithdrawn10cm.Hethen turnshishead in therightdirectionandsearches. . . .This timehegoeson to touch thenipple, firstwithhisnoseandthenwiththeregionbetweenhisnostrilsandlips....Heraiseshisheadinordertograspthenipple.(OI,pp.26,29)

Wequotetheseobservationsinsomedetailtodocumenttheextentoftheinfant’slearningduring

thefirstmonth.Theinfantlearnsnotonlytorecognizethenipple,butalsowheretolookforit.Thus,in

response to therequirementsof thesituation,heaccommodates—hedevelopsnewpatternsofaction,

whichresult infairlysystematicsearch.Howarethesepatternsofbehavior learned?Attheoutsetthe

child’sheadmovementsare“desultory,”that is,essentiallywithoutorder inrelationtothenipple.By

chance,someofthemovementsleadtograspingthenippleandsomeareunsuccessful.Astimegoeson,

the infant learnsthroughthisprocessof trialanderrorthata turnof thehead in thedirectionof the

touch on the cheek provided by the nipple leads to the reward of swallowingmilk.With increased


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experiencetheinfantbecomesrelativelyproficientandflexibleinthissearchandnowcanproceednot

onlyinasidewaysdirectiontowardthecheek,butinanupwardordownwarddirectionaswell.This

last observation is important since some head movements at birth are reflexive. When the infant is

touchedonthecheeknearthemouth,heautomaticallyturnstheheadinthatdirection.Thesideways

movement is the “rooting reflex.” Consequently, a learning explanationmay not be required for the

sidewaysmovement,butdoesseemnecessaryfortheupwardanddownwardmotions.

Such,then,isthefirststage.Theapparentlyprimitivebehavioroftheinfantinthefirstmonthoflife

in fact involves considerable complexity, and the extent of the learning achieved is not immediately

obvious.Theresultisthatthehereditarysuckingschemebecomesprogressivelymodifiedandelaborated

asafunctionofexperience.Attheendofstage1,suckingisnolongeranautomaticpatternofbehavior

providedbyheredity.Inaccordancewiththeprincipleoforganization,thesuckingschemehasbecome

elaboratedandhasdevelopedintoafairlycomplexpsychologicalstructurewhichnowincorporatesthe

resultsoftheinfant’sexperiences.

While stage 1 involves significant learning, there are also limitations on the infant’s

accomplishments.Learningisconfinedtothesphereofthereflexesanddoesnotgofarbeyondthem;the

effectsofexperiencearecenteredonthemechanismsprovidedbyheredity.Weshallseehowtheinfant

instage2beginstoovercometheselimitations.

Atthetimeitwasproposed,Piaget’sviewofinfancywasnovelinseveralrespects.Thetwomost

influential theoriesof theday—Freud’spersonalitypsychologyandHull’sexperimentalpsychology—

bothemphasizedthattheorganismseeksescapefromstimulationandexcitation.Allmotiveswereseen

asanalogoustothesexualorhungerdrives;whenthesedrivesintensify,theorganismtakesactionsto

reducethemandtoreturntoaquiescentstate.Piaget’semphasis,ontheotherhand,isthateveninthe

firstfewdaysoflifetheinfantoftenseeksstimulation.Whencapableofactivity,hetendstoperformit

(functional assimilation); when a structure is available, he tends to generalize it to new objects

(generalizingassimilation).InPiaget’sview,allbehaviorcannotbeexplainedbytheinfant’sreactingtoa

noxiousstateofaffairs;instead,theinfantsometimesactivelyseeksthestimulationwhichhisbehavior

provides.ItseemsfairtosaythatrecentpsychologicalresearchhasshownthattheHullianandFreudian

conceptsarenotfullyadequateandthatalternativeviewsdesignedtoexplaintheinpidual’spreference


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foractivityandstimulationmustbedeveloped(Hunt,1961).

STAGE 2: 1 TO 4 MONTHS

Inthesecondstageofsensorimotordevelopmenttheinfantacquirescertainhabits,which,although

fairlysimpleandcenteredabouthisownbody,neverthelesssurpasstheacquisitionsofthefirststage.

Nowthehistoricaldevelopmentofsucking,forexample,extendsbeyondthefeedingsituation.

Primary Circular Reaction

Piaget’s theory involves the notion ofprimary circular reaction. The infant’s behavior by chance

leads toanadvantageousor interestingresult;he immediatelyattempts toreinstateorrediscover the

effectivebehaviorand,afteraprocessoftrialanderror,issuccessfulindoingso.Thereafter,thebehavior

andtheresultmayberepeated;thesequencehasbecomea“habit.”Considertheseexamples:

At0;1(1)Laurentisheldbyhisnurseinanalmostverticalposition....Heisveryhungry....Twice,whenhishandwaslaidonhisrightcheek,Laurentturnedhisheadandtriedtograsphisfingerswithhismouth.Thefirsttimehefailedandsucceededthesecond.Butthemovementsofhisarmsarenotcoordinatedwiththoseofhishead:thehandescapeswhilethemouthtriestomaintaincontact....

At0;1(3)...afterameal...hisarms,insteadofgesticulatingaimlessly,constantlymovetowardhismouth...ithasoccurredtomeseveraltimesthatthechancecontactofhandandmouthsetinmotionthedirectingofthelattertowardtheformerandthatthen(butonlythen),thehandtriestoreturntothemouth. . . . [Later,though] it is no longer themouth that seeks the hand, but the handwhich reaches for themouth. ThirteentimesinsuccessionIhavebeenabletoobservethehandgobackintothemouth.Thereisnolongeranydoubtthatcoordinationexists....

At0;1(4). . .hisrighthandmaybeseenapproachinghismouth. . . .Butasonlytheindexfingerwasgrasped,thehandfelloutagain.Shortlyafter itreturned.Thistimethethumbwasinthemouth ... I thenremovethehandandplaceitnearhiswaist. . . .Aftera fewminutesthe lipsmoveandthehandapproachesthemagain.Thistimethereisaseriesofsetbacks....[Butfinally]thehandentersthemouth,thethumbaloneisretainedand sucking continues. I again remove the hand. Again lipmovements cease, new attempts ensue, successresultsfortheninthandtenthtime,afterwhichtheexperimentisinterrupted.(OI,pp.51-53)

These observations nicely illustrate Piaget’s dual role of observer and experimenter. Note how

Piagetaspatientobserverrecordsthattheinfantspontaneouslyplacesthehandinthemouththirteen

timesinsuccession.Then,Piagetasexperimenterintervenesinthenaturalcourseofeventsbyplacing

the infant’shandnearhiswaist todeterminewhether,underthesemodifiedconditions, the infant is

abletodirectthehandtothemouth.


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The observations also display the gradual and steady development of thumb-sucking. First, the

infantcannotconsistentlygetthehandintothemouthandthenslowlylearnstodoso;nexthelearnsto

suckthethumbalone,notthewholehand;and,finally,afteralongandcontinuousprocessoflearning,

theinfantisabletoperformwithrapiditytheentiresequenceofactions.

Piaget’s explanation of thumb-sucking again involves principles of assimilation and of

accommodation.However,thesequencebeginswithanunplannedorunintentionaloccurrence.Recall

thatanotherpersoninitiallyplacedLaurent’shandonhischeek;hedidnotdosohimself.Afterthehand

wasputthere,Laurenttooktheinitiativebyattemptingtograspthehandwiththemouth.Thisaction

was,ofcourse,apreviously learnedscheme:Laurenthadearlieracquiredbehaviorpatternsenabling

himtosearchforthenipple.Otherobservationsnotdescribedhererevealthatinsomecasestheinitial

behaviorisachanceoccurrence,andnotcausedbytheinterventionofanotherperson.Ineitherevent,

theunplannedbehaviorleadstoaresultwhichhasvaluefortheinfant.InthecaseofLaurentthehand

inthemouthenablesthesuckingschemetofunction.Thisisrewardingsince,accordingtotheprinciple

offunctionalassimilation,thesuckingschemeneedstofunction.Inotherwords,afortuitousoccurrence

hasgiventheinfantachancetoexerciseoneofhispreviouslyestablishedschemes,andthisactivity,in

itself,isasatisfyingevent.ButLaurent’smovementsarenotyetfullycoordinated;itoccursthatthehand

falls from themouth and interrupts the functioningof the sucking scheme.The child thendesires to

reinstate the pleasurable activity and resume sucking the thumb. This desire, stemming from the

interruption,thendirectsthechild’sbehavior.Laurentactivelytriestoinsertthehandinthemouth.In

twosenses,then,theinfant’slearningisactive:hisdesiresetsinmotionthesequenceofevents,andhe

initiatesbehaviortofulfillthisdesire.

The principle of accommodation is now operative. The infant modifies the previously aimless

movementsof thehand tomake themeffective inbringing it to themouth. Initially,Laurent ison the

wrongtrack;he tries tobring themouth to thehand. It isonlyaftersome failure thathereverses the

procedure.Thelearningisslowandseemstoinvolvetwofactors—muscularadjustmentsanddirection

bythepropercues.The infantmust learn tomakecertainnewandprecisemuscularmovementsand

mustlearntobringthesemovementsunderthedirectionofthepropercues.Whentouchingtheblanket,

thehandmustbemovedincertainways;whentouchingthecheek,itmustbemovedinotherways.The

infant learns thatparticularcuesandmovementsareusefulwhileothersarenot.Theusefulones,of


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course, are thosewhich lead to placing the hand in themouth. Thus, success “confirms” some of the

movements and cues,while failure eliminates other attempts at accommodation. Yet the observations

showthattheinfant’slearningisnotcomplete.Heapparentlyfindsitmoresatisfyingtosuckthethumb

thantheotherfingers,andthroughaprocessoflearningsimilartothatjustdescribedbecomesableto

place the thumb alone in the mouth. Further, the infant’s behavior shows the ability to distinguish

(recognitoryassimilation)thethumbfromtherestofthehand.Theresultofallthislearningisfinallya

smoothly organized and directed series of movements, a new scheme or structure, which can be

exercisedrepeatedly.

In summary, the primary circular reaction involves an action on the part of the infant which

fortuitouslyleadstoaneventwhichhasvalueforhimandwhichiscenteredabouthisownbody.The

infant then learns to repeat thebehavior to reinstate the event. The culminationof theprocess is an

organizedscheme.

Primitive Anticipations

Whilethenewborninthefeedingsituationsucksonlywhenhislipsareincontactwiththebreast,

the older infant shows a different pattern of behavior. This observation concerns Laurent at the

beginningofthesecondmonth.

assoonasheis inapositiontoeat(inhismother’sarmsoronthebed,etc.)hishandsloseinterest, leavehismouth,and itbecomesobvious that thechildno longerseeksanythingbut thebreast, that is tosay,contactwithfood...attheendofthemonth,Laurentonlytriestonursewhenheisinhismother’sarmsandnolongerwhenonthedressingtable.(OI,p.58)

. . .between0;3(15)and0;4 . . . [whenLaurent] isput inmyarmsinpositionfornursing,he looksatmeandthensearchesallaround...buthedoesnotattempttonurse.WhenIplacehiminhismother’sarmswithouthistouchingthebreast,helooksatherandimmediatelyopenshismouthwide.(OI,p.60)

Theinfant initiallysucks, then,onlywhenthenipple is inserted inhismouth.Thenipple isan

externalexcitantwhichautomaticallyelicitssucking.Afteraperiodofexperiencewithfeeding,hemakes

sucking-likemovementsbefore the external excitant can operate. During the secondmonth, Laurent

showssuckingassoonasheisplacedinhismother’sarmsoronthebed.Later,Laurent’ssucking-like

movementsarearousedonlybybeinginthemother’sarms.Onewayoflookingatthesefactsistosaythat,

whileatfirstonlythenippleservedasacueorsignalforsucking,latertheinfant’sbeinginthemother’s


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armsreplacedthenippleasasignalforsucking.Anotherwayofphrasingthematteristomaintainthat

theinfantseemstoshowaprimitiveanticipationoffeedingandthatthisexpectancy,astimegoeson,is

evokedbyfewerandmoreappropriateeventsthanformerly.Ineitherevent,thephenomenonissimilar

towhathasbeencalled“classicalconditioning,”althoughPiaget’sexplanationofthefactsdiffersfrom

thetraditionalone.

Piagetemphasizesthattheassociationbetweensuckingandthevarioussignals(e.g.,positionin

themother’sarms)thatprecedeitisnotacquiredinamechanicalway.Whathappensisthis:thesucking

schemecomestoconsistofmorethansuckingalone.Italsoinvolvesasetofposturalkinestheticcues.That

is,whentheinfantnursesinthefirstfewmonthsheisalmostinvariablyheldinthesameposition,and

theinternalbodysensationsassociatedwiththispositionbecomeapartoftheactofsucking.Thebody

sensationsandthemovementsofthelipsformawhole.Then,whentheinfantisplacedintheposition

fornursingandtheposturalandkinestheticsensationsareactivated,thewholecycleofthesuckingactis

released.Becausethetwoaspectsofthecycle—bodilysensationsandlipmovements—formawhole,the

occurrenceofoneaspectusuallyevokestheother.Piaget feelsthatthisprocessdoesnot involvemere

“passiverecording”onthepartofthechild,sincetheinfanthimselfenlargestheinitiallylimitedscheme

of sucking to include other components such as bodily cues. Furthermore, the association cannot be

maintainedifitisnotconsistently“confirmed”bytheenvironment.Thatis,forposturalcuestoprovoke

the child’s anticipatory sucking, the suckingmust ordinarily be followed by drinkingmilk. Thus, the

associationbetweenposturalcuesandsuckingderivesitsmeaningonlyfromalargersetofrelationships

existingbetweentheschemeofsuckinganditssatisfaction.Thereflexmusthaveachancetofunction

effectively (todrinkmilk)beforeanyassociations canbe formed.Thus, the sequencebodilycues—►

sucking—►satisfactionofneedformsawhole,andtoisolatethefirsttwotermsinthissequenceandcall

themaconditionedreflexomitsmuchthatisrelevant.

Curiosity

InthediscussionofthesecondstagePiagetintroducesamotivationalprincipleofgreatimportance.

Thefollowingisapreliminaryobservationinconnectionwiththeproblemofvision:

Laurent at 0;0(24) watches the back of my hand, which is motionless, with such attention and so markedprotrusionofthelipsthatIexpecthimtosuckit.Butitisonlyvisualinterest....At0;0(25)hespendsnearlyan


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hourinhiscradlewithoutcrying,hiseyeswideopen....Hestaresatapieceoffringeonhiscradle.(OI,p.64)

Whydoestheinfantattendtothesemundanefeaturesoftheenvironment?Heisnotrewardedfor

doingsoand isnot inanyotherwayencouragedtodirectattention toanobject like the fringeof the

cradle.Again,Piagetinvokestheprincipleoffunctionalassimilationtoaccountforthesefacts.Theeyes

arestructures,givenbyspecificheredity,andrequireexercise.Inthepresentinstanceexercisemeans

lookingatthing,andthethingslookedatarenecessaryforthefunctioningoftheeyes.

Thusfar,theprincipleoffunctionalassimilationhasbeenappliedtothecaseofvisioninmuchthe

samewayasitwasusedtoexplainsomefeaturesofsucking:bothschemesneedtofunction.Oneresultof

repetitiouslookingatthingsisthattheybecomefamiliartotheinfant.Throughaprocessofperceptual

learning, the infant becomes acquaintedwith the environment and comes to recognize things. These

observationsaremadenext:

At0;1(15)hesystematicallyexplores thehoodofhisbassinetwhich I shookslightly.Hebeginsby theedge,then little by little looks backward at the lowest part of the roof. . . . Four days later he resumes thisexploration in the opposite direction. . . . Subsequently, he constantly resumes examining the cradle, but,duringthethirdmonth,heonlylooksatthetoyshangingfromthehoodoratthehooditselfwhenanunwontedmovementexciteshiscuriosityorwhenhediscoversaparticularnewpoint(apleatinthematerial,etc.).(OI,p.68)

Noticehowatfirsttheinfantthoroughlyexaminesthecradleuntilheisapparentlyfamiliarwithit.

Then,duringthethirdmonthhisattentionbecomesmoreselectivethanwaspreviouslythecase.Heno

longer seems to explore the cradle and instead directs his attention to novel objects or movements

connected with the cradle. For example, he stares at toys hanging from the hood or at a previously

unnoticedpleatinthematerial.

Piaget’sexplanationoftheinfant’scuriosityinvolvesanextension—reallyafurtherspecification—

oftheprincipleofgeneralizingassimilation.Theinfant’s lookingscheme,accordingtoPiaget,tendsto

extendtherangeofobjects it“uses.”Buttheinfantdoesnotsimplylookatmoreandmorethings.His

visualpreferencesbecomeselective.The infant’sattention isdirectedat eventswhicharemoderately

novel:“oneobservesthatthesubjectlooksneitheratwhatistoofamiliar,becauseheisinawaysurfeited

withit,noratwhatistoonewbecausethisdoesnotcorrespondtoanythinginhis[schemes]”(OI,p.68).

Thismotivationalprinciplemayappeardeceptivelysimpleandtrite.Inreality,however,itrepresentsa


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pointofviewwhich isradicallydifferent fromprevious(andsomecurrent) theoriesand isonlynow

receivingtheattentionitdeserves.First,liketheprincipleofassimilation,themoderatenoveltyprinciple

isstronglyatoddswiththeorieswhichstressavoidanceofstimulationastheonlykindofmotivation.On

thecontrary,accordingtoPiaget’sview,thechildactivelyseeksoutnewstimulation—heisnotforcedto

lookatnovelobjects.Second,themoderatenoveltyprincipleisdifferentfromothermotivationaltheories

inthatitisarelativisticconcept.Thatwhichcatchesaninpidual'scuriosityisnotentirelythephysical

natureoftheevent.Itisnottheobjectpersethatattractsattention;instead,curiosityisafunctionofthe

relationbetweenthenewobjectandtheinpidual'spreviousexperience.Agiventoymayelicitinterestin

onechildandboredominanother.Presumablythefirstchildhashadexperiencewithtoysmoderately

different fromtheone inquestion; thesecondchildmayeitherhavehadexperiencewith toyshighly

similar to the newone or elsemay have had no experiencewith toys, inwhich case the new object

presumably“doesnotcorrespondtoanythinginhis[schemes].’’Insum,thenoveltyprincipleassertsthat

whatdeterminescuriosity isnot thephysicalnatureof theobject,but rather thedegree towhich the

objectisdiscrepantfromwhattheinpidualisfamiliarwith,which,ofcourse,dependsentirelyonthe

inpidual’sexperience.

Imitation

Animportantaspectoftheinfant’sbehavioris imitation.Piagetconsidersimitation, likeallother

behaviors, as yet another expression of the infant’s endeavors to comprehend reality and interact

effectivelywiththeworld.Consequently,thedevelopmentofimitationisseentoprogressconcurrently

withotheraspectsoftheinfant’sbehavior.

During stage2, aswehaveseen, the reflexesaremodified tobecomehabitsorprimarycircular

reactions.Thisextensionofthechild’shereditaryschemesleadstoarudimentaryandsporadicformof

imitation.Atthisstagethechildimitatesonlyactionswhichhehashimselfpreviouslyperformed.Since

the child’s repertory of actions is still restricted, imitation is confined to elementary vocal and visual

movements,andtograsping(prehension).Hereisanexampleoftheimitationofthisstage:

At0;1(21),Luciennespontaneouslyutteredthesoundrra,butdidnotreactatoncewhenIreproducedit.At0;1(24);however,whenImadeaprolongedaa,shetwiceutteredasimilarsound,althoughshehadpreviouslybeensilentforaquarterofanhour.


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At0;1(25)shewaswatchingmewhileIsaid“aha,ha,rra,”etc. Inoticedcertainmovementsofhermouth,movementsnotof suctionbutof vocalization. She succeededonceor twice inproducing some rathervaguesounds,andalthoughtherewasnoimitationinthestrictsense,therewasobviousvocalcontagion.

At0;3(5) Inotedadifferentation in the soundsofher laughter. I imitated them.She reactedby reproducingthemquiteclearly,butonlywhenshehadalreadyutteredthemimmediatelybefore.

At0;3(24)sheimitatedaa,andvaguelyarrinsimilarconditions,i.e.,whentherewasmutualimitation.(Play,Dreams,andImitationinChildhood,PDI,p.10)

The early forms of vocal imitation are characterized by two major features. First, there is the

phenomenon of “vocal contagion.” A person called a “model”makes a sound, and the infant tries to

reproduce it. Limited abilities, however, prevent the infant from perfect reproduction of the sounds.

Nevertheless,stimulatedbythemodel’ssounds,theinfantcontinuestoproducevocalizationsofmany

kinds having little relation to the model’s sounds. “Vocal contagion” refers, then, to the model’s

stimulationofdiffusevocalactivityintheinfant.

Second,thereis“mutualimitation.”Ifthemodelreproducesasoundwhichtheinfantiscurrently

engagedinproducing,thechildisstimulatedtorepeatthesamesound.Ifthemodelagainimitatesthe

child,thereissetinmotionapatternofalternatingimitationbyinfantandmodelwhichcontinuesuntil

oneortheothertiresorlosesinterest.Thispatternofbehaviordoesnotoccurifthemodelmakesasound

whichisnewfortheinfant.

Piagetexplainsboththecontagionandmutualimitationphenomenabyreferencetotheprinciple

of functionalassimilation.Youmayrecall thatthechildhasatendencytorepeatschemeswhichhave

alreadybeenestablished.Inthecaseofvocalcontagiontheprincipleoffunctionalassimilationisapplied

inthefollowingway.Whenthemodelmakesasoundtheinfantdoesnotdistinguishitfromhisown;itis

asiftheinfanthadmadethesound.Becauseoftheprocessoffunctionedassimilation,theinfanttendsto

repeattheactivity(notdistinguishedfromhisown)whichhasalreadybeensetinmotion;thatis,the

infantcarriesontheactivityofmakingsoundsingeneral.

In the case ofmutual imitation a similar explanation is advanced.When the infant produces a

sound, the model’s imitation merely stimulates the process of functional assimilation. The infant’s

imitation is in away illusory; the infant does not somuch reproduce themodel’s behavior asmerely

continuehisown.Notethatinbothcases—contagionandmutualimitation—theinfantrepeatsbehavior


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ofwhichheisalreadycapable.Theinfantcannotyetreproducenovelactivitiesofamodel.

Categories of Reality

Thusfar,wehavedescribedtheinceptionofseveralaspectsoftheinfant’sbehavior.Inparticular,

wehavenotedthecontributionofexperiencetowardtheelaborationoftheinfant’sactivity,andtheways

in which he extends his behavior beyond the feeding situation. As the infant begins to manipulate

surroundingobjects,hegraduallydevelopsapractical “understanding”ofexternalreality. Inplaying

withtoys,blankets,hisownbody,andadults,helearnssomethingaboutthepropertiesofthesethings

andabouttherelationsamongthem.Andasskillsincreaseinnumberandscope,theinfantacquiresan

increasinglycomplexpracticalknowledgeofcertainfeaturesoftheenvironment.

During the sensorimotor period, the infant elaborates severed basic dimensions of reality,

especially theprimitivenotionsof thepermanentobject, space, time, and causality. At first, thesebasic

dimensions of reality are closely related to the infant’s bodily actions, to themovements of his arms,

fingers,legs,andeyes.Theinfant’sinitial“understanding”oftheworldisbasedentirelyonwhatPiaget

callsthe“planeofaction.”Onlylater,afteragradualprocessofdevelopment,doestheinfantbecomeable

to elaborate the categories of reality on the “plane of thought.”One of Piaget’s central themes is that

concrete action precedes and makes possible the use of intellect. Thus, the acquisitions of the

sensorimotorperiodformthefoundationsof the inpidual’smentaldevelopment.Wewilldiscussonly

one of these categories, the concept of the permanent object. The other notions follow a similar

development.

Object Concept (Stages 1 and 2)

TounderstandthedevelopmentofwhatPiagetcallstheobjectconcept,it is important tokeep in

mindoneessentialpoint.An“object,”accordingtoPiaget,issomethingwhichtheinpidualconceivesof

ashavingarealityofitsown,andasextendingbeyondhisimmediateperception.Forexample,aman

whohashunghiscoatinaclosetknowsseveralhourslaterthat,inalllikelihood,thecoatisstillthere.

Althoughhecannotseeortouchthecoat,heknowsthat itremainsbehindtheclosetdoor.Theobject,

therefore, involvesmore than thedirectperceptionofexternal reality; theobject is conceived toexist


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independentlyofaperson’sperceptionofit.Strangeasitmaysound,theinfantisatfirstincapableofthis

apparently simple notion, and it is only after a long process of development that he elaborates the

cognitiveskillsnecessaryforamatureobjectconcept.

Duringstage1theinfant’sreactionsareevokedonlybyimmediatelypresentsensoryeventswhich

maybeinternalorexternal.Feelingthepangsofhunger,theinfantcries;experiencingatouchonthe

lips,hesucks.Thesameholdsinthecaseofvisualperception.Ifthemother’sfacesuddenlyappearsin

the visual field, the infant stares at it. But when the face is just as suddenly withdrawn, the infant

immediatelystopslookingandresumesotheractivities.Itisclearthattheinfanthasnoconceptionthat

thefacecontinuestoexistwhenhelosesvisualcontactwithit.Instead,theinfantmerelyperceivesan

unrelatedseriesofimagesorpictures,asPiagetcallsthem,whichappearandthendisappear.

Certainbehavioralpatternswhichappearinstage2areafirststeptowardtheacquisitionofthe

objectconcept.Theinfantcoordinatesvariousperceptualschemeswhich,untilthen,hadbeenusedin

unrelatedways.Considerthecoordinationofvisionandhearing.Instage1,ifasoundhadoccurrednear

anewborn,hewouldhaveshownevidence(forexample,astartle)ofhavingheardit,buthewouldhave

madenoefforttobringthesourceofthesoundintosight. Instage2,however, the infanttriestoturn

towardthesoundhehearstoseewhatproducedit.Atfirsttheseeffortsareclumsy,butwithpractice,

theygraduallyimproveandbecomemoresuccessful.Becauseofthiscoordinationofvisionandhearing,

external reality isusuallyexperienced through twoormoresenses simultaneously.The result is that

afteratimetheinfantestablishesrelationsbetweenwhatisheardandseen.Hefindsthatcertainsounds,

like the voice, usually emanate from certain sources, like themouth. The infant begins to discover a

coherenceintheworld.Insteadofmerelyperceivingisolatedandunrelatedaspectsofreality,theinfant

learnsthatsightsandsounds(andotherkindsofperceptstoo)oftengotogetherinregularways.This

coordinationofbasicschemes,sinceitintroducesameasureofcoherencetotheinfant’sworld,isavital

firststeptowardacquisitionoftheobjectconcept.

Another accomplishment of stage 2 concernspassive expectation. The clearest example involves

vision.At this stage the infant can followamovingobjectwithhis eyes.Or, asPiaget says, the infant

accommodateshislookingschemetothemovingthing.Theinterestingobservationhereisthatoncethe

objectleavesthevisualfield,theinfantcontinuestostareatthespotwherethethingdisappeared.One


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mightalmostbe temptedtostate thathealreadyhastheobjectconceptand ishoping for thethingto

return.Butthisinterpretation,Piagetfeels,isfallacious,sincetheinfantdoesnotactivelysearch forthe

vanished object as he will do in later stages. Instead, the stage 2 infant merely pursues an action

(looking)which has been interrupted. If after a shortwhile the thing does not reappear, the infant

discontinues passive watching and turns to other elements of his surroundings. But this passive

expectation,whichdoesnotgobeyondthesimplerepetitionofthealready-activatedlookingscheme,is

the firststeptowardthe lateractivesearchforthemissingobjectandhencetowardacquisitionof the

objectconcept.

In summary, the first two stages are characterized by a passive attitude toward objects which

disappearfromtheinfant’simmediateperception.Instage1,theinfantimmediatelyturnsattentionto

thosethingshecansee;instage2,hemerelyrepeatsearlieractions(looking)whichoccurredwhenthe

objectwaspresent.Whilethesecondreactionrepresentsanadvanceoverthefirst,bothindicatethelack

ofthematureobjectconcept.


Secondary Circular Reactions

Instage2, theprimarycircularreaction isalwayscenteredonthe infant’sownbody.The infant

learned,forexample,tobringthethumbtohismouth.Instage3,theinfant’shorizonsexpand.Hebegins

tocrawlandmanipulatethingsextensively.Thecircularreactionsofthisstagearecalled“secondary,”

sincetheynowinvolveeventsorobjectsintheexternalenvironment.Thesecondarycircularreactions

describetheinfant’snew-foundabilitytodevelopschemestoreproduceinterestingeventswhichwere

initiallydiscoveredbychanceintheexternalenvironment.Thefollowingexcerptisalengthyrecordof

suchareactionandillustratesPiaget’sskillandcautionasanobserver:

Laurent, from themiddleof the thirdmonth, revealedglobal reactionsofpleasure,while lookingat the toyshanging fromthehoodofhisbassinet. . . .Hebabbles, archeshimself,beats theairwithhisarms,moveshislegs,etc. ...At0;2(17)Iobservethatwhenhismovements inducethoseof thetoys,hestopstocontemplatethem,farfromgraspingthatitishewhoproducesthem....Ontheotherhandat0;2(24)Imadethefollowingexperiment....AsLaurentwasstrikinghischestandshakinghishandswhichwerebandagedandheldbystringsattachedto thehandleof thebassinet (topreventhim fromsucking), Ihad the ideaofusing the thing,and Iattachedthestrings to thecelluloidballshanging fromthehood.Laurentnaturallyshooktheballsbychance


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andlookedatthematonce(therattlemadeanoiseinsidethem).Astheshakingwasrepeatedmoreandmorefrequently Laurent arched himself, waved his arms and legs—in short, he revealed increasing pleasure andthroughthismaintainedtheinterestingresult.Butnothingyetauthorizesustospeakofcircularreaction....

Thenextday,at0;2(25)Iconnecthisrighthandtothecelluloidballs....Thelefthandisfree.Atfirstthearmmovementsare inadequateandtherattledoesnotmove.Thenthemovementsbecomemoreextensive . . .andtherattlemoves. . . .Thereseemstobeconsciouscoordinationbutbotharmsmoveequallyanditisnotyetpossibletobesurethatthisisnotamerepleasurereaction.Thenextday,samereactions.

At0;2(27),ontheotherhand,consciouscoordinationseemsdefinite,forthefollowingfourreasons:(1)Laurentwassurprisedandfrightenedbythefirstshakeoftherattlewhichwasunexpected.Ontheotherhand,sincethesecond or third shake, he swung his right arm (connected to the rattle) with regularity, whereas the leftremainedalmostmotionless.. . .(2)Laurent’seyeblinksbeforehandassoonashishandmovesandbeforetherattlemoves, as though thechildknewhewasgoing to shake it. (3)WhenLaurent temporarilygivesup thegameandjoinshishandsforamoment,therighthand(connectedtotherattle)aloneresumesthemovementwhiletheleftstaysmotionless.(4)Theregularshakes...revealacertainskill;themovementisregular.

At0;3(10) I attached a string to the left armafter six days of experimentswith the right. The first shake isgivenbychance:fright,curiosity,etc.Then,atonce,thereiscoordinatedcircularreaction:thistimetherightarm is outstretched and barelymobilewhile the left swings. . . . This time it is therefore possible to speakdefinitelyofsecondarycircularreaction.(OI,pp.160-62)

One interpretationof the infant’sbehavior is that a secondary circular reaction is involved.The

infant,lyinginhiscrib,bychancemakesanarmmovementwhichcausesthestringattachedtohishand

tomove and rattle the toys. Laurentdoesnot, of course, have this goad inmind from the outset. The

movementandrattlingareinterestingtotheinfant,andhedesirestocontinuethem.Overaperiodof

time, he learns the arm movements necessary to reproduce the interesting result. At this point, his

behaviorisintentional.

But another interpretation is possible, and it is particularly fascinating to observe how Piaget

attempts to rule it out. The alternative explanation asserts that the infant’s armmovements are not

intendedtoproducetheinterestingresult.Instead,justthereverseistrue:theinterestingeventcauses

armmovements inthe infant. Inotherwords, the infant initiallymoveshisarmbyaccident.Theballs

moveandmaketheinfanthappy.Aspartofhisjoytheinfantshowsphysicalexcitementwhichagain,by

accident,producestheshakingoftheballs;thisinturnstartsthecycleoveragainandisthecauseofthe

infant’shandmovements.

TheobservationsshowthatPiagetwasquitecautiousinhisinterpretations.Hedidnotacceptthe

first explanation (secondary circular reaction) until the facts made it abundantly clear that the


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alternative explanation was not plausible. For example, Piaget observed that Laurent seemed to

anticipate the result before it occurred; consequently, the result could not be an accident. In fact, the

sequenceofobservationsshowswhyPiaget’sobservationalprocedureisnotnecessarilyinferiortothe

formalexperimentalmethod; theadvantagesofdetailedknowledgeof thechild’shistoryareobvious,

andmanyoftheobservationsperformthesamefunctionascontrolgroupsinordinaryexperiments.

The explanation of the infant’s learning of secondary circular reactions involves many of the

principlesthatwereinvokedearlier.First,theinfant’saccidentalmovementproducesanexternalresult

which is moderately novel and which therefore interests him. Second, the infant perceives that his

actionsarerelatedtotheexternalresult.Piagetassertsthatiftheinfantdoesnotperceivetheconnection,

nofurtherlearningispossible.Third,oncetheinterestandtheconnectionbetweenactandresultare

established,theinfantdesirestorepeattheinterestingevent.Inotherwords,aftertheinfantlooksatand

listenstothetoysrattling(or,inmoretechnicallanguage,assimilatestheinterestingeventintothevisual

andauditoryschemes),hewantstoreinstatetheinterestingeventsandassimilatethemonceagaininto

theschemesoflookingandlistening.This,ofcourse,isthefamiliarprincipleoffunctionalassimilation:

onceascheme(inthiscaseviewingandhearingthetoys)isabletofunction,ittendstorepeatitself.After

thispoint,theinfant’sgoalofrestoringtheinterestingeventsmotivatesanddirectsactions.

Thusfar,theinfanthasperceivedaninterestingresult,hasrecognizedthatitisconnectedtohis

actions,anddesires torepeat theresult.The fourthstep involvesaccommodation; the infantneeds to

learn the hand movements necessary for consistent reproduction of the result. Part of the process

involvesrediscoveringthemovementswhichwerepreviouslyeffective.WhilePiagetdoesnotmakethe

matterentirelyexplicit,itisclearfromhisobservationsthatadirectedtrial-and-errorprocessisinvolved.

Theinfant’sbehaviorisdirectedinthesensethatthedesiretoreproducetheinterestingresultguides

hisactionsandinthesensethatheattemptsonlybehaviorswhichareclearlyrelevant:theinfantdoes

notkickhis feet,but limitshiseffortstoarmmovements.Withintheseconstraintstheprocess involves

trialanderrorsincetheinfantdoesnotknowatfirstpreciselywhicharmmovementsareeffective.He

has to try them out to seewhichmeetwith success andwhichwith failure. It is also clear from the

observations,andagainnotexplicitinPiaget’sexplanation,thattheinfantdoesnotsimplyrediscoverold

movements.Thismaybetheoriginalobjectiveandaccomplishment,butwithpracticetheinfantdevelops

movementswhicharemoreprecise,skilled,andeffectivethanthosewhichoriginallyandaccidentally


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obtainedthegoal.

Theresultofthisactivityisasecondarycircularreactionwhichisafarmorecomplexstructurethan

anythingtheinfanthaddevelopedearlier.Nowtheinfantisinterestedintheexternalenvironmentand

isabletodevelopbehaviorswhichserveasaprimitivemeansforobtainingvariousends.However,the

secondarycircular reactionhas twodeficiencies.First, it isnot fully intentionalas the infantdoesnot

haveagoalinmindfromtheoutset;rather,thegoalhasbeendiscoveredbyaccident,anditisonlyafter

thischanceeventhasoccurredthatthegoalguidesbehaviorandgivesittherebyapurposivecharacter.A

seconddeficiency is that the behavior is essentially conservative. The infant’s aim is to reproduce, to

duplicatesomebehaviorwhichproducedinterestingresultsinthepast.Hedoesnotattempttoinvent

newbehaviors.ThesetwodeficienciesleadPiagettomaintainthatthesecondarycircularreactiondoes

notyetconstituteintelligentbehavior.

Primitive Classes

OneofthemostinterestingaspectsofPiaget’stheoryhastodowiththeinfant’sformationofclasses

ormeaning.Theirdevelopment,accordingtoPiaget,beginsveryearlyinlife.Thefollowingobservations

illustratethematter:

At0;6(12)Lucienneperceivesfromadistancetwocelluloidparrotsattachedtoachandelierandwhichshehadsometimes had in her bassinet. As soon as she sees them, she definitely but briefly shakes her legs withouttryingtoactuponthemfromadistance....Sotoo,at0;6(19)itsufficesthatshecatchessightofherdollsfromadistanceforhertooutlinethemovementsofswingingthemwithherhand.

From0;7(27) certain too familiar situationsno longer set inmotion secondary circular reactions, but simplyoutlinesofschemes.Thuswhenseeingadollwhichshehasactuallyswungmanytimes,Luciennelimitsherselftoopeningandclosingherhandsorshakingherlegs,butverybrieflyandwithoutrealeffort.(OI,pp.186-87)

Inessence,Piagethasobservedthatwhentheinfantcomesintocontactwithsomefamiliarobjecthe

does not apply to it the secondary circular reaction which normally would be employed. Instead,

Lucienneexhibitsanabbreviatedformofthebehavioranddoesnotseemtointendtoproducetheusual

result.Theabbreviatedactiondoesnotseemmechanical,likeaconditionedresponse.Further,theinfant

is‘‘perfectlyserious”andrepeatstheactiononanumberofdifferentoccasions.

Piaget’s interpretation is that theabbreviatedactsarespecialcasesofrecognitoryassimilation. If


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youwill recall, inearlier stages the infant’sovertbehaviorshowed theability todistinguishbetween

variousobjects;forexample,whenhungryhesuckedthenipplebutrejectedapacifier.Thus,theinfant’s

behaviorissaidtoinvolverecognitoryassimilationwhenheisselectiveinapplyingspecificschemesto

variousaspectsoftheenvironment.

Thecaseofabbreviatedmovements involvesasimilarselectivity.Lucienne, forexample,kicks in

responsetotoyswhichshehasswung,butnotinresponsetoothertoys.However,thepresentinstance

involvesmorethanselectivity.Theinfant’sbehaviorisabbreviated;shedoesnotchoosetodisplaythe

entireschemewhenitwouldbequitefeasibletodoso.Piagetinterpretstheabbreviationasabehavioral

precursorofclassificationormeaning. Lucienne,of course,doesnothaveanabstract conceptionof the

parrot.Shecannotverbalizeitspropertiesoridentifyitasaninstanceoftheclassofanimaltoys.Butthe

abbreviatedbehaviorshowsthatLuciennemakesabeginningattemptatclassificationoftheobject.The

brief kicking, for instance, is the first step toward thinking the thought, "That’s the parrot; that’s

somethingtobeswung."Her"understanding"isofcoursequiteprimitiveanddoesnotyetoperateona

mentallevel.Nevertheless,shehasmadeprogressoverstages1and2,sinceshedisplaysbehaviorwhich

indicatesthattheinitialstepstowardinternalizationofactionareoccurring.Theabbreviatedschemeis

thefirstapproximationtothought.

Piagetproposesatechnicalterminologyfordescribingtheseevents.Hedesignatesasasignifieran

objectoreventthatstandsforsomethingelse;thechild’sreactiontotheobjectoreventisthesignified.In

thepresentcasethesignifieristheparrot,andthesignifiedisthechild’sbriefkicking.Thesignifieristhe

“thing,”andthesignifiediswhatitmeanstotheinfant.Withdevelopment,thesignifiermaybenolonger

athingbutaword,andthesignifiedmaybenotabehaviorbutanactofintellectualunderstanding.

Primitive Relations

Asweshallseelater,inChapter4,classificationisconsideredavitalaspectofthechild’sthought

andisinvestigatedingreatdetail.Similarly,weshallseeinthesamechapterthatthenotionofrelation

occupies a prominent place in Piaget’s theories. And relations, too, have primitive behavioral origins

whichariseinthecourseofthefirstseveralstages.Hereisanexample:

Intheeveningof0;3(13)Laurentbychancestrikesthechainwhilesuckinghisfingers...hegraspsitandslowly


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displaces itwhile looking at the rattles.He then begins to swing it very gentlywhich first produces a slightmovement of thehanging rattles and an as yet faint sound inside them. Laurent thendefinitely increasesbydegrees his ownmovements: he shakes the chainmore andmore vigorously and laughs uproariously at theresultobtained.—Onseeingthechild’sexpressionitisimpossiblenottodeemthisgradationintentional.(OI, p.185)

Inotherwords,theinfantseemstoseethedifferencebetweenaslightmovementonhispartanda

strongone;similarly,hecandiscriminatebetweenaloudandasoftrattle.Theinfantcanputtwosounds

or two movements into relationship with each other. Furthermore, the infant seems to see that the

intensity of his movements is directly related to the intensity of sounds made by the rattle. These

perceptionsofdifferences in intensity are theoriginsof quantitative thought.We shall see laterhow

theserelationshipsaredevelopedinstage4.

Imitation

Instage3theinfant’sattemptsatimitationbecomeincreasinglysystematic.Throughthesecondary

circularreactionstheinfantacquiresincreasinglyextensiveexperienceoftheenvironment.Theinfant’s

schemesincreaseinnumberandrange,withtheresultthatheismorecapablethanformerlyofbehavior

whichmatchesthatofamodel.Sincehecannowassimilatemoremodels,thereisgreateropportunityfor

imitation. It is still the case, however, that the infant continues to imitate onlywhat is familiar—only

actionswhichhealreadycando—andcannotyetreproducenovelactions.Thisconservativefeatureof

imitationisanalogoustothatdisplayedbythesecondarycircularreactions.

Object Concept

Instage2wesawthattheinfantmadenoattempttosearchforavanishedobject.Stage3,onthe

other hand, is characterized by the acquisition of four new behavior patterns which represent

considerableprogressintheformationoftheobjectconcept.

First,thereisvisualanticipationofthefuturepositionsofobjects.If,forexample,anobjectdrops

veryquicklyandtheinfantcannotseeallthemovement,hecanneverthelessanticipatethefinalresting

placeof theobject.At first the infantdoesthisbest ifhehimselfhasdroppedtheobject.Later,hecan

anticipatethepositionofanobjectdroppedbysomeoneelse.Considerthefollowingillustration:


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At0;6(3) Laurent, lyingdown,holds inhis handabox five centimeters indiameter.When it escapeshimhelooksforit intherightdirection(besidehim).Ithengrasptheboxanddropitmyself,vertically,andtoofastfor him to be able to follow the trajectory.His eyes search for it at once on the sofa onwhichhe is lying. ImanagetoeliminateanysoundorshockandIperformtheexperimentathisrightandathisleft;theresultisalwayspositive.(TheConstructionofRealityintheChild,CR,pp.14-15)

Herewesee that the infantno longercontinuespassiveviewingof theplacewherehesawthe

objectvanish,ashedidinthepreviousstage,buthenowvisuallysearchesforitinanewlocation.This

behavior shows that the infant anticipates that the object’smovementwill continue even though he

himself isunable tosee it. In thissense the infantconferson theobjectapreliminarysortof intrinsic

permanencewhich,however,remainssubjectivesinceitiscloselyrelatedtohisownactions.Hesearches

fortheobjectchieflyifhehimselfhascauseditsdisappearance.

Asecondachievementof thisstage iswhatPiagetcalls interruptedprehension.This is the tactual

equivalent to the above-mentioned behavior of visual accommodation to rapid movements. In other

words,iftheinfanthasalreadysetinmotioncertainmovementsofthehandorfingersforthepurposeof

graspinganobjectandthenlosesitordoesnotsucceedingraspingit,hewillsearchfortheobjectby

continuingthemovements.

Asinthecaseofvisualaccommodation,theinfantattributesonlyasubjectivepermanencetothe

object.Theobjectexistsonly inrelationto theactionhewasperformingwhen itvanishedorslipped

fromhisgrasp.

Theinfantoriginatesnonewmovementstoretrievethelostobject,butmerelyrepeatspastgestures

ofholdingorattemptingtoholdtheobject.Also,ifnomovementstowardtheobjecthadbeeninitiatedin

thefirstplace,theinfantmakesnoactiveattempttosearchforadisappearingobject.

Third,wecanobserveduringthisstageabehaviorwhichiscalleddeferred,circularreaction.Inthis

caseacircularreactioninvolvinganobjectisinterruptedandresumedspontaneouslybytheinfantata

latertime.Theresumptionoftheactionsonanobjectimpliesthattheinfantexpectsittocontinuetobe

available.Forexample,

At0;8(30)Lucienne isbusy scratchingapowderboxplacednext toheronher left, but abandons that gamewhensheseesmeappearonherright.Shedropstheboxandplayswithmeforamoment,babbles,etc.Thenshesuddenlystopslookingatmeandturnsatonceinthecorrectpositiontograspthebox;obviouslyshedoesnotdoubtthatthiswillbeatherdisposalintheveryplacewheresheuseditbefore.(CR,p.25)


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This is an important step forward, since suchbehavior isnotmerely a continuationofprevious

movementswhenanobjectislostfromsightortouch.Heretheactionhasbeencompletelyinterrupted

andreplacedbyanotherquitedifferentpatternofbehavior.Yetatalaterpoint,nottoofarremovedin

time,theinfantofhisownaccordreturnstotheplacewherehehadbeenplayingandexpectswhathe

hadbeenplayingwithtobetherestill.Thisshowsthattheinfantattributesatleastsomepermanenceto

theobject.Despitethisaccomplishment,theinfant’sobjectconceptisnotyetfullydeveloped.Bycontrast

with advances to bemade in the future, the infant’s behavior in the present stage is still too closely

associatedwithapracticalsituationandpreviousactivities,anddoesnotyetinvolveanentirelymature

objectconcept.

Ina fourthreactiontypicalof thepresentstage, the infantcannowrecognizean invisibleobject

evenwhenabletoseeonlycertainpartsofit.Iftheinfantisshownatoywhich(whilehewatches)is

completelycoveredbyacloth,hemakesnoattempttosearchforthetoy.If,however,certainpartsareleft

visible the infant tries to lift the cloth todiscover the rest of the toy.But even this ability is curiously

limited; he is able to recognize thewhole onlywhen some portions are visible. For example, one of

Piaget’schildrenwasabletorecognizehisbottleonlyifeitherendwasvisibleandthemiddlehidden.If

onlythemiddleportionwereshown,hewasnotabletorecognizethebottleandmadenoattempttosuck

onit.

Therecognitionofpartlyhiddenobjectsoccursonlyafterthechildhasacquiredsufficientskillin

manipulating things. While handling a variety of toys and other objects, the infant explores them

visually.Byvaryingthedistancesandanglesofthesethings,bringingthemclosertotheeyes,turning

themaround,andmovingthemfromsidetoside,theinfantwillgraduallygainabetterknowledgeof

theirshapeandtheirotherproperties.Thissortofknowledge,ofcourse,isnecessaryforsuchactivityas

therecognitionofpartlyhiddenobjectsandthuscontributestowardthedevelopmentofagenuineobject

concept.

In brief, we see that the four behaviors of the present stage—(1) visual anticipation of rapid

movements, (2) interruptedprehension, (3)deferred circular reactions, and (4) reconstructionof an

invisiblewholefromavisiblefraction—allpresentsimilarlimitationsandshortcomingswithrespectto

the object concept. These behaviors all indicate that at this stage the object does not have a fully


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independent or inpidual existence but is closely related to the infant’s own action.When the object

disappears, the infant is content to repeat actions that were being performed at the time of its

disappearance.Theinfant’sattemptstorediscoverthelostobjectconsistonlyofarepetitionofthepast

actionsassociatedwiththeobject.Nonovelbehaviorisintroduced.


Coordination of Secondary Schemes

Thefollowingobservationsshowhowafterinitialfailurethechilddevelopsthebehaviorpatterns

characteristicofstage4:

at 0;6(0) I present Laurent with a matchbox, extending my hand laterally to make an obstacle to hisprehension.Laurenttriestopassovermyhand,ortotheside,buthedoesnotattempttodisplaceit.AseachtimeIpreventhispassage,heendsbystormingattheboxwhilewavinghishand....Samereactionsat0;6(8),0;6(10),0;6(21),etc.

Finally,at0;7(13)Laurentreactsquitedifferentlyalmostfromthebeginningoftheexperiment.Ipresentaboxofmatches abovemyhand, but behind it, so that he cannot reach itwithout setting theobstacle aside.ButLaurent,aftertryingtotakenonoticeofit,suddenlytriestohitmyhandasthoughtoremoveorlowerit;Ilethimdo it tomeandhegrasps thebox. I recommence tobarhispassage,butusingasascreenasufficientlysupplecushiontokeeptheimpressofthechild’sgestures.Laurenttriestoreachthebox,andbotheredbytheobstacles,heatoncestrikesit,definitelyloweringituntilthewayisclear....

Moreover,onenotesthattheintermediateactservingasmeans(removingtheobstacle) isborrowedfromafamiliarscheme:theschemeofstriking.WerecallthatLaurentfrom0;4(7)andaboveallfrom0;4(19)hasthehabitofhittinghangingobjectsinordertoswingthemandfinallyfrom0;5(2)ofstrikingtheobjects. . . .Now,thisistheusualschemeofwhichLaurentmakesuseatthepresenttime,nolongerinthecapacityofanendinitself(of

afinalscheme)butasameans(atransitionalormobilescheme).(OI,pp.217-18)

The interpretationofLaurent’sbehaviorutilizesmanyof theprinciplesdiscussed inconnection

withstage3.Thereare,however,someimportantdifferences.OnedifferenceisthatLaurenthasthegoal

inmindfromtheoutset.Ifyouwillrecall,instage3theinfantaccidentallydiscoversagoalandonlythen

pursuesit. Instage4,ontheotherhand,Laurent initiallyperceivesthepresentedobjectasafamiliar

goal. The infant has already developed schemes for dealing with the goal and immediately tries to

assimilateitintothem.Orinsimplerlanguage,theinfantalreadyknowswhattodowiththeobjectand

wantstodoit.Thedirectionalforceaffectingtheinfant’sbehavior—hisdesiretoachievethegoal—is,of


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course, once again a matter of functional assimilation. Once the scheme of the goal—grabbing the

matchbox—isactivated,itneedstofunction.

Butanobstaclearises(thefather’shandorthecushion)whichpreventsthechildfromattaining

thegoal.Nowwecanseethesecondfeaturewhichdistinguishesbehaviorinstage4fromthatinstage3.

Theinfantisnowrequiredtodevelopnewmeansforremovingtheobstacletoachievehisends.Unlike

stage3,itisnotnowsimplyamatterofrediscoveringsomebehaviorwhichearlierled(accidentally)to

thegoal.Theinfantmustshowsomedegreeoforiginalitytoremovetheobstacle.Butthisoriginalityisof

avery limitedsort. Insteadof inventing newmeans fordealingwith theobstacle, Laurent attempts to

utilizeasmeansschemeswhichhavebeendeveloped inconnectionwithothersituations.That is,he

generalizespatternsofpreviouslylearnedbehaviortothenewproblem(generalizingassimilation).In

thecourseofthisgeneralization,theolderschemesmaybesomewhat,butnotfundamentally,modified.

Also,hemaytryoutseveralschemes,butintheendretainsonlytheonewhichworksbyremovingthe

obstacle.Accommodationisonceagaindependentonpracticalsuccess.Theresultisacoordinationoftwo

secondaryschemes,eachofwhichhadbeenlearnedearlier,andeachofwhichisonlyslightlymodified

for the present occasion. One scheme serves as the means and the other as the ends. The child’s

originalityrestsnotininventingtwoseparateschemesbutincombininginanovelwaytwopreviously

learnedpatternsofbehavior.

Several features of this coordination are emphasized by Piaget. First, it is still essentially

conservative.Theinfant’saimistotreatthegoalobjectinthesamewayaspreviously.Oncetheobstacleis

removed,theinfantappliesafamiliarscheme.Second,theinfant’sbehavioratthisstageisforthefirst

timetrulyintentionalandtherefore“intelligent.”Piaget’scriteriafortheexistenceofintentionarethree

innumber:(1)theinfanthasthegoalinmindfromthebeginninganddoesnotdiscoveritaccidentally

as was the case in stage 3, (2) an obstacle arises which prevents direct attainment of the goal and

necessitates some kind of indirect approach, and (3) to overcome the obstacle, the infant employs a

scheme(means)whichisdifferentfromthatemployedinthecaseofthegoal(ends).

AthirdfeatureofthiscoordinationemphasizedbyPiagetisthatthebehaviorunderdiscussionis

mobile.Thenovelcoordinationbetweentwoschemesnotpreviouslyassociatedismadepossiblebythe

infant’srelativelynewabilitytodetachhisschemesfromtheirusualcontents.Inotherwords,thescheme


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usedasmeansisgeneralizedortransferredfromthesituationinwhichitwasoriginallylearned.This

flexibilityintheapplicationofschemesiswhatconstitutesmobility.

Relations

Instage3wediscussedtheveryfirstmanifestationsofrelationsintheinfant.Withthecoordination

ofschemesinstage4,theinfantbecomescapableofestablishingmorecomplexrelationships.

Letus recall, forexample,Laurent’s coordinationof secondary schemes: removinganobstacle to

attainagoal.WhenLaurentdoesthis, it isas ifhe“understands” that theobstaclestands inacertain

relationshiptothegoal.Theobstacleisinfrontofthegoal,anditmustberemovedbeforethegoalcanbe

attained.Inotherwords,justasanabbreviatedperformanceofoneschemeisaprimitiveindicationofa

class,sothecoordinationoftwoschemesimpliesabehavioralanalogueoftheunderstandingofrelations.

Letustakeanotherexample:

at0;9(17),Laurentliftsacushioninordertolookforacigarcase.Whentheobjectisentirelyhiddenthechildlifts thescreenwithhesitation,butwhenoneendof thecaseappearsLaurent removes thecushionwithonehand and with the other tries to extricate the objective. The act of lifting the screen is therefore entirelyseparate from that of grasping the desired object and constitutes an autonomous “means,” no doubt derivedfromearlierandanalogousacts.(OI,p.222)

Thusthesequenceisaclearcaseofsecondarycircularreaction.Laurenthaslearnedhowtogetthe

goal.Buthashenotalsolearnedsomethingoftherelationbetweenobstacleandgoal?Laurent’sbehavior

maybeinterpretedasshowingaconcreteunderstandingofcertainrelations:thecushionisontopofthe

cigarboxwhichinturnisunderthepillow.Weemphasizeonceagainthatthechild’s“understanding”of

relationsisnotabstractliketheadult’s;instead,itisentirelycontainedinhismeans-endbehavior.

Perhapsthemostremarkablefeatureofrelationsisthateveninthefirstfewstages,theyinvolvean

elementofquantity.Forexample,

At 0;9(4) Laurent imitates the soundswhich he knows how tomake spontaneously. I say “papa” to him, herepliespapaorbaba.When I say “papa-papa” he repliesapapa orbababa.When I say “papapapapapapa” herepliespapapapa,etc.Thereexistsaglobalevaluationofthenumberofsyllables:thequantitycorrespondingto2isinanycasedistinguishedfrom3,4,or5....

At0;10(4)LaurentrepeatspawhenIsay“pa,”papafor“papa”andpapapaforanumberof4ormorethan4.


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(OI,p.241)

Thus the infant shows a primitive appreciation of number in the ability to discriminate among

differentnumbersofsyllables.

Anticipation

If youwill, recall that in connectionwith the abbreviated schemes of stage 3,we discussed the

developmentoftheoperationsofclassificationandtherelationbetweenthesignifierandthesignified.

Forexample,whenLuciennebrieflyshakesherlegsatthehangingparrots,thesightofthetoysisthe

signifierandtheabbreviatedmotionisthesignified—theprimitivemeaningoftheparrotsforthechild.

Inthepresentstage,thesystemofmeaningsisusedintheserviceofanticipation.(Thisoccursalsoin

stage3,butinrudimentaryform.)HereisanexampleconcerningJacqueline:

At0;9(16)...shelikesthegrapejuiceinaglass,butnotthesoupinabowl.Shewatcheshermother’sactivity.Whenthespooncomesoutoftheglasssheopenshermouthwide,whereaswhenitcomesfromthebowl,hermouthremainsclosed. ...At0;9(18) Jacquelineno longerneeds to lookat thespoon.Shenotesby thesoundwhether the spoonful comes from the glass or from the bowl and obstinately closes hermouth in the lattercase....

Luciennehas revealedmostof thesamereactions.Thusat0;8(23)shealsocloseshermouth to thespoonfulcomingfromthebowl(ofsoup)andopensittothosecomingfromtheglass(offruitjuice).(OI,p.249)

Howcanwe interpret these reactions?First, note that theyareanticipatory. The infantdoesnot

avoidthesoupwhenitisinhermouth,butbeforeitgetsthere.Apparentlythesightofthesouporeven

itsdistinctivesoundisasignifier,andthesignifiedistheunpleasanttasteofthesoup.Inotherwords,

theinfantseesorhearsthesoup,anditsmeaningforherisanunpleasantexperience.Shethencloses

hermouth,notinresponsetotheactualtasteofthesoup,buttothemeaningthatsouphasforherbefore

it entershermouth. Furthermore, the infant in this stagedoesnot formonly anticipationswhich are

connectedwithherownactions.Forexample, Jacquelineoncecriedwhenshesawsomeonewhowas

sittingnexttohergetup.ApparentlyforJacquelinethesightofthepersongettingupwasasignifierof

his expected imminent departure (the signified), and it was to this signified (the expectation of

departure)thatshereacted.

Howdotheseanticipationsdevelop?Formerly,Jacquelinehadobservedthatthesignifier—inthis


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case the person getting up—was followed by another event, his departure. She had consequently

perceivedaconnectionbetweenthe twoevents, so thatnowthesignifiergivesrise toananticipation

concerningtheeventtofollow.

Imitation

Considerable progress in imitation occurs during stage 4. The infant can now establish

relationshipsbetweenthemovementsofamodelandthecorrespondingmovementsofinvisiblepartsof

hisownbody.Also,hebeginstoimitatenewactionsofmodels.

Considerthisexampleofthefirstcase:

at0;8(4)Jacquelinebeganbymakingaslightnoisewithhersalivaasaresultofthefrictionofherlipsagainstherteeth,andIhadimitatedthissoundattheoutset.[Onthesameday]Jacquelinewasmovingherlipsasshebit her jaws. I did the same thing and she stopped andwatchedme attentively.When I stopped she beganagain.Iimitatedher.Sheagainstoppedandsoitwenton.(PDI,pp.30-31)

Herewe see that Jacqueline establishes a connection betweenwhat she sees in themodel (the

movement of his lips) and what she cannot see in herself, but can only feel, namely, her own lip

movements.Howdoesshemanagetodothis?Atfirstwithhersalivashemakesasoundwhichisimitated

byPiaget. Jacquelinerepeatsthissoundandat thesametimecarefullywatchesthemovementsof the

model’smouth.NowwhilesheisreproducingthesoundofthesalivaandwatchingPiaget’smouth,she

becomes aware of certain tactile-kinesthetic feelings. The sound becomes associated on the one hand

withthesefeelings,andontheotherwiththesightofthemodel’slipmovements.Thus,thesoundisa

commondenominatorlinkingthevisualandkinestheticcues.Laterthesoundisnolongernecessary,and

shebecomesabletoimitatemouthmovementswithouteitherthemodelorherselfhavingtoproducethe

soundfirst.

Thefollowingisanexampleoftheimitationofnewactionsofamodel:

At0;9(12)Ialternatelybentandstraightenedmyfinger,andshe[Jacqueline]openedandclosedherhand.At0;9(16) she reacted to the samemodel several times in succession bywaving her hand, but as soon as shestopped trying to imitate me she raised her finger correctly. When I resumed she again began to wavegoodbye.

At0;9(19)Itriedthesameexperiment.Sheimitatedme,butusedherwholehandwhichshestraightenedand


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bentwithouttakinghereyesoffmyfinger.

. . .Finallyat0;9(22)shesucceededinisolatingandimitatingcorrectlythemovementoftheforefinger.(PDI,pp.46-47)

HerePiagetinitiatesanewmovementinfrontofthechild.Jacqueline,contrarytoherreactionsof

theprecedingstage,nolongerignoresthenewmovement,buttriestoimitateit.Tworestrictionsonthe

initial imitationofnovelbehaviorareapparent inthe foregoingexample. Inthe firstplace, the infant

imitatesonlymovementswhicharesimilartothosesheisalreadyabletoperform.Forinstance,bending

andstraighteningthefingerisnottoodifferentfrombendingandstraighteningthehand.Theinfantis

consequently interested in imitatingsuchbehaviorsinceshecanassimilate it tosomeknownscheme.

Furthermore,imitationisonlyveryapproximateatthispoint.Theinfantrarelysucceedsinreproducing

thecorrectmovementon the first trial. Shegradually improvesher techniquewithpracticeand,bya

successionofadjustments,accommodatesherschemestothenovelmovement.

Object Concept

Thebehaviorofthestage4infanttowardobjectsshowsamarkedprogressincomparisonwiththat

ofthepreviousstageandisaresultoftheinfant’simprovedmanipulatoryskills.Sincetheinfantisnow

betterabletocoordinatehandandeyemovements,hecanexploreobjectsmoreadequatelythanbefore.

Byholdinganobjectwhilehebringsitclosertoorfurtherfromtheeyes,orbyturningitaroundinthe

hand,hebecomesawarethattheobjectremainsthesameeventhoughmanyvisualchangeshavetaken

place.Thisdiscovery leads to theattributionofqualitiesofpermanenceandsubstance toobjects.Asa

result,whenanobjectvanishestheinfanttriestofinditagainbyactivesearch.Henolongerattemptsto

rediscovertheobjectbymerelyprolongingorrepeatingtheactionsalreadyunderwaywhentheobject

disappeared.Instead,theinfantnowinitiatesnewmovementsandactionswhichindicatethattheobject

hasbecomedetachedfromitsprevioussubjectiverelationshipwiththeinfant’sownactivity.

Incertainconditions,however,theobjectconceptcontinuestoretainsomeofitssubjectivequalities.

Thisphenomenonmaybeseenclearlyfromthefollowingobservation:

At0;10(18)Jacquelineisseatedonamattresswithoutanythingtodisturbordistracther(nocoverlets,etc.).Itakeherparrotfromherhandsandhideittwiceinsuccessionunderthemattress,onherleft,inA.BothtimesJacquelinelooksfortheobjectimmediatelyandgrabsit.ThenItakeitfromherhandsandmoveitveryslowlybefore her eyes to the corresponding place on her right, under the mattress, in B. Jacqueline watches this


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movementbut at themomentwhen theparrotdisappears inB she turns toher left and lookswhere itwasbefore,inA.(CR,p.51)

Jacquelinepresentsthereactiontypicalofthisstage.Incertainsituationstheinfantisunabletotake

intoaccountthenumberorcomplexityofthemovementsofanobject,andattemptstolookfortheobject

intheplacewhereshehadpreviouslysucceededindiscoveringit.Inotherwords,ifthesituationistoo

complex, she tends to attribute to the object a sort of absolute or privileged position which is that

associatedwithpreviouslysuccessfuldiscoveries.If,ontheotherhand,theobjectsimplydisappearsin

onespot,theinfantsearchesforitintherightplace.

Instage4,then,theinfantsometimesattributestotheobjectqualitiesofsubstanceandpermanence.

Instraightforwardsituationstheobject isdetachedfromtheinfant’sactionsandisanobjectiveentity.

Should itsmovementsbecometoocomplicated for the infant to follow,however, theobjectonceagain

takesoncertainsubjectivepropertiesandbecomesrelatedtotheinfant’spastactions,especiallythose

whichhadpreviouslyprovensuccessfulindiscoveringtheobject.


Tertiary Circular Reaction

In stage5behavior loses its conservativeemphasis, and the child,whohasnowbegun towalk,

beginstosearchfornovelty.HereisanobservationonLaurent:

at0;10(2)Laurentdiscoveredin“exploring”acaseofsoap,thepossibilityofthrowingthisobjectandlettingitfall.Now,whatinterestedhimatfirstwasnottheobjectivephenomenonofthefall—thatistosaytheobject’strajectory—but the very act of letting go. He therefore limited himself, at the beginning, merely toreproducingtheresultobservedfortuitously.

... at 0; 10(10) . . . Laurent manipulates a small piece of bread. . . . Now, in contradistinction to what hashappenedontheprecedingdays,hepaysnoattentiontotheactof lettinggowhereashewatcheswithgreatinterestthebodyinmotion...[thefallingbread].

At0;10(11)Laurentislyingonhisback....Hegraspsinsuccessionacelluloidswan,abox,etc.,stretchesouthis armand lets them fall.He distinctly varies thepositions of the fall. Sometimeshe stretches out his armvertically, sometimes he holds it obliquely, in front or behind his eyes, etc. When the object falls in a newposition (forexample,onhispillow),he lets it fall twoor threemore timeson the sameplace, as though tostudythespatialrelation; thenhemodifiesthesituation.Atacertainmomenttheswanfallsnearhismouth;nowhedoesnotsuckit(eventhoughthisobjecthabituallyservesthispurpose),butdropsitthreetimesmorewhilemerelymakingthegestureofopeninghismouth.(OI,pp.268-69)


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The striking thing about theseobservations is Laurent’s curiosity about theobjects inhisworld.

Laurentdoesnotfocusinterestonhimselforonthosepropertiesofanobjectwhichaidinattainingsome

goal;instead,heseemscuriousabouttheobjectasanobject,andheseemsdesirousoflearningallhecan

aboutitsnature.Thisinterestinnoveltyforitsownsakeiscalledatertiarycircularreaction.

Piaget’sexplanationbeginswithnotingthattheinfantoftendiscoverstheinitialresultbychance.

Forexample,intheprocessofplayingwithhissoapdishLaurentaccidentallydroppeditandobserved

thefall.Moreover,theinitialchanceeventintereststheinfant,andthisinterestcanbeexplainedinterms

of the moderate novelty principle described earlier. The infant, of course, desires to reproduce the

interesting event, and this behavior involves the principle of functional assimilation. Consequently,

Laurentrepeatstheoriginalactanddropsthecaseofsoapseveraltimesinsuccession.

Thusfartheinfant’sbehaviorisnodifferentfromthatofstage3:aninterestingresultaccidentally

occurs, and the infant attempts to find a means by which to conserve it. However, at this point two

distinctivefeaturesofthetertiaryreactionmanifestthemselves.First,insteadofcontinuingsimpleand

rigidrepetitionoftheinterestingevent,Laurentinitiatesbehavioralchangeswhichproducevariations

in theevent itself.Laurentdrops thebreadandthenthe toys fromdifferentheightsor fromdifferent

positions. Second, he acts as if he now has interest in the new actions of the objects themselves and

searchesfornovelties—fortheunexpected.Heseemstotreattheunanticipatedtrajectoriesofthetoysas

somethingtobeunderstood.

Theexplanationofthetertiarycircularreactioninvolvesseveralsteps:

1.Atfirsttheinfanttriestoassimilatethenewobjectsintohisusualschemeofdropping.Hefinds,however,thatthehabitualschemedoesnotworkverywellashemeetswithresistance.Thatis,theinfanttriestodropthepieceofbreadinthesamewayhedroppedthesoapcase;thenhetriestodroptheswaninthesamewayhedroppedthebread.Sincealltheseobjectsdonotfallinthesameway,hemeetswitharesistancewhichisimposedbytherealityoftheobjectsthemselves.Laurentfindsthathisavailableschemeofdroppingdoesnotapplyinthesamewaytoalloftheobjects.Eachobjecthaspropertiesofitsownwhichmustbetakenintoaccount.

2. The infant becomes interested in these resistances. Piaget points out that at this stage ofdevelopmenttheinfantismorecapablethanbeforeofappreciatingnovelty.Ifyouwill


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recall,the“interesting”wasdefinedasthatwhichismoderatelydifferentfromwhattheinfantrecognizesasfamiliar.Consequently,themorethingstheinfantisfamiliarwithand themoreschemeshehas, themoreobjectsandeventshe is able to recognizeasnovel and interesting. The newborn’s world is largely restricted to sucking; eventsoutsidetheoralsphere(asmosteventsare)cannotbeinterestingbecauseofthelackofschemesrelevanttothem.Buttheinfantatstage5hasdevelopedskillswhichpermitcontactwithincreasinglylargersegmentsoftheworld;consequently,thereismuchthathewillfindinteresting.Insummary,themorecomplexthesystemofschemes,themorethe infant will be attracted to novelty. He will then be interested in the resistancesencounteredbyapplyingoldschemestonewevents.

3.Theinfantisinterestedinthepropertiesofobjectsfromanotherpointofview,too.Atthisstagetheinfanthasbeguntoattributepermanencetoobjectsandrecognizesthattheyhaveanexistenceindependentofhisown.Infact,objectsareeven“centersofforces,”withpowers and properties of their own. This new objectification of the world alsocontributestotheinfant’sdesiretoexplore.

Oncetheinfantrecognizesandhas interest inthepotentialnoveltiesofasituation,hebeginsto

accommodate,by“groping”orusingakindoftrial-and-errorproceduretodiscoverthepropertiesofthe

objects. The infant’s groping does not involve completely random responses; rather each of his

explorationsguides thenext.The resultsof one “experiment” lead tonewexperiments. For instance,

Laurentmayreleasetheswanfrompointswhichareincreasinglyhighabovehisheadandobservethe

extenttowhichtheswanbounceswhenithitsthebed.Theinfant,ofcourse,doesnotknowbeforehand

whatwillhappen;hemodifieshisbehaviortofindout.Byexploringtheobjectandaccommodatinghis

ownbehaviortoit,theinfantmayeventuallybecomeabletomastertheobject—toassimilateitwithout

difficultyintohis(modified)schemes.Inthiswayhebeginstoexploreandunderstandnovelaspectsof

theworld.

Discovery of New Means

Theinfant’stendencytowardexperimentationpermitsthediscoveryofnewmeansforattaininga

goal.ConsiderthefollowingobservationonLucienneat1;0(5).Piagetpresentsherwiththisproblem.

Ona table is a largebox turnedupsidedown.Thebox is so arranged that itmovesonlybypivoting

arounditscenterpoint.Onthebox,awayfromtheinfant’sreach,isanattractivetoy,abottle.

Lucienneat first tries to grasp thebox, but she goes about it as though thehandkerchiefwere still involved.


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[PullingahandkerchiefwasaschemewhichPiagethadpreviouslyobservedinthechild.]Shetriestopinchitbetween two fingers, in the center, and tries this for amomentwithoutbeing able to grasp it. Then,with arapidandunhesitatingmovementshepushesitatapointonitsrightedge....Shethennotestheslidingoftheboxandmakesitpivotwithouttryingtoliftit;astheboxrevolves,shesucceedsingraspingthebottle.(OI, p.287)

Togettheobject,Lucienneatfirstattemptedtoapplyanalreadyavailablescheme;pinchingthe

boxlikeahandkerchief.Then,however,she“groped”andaccommodatedherbehavior inatrial-and-

errorsortofway.Theresultwasdiscoveryofanewmeans.Luciennestruckthebox,andthisactionwas

successfulinbringingthetoyclose.Butwhileherbehaviorwastosomeextentcharacterizedbygroping,

ortrialanderror,heractionswereneverthelessdirectedintwosenses.First,heraccommodationswere

directed by the goal: Lucienne wanted to get the bottle and was trying out various means for this

purpose.Themeanswerehardlyselectedinarandomfashion;shedidnot,forinstance,trytoobtainthe

toybytakingoffhersocks.Second,Lucienneinterpretedthegropingbymeansofheralreadyavailable

schemes.Thatis,afterLuciennebychancehittheboxandsawitmove,shewasable,throughherpast

experience,to“understand”themeaningofheraction.Sheinterpretedthehittingasanothermethodfor

displacingobjects.Thusthechild’sgroping isdirectedbothbythegoalandbyearlierschemeswhich

enablehertounderstandwhatishappening.Therefore,learningisnotexplainedsolelybycontactwith

the environment, that is, by experiencewith aworld that simply forces the infant’s behavior to take

certain forms. The infant herself also makes an important contribution as she interprets and gives

meaningtothedataofexperience.

Imitation

At stage5 the childbecomes capable of the systematic imitationof newmodels. In theprevious

stage, the infant had begun to imitate new models which were not too different from his own

spontaneousactions,buthewasrarelycorrectonthefirsttrial.Inthepresentstagetheinfantbecomes

moresystematicinhistechniquesofimitation.Hereisanexample:

At0;11(20)she[Jacqueline]watchedmewith interestwhenI touchedmy foreheadwithmy forefinger.Shethen put her right forefinger on her left eye, moved it over her eyebrow, then rubbed the left side of herforeheadwith the back of her hand, but as if shewere looking for something else. She reached her ear, butcamebacktowardhereye....

At 0; 11(28) J., confronted with the same model, continued merely to rub her eye and eyebrows. Butafterwards,whenIseizedalockofmyhairandmoveditaboutonmytemple,shesucceededforthefirsttime


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inimitatingme.Shesuddenlytookherhandfromhereyebrow,whichshewastouching,feltaboveit,foundherhairandtookholdofit,quitedeliberately.

At0;11(30)sheatoncepulledherhairwhenIpulledmine.ShealsotouchedherheadwhenIdidso,butwhenIrubbedmyforeheadshegaveup....Itisnoteworthythatwhenshepulledherhairshesometimesturnedherhead suddenly in an attempt to see it. This movement is a clear indication of an effort to discover theconnectionbetweentactualandvisualperception....

At1;0(16),J.discoveredherforehead.WhenItouchedthemiddleofmine,shefirstrubbedhereye,thenfeltaboveitandtouchedherhair,afterwhichshebroughtherhanddownalittleandfinallyputherfingeronherforehead.Onthefollowingdaysheatoncesucceededinimitatingthisgesture,andevenfoundapproximatelytherightspotsindicatedbythemodel.(PDI,pp.55-56)

Twopoints are of interest concerning these examples. First, they clearly show that the infant is

moreadeptthansheformerlywasattheimmediateimitationofnewactionsofmodels.Theinfanttriesto

controlhermovementsinasystematicway.Forexample,Jacquelinetriestolookatherhairwhenshe

pullsit.Second,theexamplesillustratesomegeneralprocessesofimitation.Thechiefaimofimitationis

toreproducetheactofamodel.Whenthemodel’sactionsarenew,asinthepresentcase,accommodation

is required. That is, the infant must modify her movements to make them like the model’s. Thus,

accommodationhaspriorityoverassimilation.Inthecaseofintelligentbehavior,ontheotherhand,the

processes of assimilation and accommodation are in balance. The infant attempts both tomodify her

behavior in response to the demands of the environment (accommodation) and to understand this

environmentintermsofherownschemes(assimilation).

Object Concept

Instage5theinfantisfinallyabletofollowcorrectlyavisiblesequenceofanobject’smovements.He

nowunderstandspositionalrelationshipsbetweentheobjectandotherelementsof theenvironment.

Therefore,eveniftheobjectdisappearssuccessivelyinanumberofplacestheinfantwillsearchforitin

theplacewhereitwaslastseen.Theinfantdoesnot,asinstage4,lookfortheobjectintheplacewhereit

hadpreviouslybeendiscovered.Thus,theobjectisnolongerconnectedwithapracticalsituation(the

infant’spastsuccesses),buthasacquiredapermanenceofitsown.Atthisstage,though,theinfantcan

understandonlyvisiblemovementsoftheobject.Ifheisunabletoseeallthedisplacementsandmust

therefore infer thatsomeare invisible, the infantreverts toanearlierreaction—looking for theobject

wherehehadbeensuccessfulinfindingitinthepast.Thereasonforthefailureisthatwheninvisible


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movementsoftheobjectareinvolved,theinfantmustinferrelationshipsofpositionbutisnotyetcapable

ofinference.Considerthefollowingillustration:

At1;1(18)Lucienne isseatedonabed,betweenshawlAandclothB. Ihideasafetypin inmyhandandmyhandundertheshawl.Iremovemyhandclosedandempty.Lucienneopensitatonceandlooksforthepin.Notfindingit,shesearchesundertheshawlandfindsit....

Butwithaberet,thingsbecomecomplicated.IputmywatchintheberetandtheberetunderpillowA(ontheright);Lucienneliftsthepillow,takestheberet,andremovesthewatchfromit.ThenIplacetheberet,againcontainingthewatch,undercushionBontheleft;LuciennelooksforitinBbut,asitishiddentoofardownforhertofinditatonce,shereturnstoA.

Then,twice,IraisecushionBsothatLucienneseestheberetobviouslycontainingtheobject;bothtimessheresumeslookinginBbut,notfindingthewatchrightaway,returnstoA!ShesearchesevenlongerinAthaninBafterhavingseentheobjectinB!(CR,pp.76-77)

Hereweseethattheobjectseemstobeendowedwithadualnature.Ontheonehand,iftheinfant

is able to follow the object’smovements perceptually, she believes in its permanence and continued

existence.If,however,shecannotfollowthemovementsvisuallybutmustimaginethem,theinfantno

longerendowstheobjectwiththepropertyofpermanence.Theobjectrevertstoitsearlierstatusofbeing

associatedwithapreviouslysuccessfulscheme.

STAGE 6: 18 MONTHS TO 2 YEARS

Beginning of Thought

Inthecourseofhisfivestagesofdevelopment,theinfanthasmostcertainlymadegreatprogress.

The newborn displays simple patterns of learning which are limited to the sphere of hereditary

mechanisms;theinfantinstage5hasagenuineinterestinthethingsoftheenvironment,exploresthem,

andevenhastheabilitytoinventnewwaysofdealingwiththeworld.Buttheinfant’sachievementto

thispointisasnothingcomparedwiththenextdevelopment.Beforestage6theinfantwasnotcapableof

thoughtorlanguageandsowaslargelylimitedtotheimmediatedataofexperience.Stage6,however,

formsthetransitiontothenextperiodofdevelopmentinwhichtheinfantisabletousementalsymbols

andwordstorefertoabsentobjects.Thisperiodofsymbolicthoughtbeginstofreetheinfantfromthe

concretehereandnowandintroduceshimtotheworldofpossibilities.InChapter3weshalldiscuss

symbolicthoughtindetail;atpresentwewilllimitourselvestoabriefdescriptionofitsbeginnings,as


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illustratedbytheseobservations:

Piaget isplayingwithLucienne, at1;4(0)andhidesanattractivewatch chain insideanempty

matchbox.

Iputthechainbackintotheboxandreducetheopeningto3mm.ItisunderstoodthatLucienneisnotawareof the functioningof theopeningandclosingof thematchboxandhasnot seenmeprepare theexperiment.Sheonlypossessestwoprecedingschemes:turningtheboxoverinordertoemptyitofitscontents,andslidingherfingers intotheslit tomakethechaincomeout. It isofcoursethis lastprocedurethatshetriesfirst:sheputsherfingerinsideandgropestoreachthechain,butfailscompletely.ApausefollowsduringwhichLuciennemanifestsaverycuriousreaction....

Shelooksattheslitwithgreatattention;then,severaltimesinsuccession,sheopensandshutshermouth,atfirstslightly,thenwiderandwider!

[Then]...Lucienneunhesitatinglyputsherfingerintheslit,andinsteadoftryingasbeforetoreachthechain,shepullssoastoenlargetheopening.Shesucceedsandgraspsthechain.(OI,pp.337-38)

Thisobservationrevealsanimportantadvanceinthechild’scapabilities.Luciennewasconfronted

withasituationforwhichanewsolutionwasrequired.Togetthechainoutoftheboxshetriedmethods

whichhadinthepastbeensuccessfulinsimilarsituations.Buttheseschemeswerenotadequateforthe

newproblem.Whatwould the stage 5 infant do in these circumstances?Hewould experimentwith

variousnewmeansuntiloneoftheinventionswassuccessful.Hisbehaviorwouldshowgroping.

ButLuciennedoesnotdothis.Instead,shepausesandlooksattheboxintensely.Herchiefovert

behavioratthistimeisonlyanopeningandclosingofthemouth.Afterthisdelay,sheimmediatelysolves

theproblem.Whatdoestheopeningandclosingofthemouthsignify?Piagetinterpretsitasshowingthat

shetriestothinkaboutwaysofsolvingtheproblem.Lucienneisnotyetproficientatthought;sheisnot

yetcapableofrepresentingthesituationtoherselffullyinmentalterms.Consequently,she“thinksout”

the problem partly by way of movements of the mouth. Even though her thought is not yet fully

internalized,itinvolvesaconsiderableshortcutoverthegropingofstage5.NowLucienneneednotact

outherattemptedsolution,forsheisatleastpartiallyabletoemployamoreeconomicalprocedure:to

think. Thus, Lucienne is on the threshold of a new period of intellectual development in which the

acquisitionofthesymbolicfunctionpermitsthegrowthoftruementalactivity.


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Imitation

The notable achievement of stage 6 is the appearance of the capacity to representmentally an

objectoractionwhichisnotperceptuallypresent.Thecapacityforsuchrepresentationhasrepercussions

fortheprogressofimitationandcontributestotheappearanceoftwonewreactionsduringstage6.In

thefirstplace,whenfacedwithnewmodels,theinfantnolongerneedstoperformovertlytrialattempts

at imitation; instead, he now tries out the variousmovementsmentally. Havingmade the necessary

mentaladjustments,theinfantcanthenperformthecorrectaction.Sincetheprocessislargelymental,

thestage6infantcanimitatemorequicklythantheonewhomustfirsttryoutallthemovements.The

internalizationof the trial-and-errorprocess consequently leads towhat appears to be an immediate

imitationofmodels.

Anotherfeatureofthepresentstageisthattheinfantbecomescapableofimitatingforthefirsttime

amodelwhichisnolongerpresent.Thisdeferredimitationisduetothefactthattheinfantcanimagine

themodeleventhough it isabsent.That is, the infant iscapableofevoking(representing) theabsent

modelinsomeinternalsymbolicform,forexample,bymeansofavisualimage.Considerthefollowing

exampleofdeferredimitation:

At1;4(3)Jacquelinehadavisitfromalittleboyof1;6whomsheusedtoseefromtimetotime,andwho,inthecourseoftheafternoon,gotintoaterribletemper.Hescreamedashetriedtogetoutofaplaypenandpusheditbackward,stampinghis feet. Jacquelinestoodwatchinghim inamazement,neverhavingwitnessedsuchascenebefore.Thenextday,sheherselfscreamedinherplaypenandtriedtomoveit,stampingherfootlightlyseveraltimesinsuccession.(PDI,p.63)

Theinternalizationoftheactionisquiteclear.Theinfantdoesnotreproducethesceneatthetime

of its occurrence, but at some later period. Therefore, representation was required for the child to

preservetheoriginalsceneforittobeevokedatalatertime.

Object Concept

Finally,atstage6theconceptofthepermanentobjectisfullyelaborated.Theinfantnotonlytakes

into account visible displacements of the object, but can also reconstruct correctly a series of invisible

displacements.Forexample,

At 1;7(23) Jacqueline is seated opposite three object-screens, A, B and C (a beret, a handkerchief, and her


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jacket)alignedequidistantfromeachother.Ihideasmallpencilinmyhandsaying,“Coucou,thepencil.”[Thechild had previously found it under A.] I hold outmy closed hand to her, put it underA, then under B, thenunder C (leaving the pencil under C); at each step I again extendmy closed hand, repeating, ‘‘Coucou, thepencil.”JacquelinethensearchesforthepencildirectlyinC,findsitandlaughs.(CR,pp.79-80)

JacquelinehasseenthepencildisappearonlyonceandintoPiaget’shand.Shedoesnot,however,

look into his hand to find the pencil, but under the last objectwhere he had placed his hand. This

reactionindicatesthatshebelievesthatthepencilcontinuedtoexistwithinthehandduringthewhole

sequenceofdisplacements,andthatshehasinferredthattheinvisibleobjectwasdisplacedfromAtoBto

C.Inotherwords,Jacquelinehasformedamentalimageofthepencilandcanfollowtheimagethrougha

seriesofcomplexdisplacements.

SUMMARY AND CONCLUSIONS

Theinfant’sdevelopmentinthesensorimotorperiodisatrulyremarkableachievement.Instage1,

the newborn depends heavily on reflexes for interaction with the environment. The environment,

however,doesnotsimplyturnonandoffthesetoolsprovidedbyheredity.Theinfant,eveninthefirst

monthoflife,profitsfromexperienceandactivelymodifiesthereflexschemes.Helearns,forexample,to

recognizethenippleandtosearchforit.

Instage2,theinfantshowsbehaviorpatternswhichareremovedfromthefeedingsituation.(1)He

developstheprimarycircularreactions,forexample,themotorcoordinationsnecessaryforbringingthe

handtothemouth.(2)Theinfantlearnsinaprimitivewaytoanticipatefutureevents.Whenplacedin

theappropriateposition, the infantanticipatesnursingby initiatingsuckingmovements. (2)The first

signs of curiosity appear. The infant shows an interest in moderately novel events. (4) The infant

sometimesrepeatsthebehaviorofmodels.Thisisaveryprimitivekindofimitation,sinceitoccursonly

whenthemodelperformsanactionhighlysimilartoaschemeavailabletotheinfant.Itisasiftheinfant

didnotdistinguishthemodel’sactsfromhisown;therefore,theapparentimitationismerelytheinfant’s

repetition of behavior no different from his own. (5) The infant lacks a mature object concept, but

developsseveralpatternsofbehaviorwhicharepreliminarystepsintherightdirection.Hecoordinates

the previously independent schemes of looking and hearing, among others, and shows passive

expectancybywatchingforabrieftimethespotwhereanobjecthasdisappeared.


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In stage 3, the infant’s behavior and interest extend beyond his own body and makes more

extensive,butstillimmature,contactwiththeexternalenvironment.(1)Theinfantdevelopssecondary

circularreactions.Bychance,hediscoversaninterestingenvironmentaleventandattemptstoreproduce

theactionswhichcausedit.(2)Theinfantshowspreliminaryindicationsofclassificationormeaning.

Presentedwith a familiar object, he sometimes reactsby showingmere abbreviationsof the actions it

usuallyelicits.Thisbehaviorappearstobeaprecursorofmentalrecognitionandunderstandingofthe

object.(3)Theinfant’simitationisnowmoresystematicandprecise.Heisfairlysuccessfulatimitationof

models, butonlywhen familiarpatternsofbehaviorare involved. (4)The infantmakes considerable

progresstowardattainmentoftheobjectconcept.Ifhehimselfhascausedanobject’sdisappearance,the

infantattemptsavisualortactualsearch.Thissearchonlyinvolvescontinuationofbehavior(likelooking

or grasping) which is already under way. To this extent the object concept remains subjective—

intimatelyboundtotheinfant’sownbehavior.

In stage4, the infant’s behavior is increasingly systematic andwell organized. (1)He is able to

coordinatesecondaryschemes.Hehasagoalinmindfromtheoutsetandusesoneschemeasameansfor

attaining the goal and a second scheme for dealing with the goal. This behavior is purposive and

therefore intelligent. (2) By interacting with the environment, the infant learns something about

relationsamongobjects.Inremovinganobstacletoagoal,forinstance,thechildachievesapreliminary

andconcreteunderstandingofthefactthattheobstacleisinfrontofthegoalandmustberemovedbefore

thegoalcanbeattained.(3)Theinfant’sincreasingunderstandingoftheenvironmentisapparentinthe

ability toanticipateeventswhichdonotdependonhisownactions.At thisperiodthe infantexpects

people toact in certainways;hebegins to recognize that theyare “centersof forces” independentof

himself.(4)Theinfantbeginstoimitatethenovelbehaviorofmodels,butisnotyetstrikinglysuccessful.

Alsohe imitatesactions—likestickingout the tongue—whichhecannot seehimselfperform. (5)The

infant’sobjectconceptisalmostfullydeveloped.Heemploysavarietyofbehaviortosearchforvanished

objects.Heclearlyattributestothingsadegreeofsubstanceandpermanenceandbeginstoconceiveof

objects as autonomous and as independent of his own subjective state. Nevertheless, he is not yet

successfulatfollowingacomplexseriesofdisplacementsofanobject.

Stage 5 is the climax of the sensorimotor period. (1) The infant shows an active interest in

producing new behavior and novel events. Before this stage, the infant’s behavior was essentially


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conservative.Hetriedtorediscoveroldactionswhichhappenedtoleadtointerestingresults.(2)When

confrontedwithanobstacletheinfantattemptstodevelopnewmeansfordealingwithitanddoesnot

relysolelyonschemeswhichweresuccessfulpreviously. (3)The infant isnow increasinglyadeptat

imitating new actions of models. The infant attempts, for instance, to produce sounds he has never

utteredbefore.(4)Theinfanthasreachedafurtherstageinthesensorimotordevelopmentoftheobject

conceptandcannowcomprehenda complex seriesofdisplacementsandsearch for theobject in the

properplace.

Stage6formsthetransitiontosymbolicthought.(1)Inourpreliminaryoverviewwesawthatthe

infantattemptedtothinkaboutaproblem,todevelopsolutionsonamentalratherthanaphysicallevel.

(2)Similarly,theinfantcannowimitateamodeleventhoughthelattermaynotbepresent.Itisapparent

thatafterobservingamodel,theinfantformsamentalrepresentationofit,sothatthelaterimitationis

basednotonaphysicallypresentmodel,butonitsmentalsurrogate.(3)Theinfantnowcanreconstruct

aseriesofinvisibledisplacementsofanobjectbecauseofthesenewabilitiesinrepresentation.

Inthemostgeneralsense,developmentrevealsaprocessofdecentration.Theinfantbeginslifein

anundifferentiatedstate,notseparatingselffromenvironmentorwishfromreality.Heiscenteredabout

theself.Forexample,wehaveseenhowtheinfantinthefirstfewstagesdoesnothaveamatureobject

concept.Athingceasestoexistwhenitpassesoutsidehis immediateperception.Furthermore, forthe

infant theworld ismerely a series of unstable andunconnected “pictures.”Neither self nor external

environmentexistasautonomousentities. Inthecourseofdevelopmentthe infantadvancesfromthis

“adualistic”orundifferentiatedstatetooneofgreaterseparationofselfandenvironment.Hedecenters

fromtheself.Inthecaseoftheobjectconcept,forexample,theinfantnowconceivesofthingsexisting

independently.Objectsnowarecentersofforcesandhavepropertieswhichdonotdependonhiswill.

Thisgreaterunderstandingoftheexternalworldisatthesametimeanincreasedcomprehensionofthe

self.Therealizationoftheseparatenessofthingsnecessarilyinvolvesthesimultaneousapprehensionof

theexistenceofself.Inotherwords,thepersonwhobelievesthathiswishesinfluencethemovementsof

thingsdoesnotunderstandeitherselforthings;thepersonwhobelievesthatthetwoareseparatehasa

greaterunderstandingofboth.

Piagetstressesseveredpointsconcerningdevelopment inthesensorimotorperiod.First, theage


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normsareonlyapproximate.Aswenotedearlieritisimpossibletogivepreciseagenormsbecauseonly

threeinfantsprovidethedataforstudy.Moreimportant,Piagetfullyrecognizesthatthetimingofthe

stagesdependsonahostof factorswhichvaryamongchildren.Development isa functionofcomplex

interactionamongmanyfactors,amongwhichmaybethenatureofthesocialenvironment,theinfant’s

rateofphysicalmaturation,andsoon.Giventhesecomplexities,itisclearthatinfants’progressthrough

thestageswillshowmanyinpidualdifferences.Forinstance,PiagetcitestheexampleofJacquelinewho

wasborninthewinter.Becauseshewasbundledupinthecarriagetoprotectheragainstthecold,she

did not have as much opportunity as did the other children, born in warmer weather, to develop

coordinationbetweenhandandeye.Fromfindings likethese,Piagetconcludedthatthesensorimotor

stagesdonotappearatpreciselydefinedagesintheinfant’slife.

Second, Piaget insists, however, that the ordering of the stages is invariant. A child must pass

throughstage3beforestage4,andthereversecannotoccur.Also,achildcannotskipastageentirely.

ThereasonsforPiaget’sassertionarebothempiricalandtheoretical.First,Piaget’sobservationsshowed

thathisthreechildrenfollowedthesequenceofdevelopmentintheorderdescribed.Second,eachstage

isbothaculminationoftheoneprecedingandapreparationfortheonetofollow.Sinceeachstagelays

thegroundworkforthefollowingstage,itishardtosee,onrationalgroundsalone,howtheorderofany

twostagescanbereversed.

Third,Piagetemphasizesthatdevelopmentisagradualandcontinuousprocess.Onedoesnotfind

suddentransformationsinaninfant’sbehaviorsothatonedayheischaracterizedbystage3andthe

nextbystage4activities.Developmenttakestime,andbecauseofthisoneseldomsees“pure”examples

ofthebehaviorswhichPiagetusestodescribeastage.Piaget’sstagesare,infact,idealtypeswhichare

abstractedfromthecontinuumoftheinfant’sdevelopment.Whiletheseabstractionsareveryusefuland

convenient,Piagetiscarefultoremindusthatinthenormalcourseofeventstheinfant’sbehaviortakes

many forms intermediary between those described by the stages. Also, development is not always

consistentacrossallspheresofbehavior.The“stage4infant”isagainonlyanabstraction.Infact,onesees

infants whose object concept may be characterized by stage 4, while at the same time their level of

imitationisstage3,andsoon.

Fourth,Piagetstressesthatthebehaviorscharacteristicofagivenstagedonotdisappearwhenthe


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infantattainsthenextstage.Instead,evenasnewabilitiesareaddedtheinfantretainsmanyoftheold

ones.Forexample,thestage5infant,confrontedwithanobstacleandtryingtoremoveit,mayfirstapply

schemeswhichhavebeensuccessfulinothersituations(stage4behavior),andonlythenmayheattempt

toinventnewmeans(stage5behavior).

Inconclusion,wewouldliketomakeafewgeneralcommentsaboutPiaget’stheoryofinfancyand

clarifysomeaspectsthatareoftenmisunderstood.First,Piaget’spositionontheroleoftheenvironmentis

subtle, and consequently oftenmisinterpreted.He feels that it is obvious that the environment exerts

effects on the infant, but acceptance of this proposition hardly solves any problems. The task then

becomes to discoverhowthe environment operates. Piaget feels that the environment does notmold

behaviorbysimplyimposingitselfonapassivesubject,evokingtheinfant’sresponseandrewardingit.

Instead, Piaget’s central theme is that the infant is active; that is, the infant seeks contact with the

environment. His curiosity does not permit waiting for environmental events to happen; rather he

searchesthemoutandseeksincreasedlevelsofstimulationandexcitation.Whensomeenvironmental

eventoccurs,theinfantdoesnotregisteritpassively,butinsteadinterpretsit.Itisthisinterpretation,not

theeventitself,whichaffectsbehavior.Supposewehavetwoinfants,onewhoiscapableofanticipations

concerningadultsandonewhoisnot.Bothwitnessanadultwhorisesandputsonacoat.Oneinfant

cries and the other remains calm. “Experience”—seeing the adult get up and put on the coat—has

affectedtheinfantsdifferently.Theexplanationisthatoneinfantexpectedhimtoleaveandtheother

didnot.Theinfantsinterpretedtheeventsindifferentways.Wemightevensaythatthereexistedtwo

different“realities,”eachoneconstructedbyaninfant.Theinfantsassimilatedtheperceivedeventinto

theirdifferingexpectationsconcerningadultbehavior.Thisassimilationorinterpretationgavetheevent

meaningandproducedthesubsequentbehaviors.Sotheinfantsdidnotpassivelyregisteramere“copy”

ofreality;instead,theyinterpreted,constructed,andassimilated,or,inshort,gavemeaningtotheevents.

Experience,then,doesnotexerteffectsonaninfant,butinstead,exertseffectswithaninfant.The

childmodifiesrawexperienceasmuchasitchangeshim.

Second,Piaget is sometimesmisunderstood concerninghis viewsof the rolesofmaturationand

learning.ItshouldbeabundantlyclearthatPiagetisnotasimplematurationist.Hedoesnotbelievethat

theinfant’sdevelopmentunfoldssolelyasaresultofsomekindofphysicalmaturation.Piaget’sposition


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isthatmaturationplaysaroleindevelopment,butitcertainlyisnottheonlyfactor.Aswehaveseen,he

believesthattheeffectsoftheenvironmentarequiteimportant,andtothisextentPiagetisinagreement

withtheenvironmentalists.But,ashasbeennoted,Piaget’saccountoflearningisquitesubtleandisin

manywaysatvariancewithothertheoriesof learning.Forexample,he introducesnovelmotivational

principles, such as assimilation and the moderate novelty principle, and emphasizes the infant’s

interpretationoftherawdataofsensoryexperience. Inshort,Piaget isneitheramaturationistnoran

environmentalist,atleastnotinthedominantbehavioristtradition.Hispositionincorporateselementsof

bothtraditions,and,inaddition,elaboratesontheminhighlyoriginalways.Hethinksofhimselfasan

“interactionist,”forhistheorystressesthatintellectualdevelopmentresultsfromaninterplaybetween

internalandexternalfactors.

AsweshallseeinChapter6,Piagethaselaboratedandsupplementedhisaccountofexperience

andmaturationsincehiswritingofthebooksoninfancy.Thelatertheoryof“equilibration”expandson

theroleofexperienceand,inaddition,introducestheconceptofinternedcognitiveconflict.

Third, thenatureofPiaget’sstages isoccasionallymisunderstood.Piaget issometimescompared

withGesell,whoofferedanaccountof infancy in termsofstagesofdevelopment.Gesell’sstageswere

merelylistingsofspecificbehaviorswhichoccurredatdifferentages.Forexample,theinfantisfoundto

crawlatsuchandsuchanage,towalkatanother,torunatanother,andsoon.Whilesuchinformation

may be valuable, it is clear that Gesell’s stages merely list the empirical phenomena and have no

theoreticalcontentwhatsoever.Bycontrast,Piaget’sstagesareatheoreticaltaxonomy.Take,forexample,

stage4,whichisconcernedwiththecoordinationofsecondaryschemes.Piaget’stheoryproposesthatin

this stage the infant can coordinate two previously disparate patterns of behavior to attain a

preconceived goal. This statement—the theory of this stage—is an abstraction which transcends the

detailsofanyspecificbehaviorsthatmerelyillustratethestage.Thestatementisintendedtoallowusto

understandwhat the infant does regardless of the particular behaviors involved. Piaget’s stages are

thereforetheoreticalorexplanatory,andassuchareradicallydifferentfromGesell’s.

Notes

1Forexample,seeInaC.Uzgiris,“OrganizationofSensorimotorIntelligence,”inM.Lewis,ed.,OriginsofIntelligence (NewYork:PlenumPress,1976).


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2Indeed,thereadershouldrecognizethatunorthodoxprocedureshaveledtomanyofthegreatdiscoveriesinpsychology,includingFreud’sfreeassociationtechnique,Wertheimer’sdemonstrationexperiments,Chomsky’sintrospectiveanalysesoflanguage,Brown’snaturalistic observations of the language of three children, Skinner’s studies of inpidual pigeons, and the Gardner’sexaminationofWashoe’ssignlanguage.

3Forexample,seeT.Appleton,R.Clifton,andS.Goldberg,“TheDevelopmentofBehavioralCompetenceinInfancy,”inF.D.Horowitz,ed.,ReviewofChildDevelopmentResearch,Vol.IV(Chicago:UniversityofChicagoPress,1975).

4Inthisandsubsequentchapters,whenabookisfrequentlycited,wegivefirstanabbreviatedtitle(e.g.,OriginsofIntelligence)followedbybriefinitials(e.g.,OI).Inlaterreferencesonlytheinitialsareused.

5Piaget’s“recognitoryassimilation”combinesseveralprocessesusuallytreatedunderdifferentrubricsbythetheoryofperceptuallearning.Theinfantdiscriminates(aswhenheseesthatoneareaofthebreastlooksdifferentfromanother);herecognizes(aswhenheknowsthathehasmadecontactwiththebreastbefore);andheidentifies(aswhenhelearnsthatthenipplegivesmilk).Forafullerdiscussionofperceptuallearning,seeE.J.Gibson,PrinciplesofPerceptualLearningandDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1969).


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The Years 2 through 11:The Semiotic Function and Piaget’s Early Work

The present chapter covers two broad topics. The first to be considered is the development of

cognitiveprocessesinthechildofapproximately2to4years.Atthistimesomeveryimportantadvances

occurinthechild’sthought.Onesuchadvanceistheonsetofthesemioticfunction.Wewillconcentrate

on the young child’s useofmental symbols andwords, andon symbolic play.The second topic tobe

consideredisthedevelopmentofcertaincharacteristicsofthoughtinthechildfrom4to11years.We

shallreviewPiaget’searlyworkonthistopicandcoversuchmattersasegocentrism,communication,and

moraljudgment.

THE SEMIOTIC FUNCTION

Thesensorimotorperiodinvolvesarapidandremarkabledevelopmentofbehavioralschemes.The

newbornenteredtheworldwithonlya limitedrepertoryofautomaticbehaviorpatternsprovidedby

heredity. Yet after a period of only about two years, the infant can interact quite effectivelywith the

immediateworldofthingsandofpeople.Hepossessesschemesenablinghimtomanipulateobjectsand

usethemasmeansfortheattainmentofhisgoals.Theinfantalsoexperimentswiththingstoachievea

practicalunderstandingoftheirproperties.Butalloftheseabilities,ad-thoughuseful,arenevertheless

concrete,thatis,limitedtoimmediatelypresentobjects.Forexample,whiletheinfantmaybeabletouse

asticktobringanobjectwithinreach,hecannotconceiveofrelationshipsbetweenobjectsthatarenot

withinhisimmediatescopeofvision.Theinfantisabletoactonlyonthingswhichareperceiveddirectly.

Towardtheendofthesecondyear,thechildbeginstodevelopnovelcognitive,ormental,processes.

One important aspect of cognitive development is the appearance of the semiotic Junction. This

refers to the fact that from2 to 4 years the child begins to develop the ability tomake something—a

mental symbol, aword, or anobject—stand foror represent somethingelsewhich isnotpresent. For

example,thechildcanuseamental“picture”ofabicycle,ortheword“bicycle,”orasmallschematictoyto

standfortherealbicyclewhenitisnotinimmediateview.Theabilitytorepresentinthiswaymakesit


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possibleforthechildtooperateonnewlevels.Atthisstagethechildisnotrestrictedtoactingonthings

in the immediate environment because the semiotic function allows the evocation of the past. For

example,hismentalsymbolofthebicyclepermitstherecollectionofpreviousexperiencewiththistoy.

Thesemioticfunctionmanifestsitselfinseveralways.Duringtheperiodfrom2to4yearsthechild

begins toemploymentalsymbols, toengage insymbolicplay,andtousewords.Letusrevieweachof

theseactivitiesinturn.

Mental Symbols

Oneexampleoftheuseofmentalsymbolsinvolvesdeferredimitation.Letusrecalltheexampleof

thetempertantrum:

At1;4(3)[Jacqueline]hadavisitfromalittleboyof1;6,whomsheusedtoseefromtimetotime,andwho,inthecourseof theafternoon, got intoa terrible temper.He screamedashe tried togetoutof aplaypenandpushed it backward, stamping his feet. J. stoodwatching him in amazement, never havingwitnessed such ascenebefore.Thenextday,sheherselfscreamedinherplaypenandtriedtomoveit,stampingherfootlightlyseveraltimesinsuccession.(Play,Dreams,andImitation,PDI,p.63)

The important featureof theobservation is that Jacqueline’s imitationwasdeferred: it occurred

sometimeaftershehadoriginallyseentheboythrowingthetantrum.Herbehaviorthereforedidnot

simply copy an immediately observable model. If she could not see the tantrum, on what was her

behaviorbased?Howcanweexplaindelayedimitation?OneinterpretationisthatwhenPiagetobserved

her,Jacquelinehappenedtothrowatantrumforthefirsttime,quiteindependentlyofanythingtheboy

haddone.Buttheexplanationisquiteimplausible,becauseherbehaviorwassomuchlikethatofthe

boy. Consequently, we are forced to postulate a more complicated explanation that involves mental

symbolism.Thereasoningisasfollows.WeknowthatinthrowingthetantrumJacquelinedidnotsimply

copy an immediately present model. Nevertheless, her behavior was clearly similar to the boy’s.

Consequently,weassumethat Jacquelinemusthave formedamentalsymbolof thetantrumandthen

basedherbehavioronthissymbol.Inotherwords,Jacquelinemusthavehadavailableamentalevent

whichstoodfororrepresentedtheboy’srealaction.Theabilitytosymbolizeinthiswayallowedherto

copytheboy’sbehavioratalatertime.

What is the nature of mental symbols? It is difficult to answer this question since we have no


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methodwhichpermitsadirect“look”atthechild’sthought.Onepossibility,however,isthatthechild’s

mental symbols are, at least in part, comprised of visual images. Perhaps Jacqueline “pictured” the

tantrum toherself.While visual imagerydoes indeedoccur (andmayormaynothavebeenusedby

Jacqueline),Piagetremindsusthatmentalsymbolsmaytakeotherformsaswell.Althoughsometimesa

personmayusevisualimagery,hemayatothertimesrepresentobjectsbytheirsounds,orevenbyan

abbreviatedformoftheirmovements.Piagetalsoproposesthattheinpidualmaynotevenbeconsciousof

thesementalsymbols.Achildmaydisplay imitativebehaviorwithoutrealizing that it isbasedon the

actions of anotherperson. Surely, after Freud’swork, it should come as no surprise thatmanyof our

thoughtprocessesareunconscious.

We have seen, then, that themental symbolmay ormay not be conscious andmay ormay not

involve visual imagery.Does themental symbol involve language?Was Jacqueline able to imitate the

tantrumbecauseshecarriedinherheadthewords,“Heis liftinghisarms,heisshouting,”andsoon?

Althoughthissortofinterpretation—averbalmediationapproach—hasitsadherents,Piagetrejectsit.

Hecitestwomajorreasons.First,certainexperimentswithanimalsshowthatchimpanzees,forinstance,

havementalsymbolswhichofcoursecouldnotbebasedonlanguage.Ifnonverbalsymbolismispossible

inanimals, thenwhynot inthehumantoo?Second,observationof thechildshowsthatbehavior like

deferredimitationoccurswhilelanguageskillsarestillveryprimitive.ItisquiteunlikelythatJacqueline

was at that time capable of a reasonably full verbal description of the boy’s temper tantrum. Yet, her

imitationwasquiteaccurate.Sinceamentalsymbolbasedonthechild’scrudelanguagecouldnothave

provided a basis for such accurate imitation, the linguistic explanation must be ruled out. Thus, to

explain Jacqueline’s deferred imitation,wemust postulate her use ofmental symbols. These symbols

probablydonotinvolvelanguagetoasignificantdegree,butwecannotconfidentlyspecifytheirexact

nature.

Asecondexampleofmentalsymbolismcanbeseeninthechild’sreactiontohiddenobjects.Ifyou

will recall, in stage 6 of the sensorimotor period, the child could reconstruct a series of invisible

displacementsofanobject. Inanobservationdescribed inChapter2,Piagethida smallpencil inhis

handandthenplacedthehandconsecutivelyunderaberet,underahandkerchief,andfinallyundera

jacketwhereheleftthepencil.Jacquelinedidnotlookforthepencilinherfather’shand,whichwasthe

last place shehad seen it, andwhich iswhere the younger child searches; instead, she immediately


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reachedunderthejacketandfoundthepencil.

Howcanweexplain Jacqueline’sbehavior? Itwasnotrandom,sincesheacted inessentially the

samewayonmanyoccasions.PiagetassumesthatJacquelineformedamentalsymbolofthepencil.When

Piagetcoveredthepencilinhishand,Jacquelinebelievedinitscontinuedexistence.Whenthehandwas

placedunderasuccessionofobjects, theuseof thementalsymbolenabledher to followmentally the

invisibledisplacements.Theavailabilityofamentalsymbolisthusnecessaryforamatureobjectconcept.

Thus far, we have seen two kinds of behavior—deferred imitation and search—whichmay be

interpretedasdemonstratingtheexistenceofmentalsymbolisminthechild.Wemaynowexplorethe

developmentofmentalsymbols.

The Formation of Mental Symbols

Howdoes thechild formmentalsymbols?Thereseemtobeat least twopossibleanswers to this

difficult question. One explanation is that the ability to symbolize is an entirely new functionwhich

suddenly makes its appearance when the child is about 2 years of age. Another possibility is that

symbolism has precursors in the sensorimotor period. Emphasizing continuity in intellectual

development,Piagetadoptsthesecondalternative.Hepostulatesthatthesemiotic function isderived

fromimitation.Considerthefollowingobservationfromthesensorimotorperiod:

At1;3(8)J.[Jacqueline]wasplayingwithaclownwithlongfeetandhappenedtocatchthefeetinthelowneckofherdress.Shehaddifficultyingettingthemout,butassoonasshehaddoneso,shetriedtoputthembackinthesameposition....Asshedidnotsucceed,sheputherhandinfrontofher,bentherforefingeratarightangleto reproduce the shape of the clown’s feet, described exactly the same trajectory as the clown and thussucceeded inputtingher finger into theneckofherdress.She lookedat themotionless finger foramoment,thenpulledatherdress,withoutofcoursebeingabletoseewhatshewasdoing.Then,satisfied,sheremovedherfingerandwentontosomethingelse.(PDI,p.65)

Herewehaveacaseofimitationputtotheserviceofunderstandinganunusualphenomenon.In

thecourseofplayingwithafamiliartoy,Jacquelinediscoveredthattheclowndidsomethingunexpected

andinitiallyunexplainable.Itsfeetcaughtherdressinawaythathadnotoccurredbefore.Jacqueline

immediatelytriedtounderstandthecauseoftheunexpectedevent.Hermethodofdoingsowasthrough

imitativeaction:sheformedherfingerintotheshapeoftheclown’sfoot,placedthefingerinherdress,

and thenpulled to seewhatwouldhappen. Shediscovered that the fingergot caught and therefore


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preventedfreemovementofherarm.Inthiswayshecametounderstandthattheshapeoftheclown’s

footsimilarlyrestricteditsremoval.Anotherwayoflookingattheobservationistosaythatitinvolvesa

specialkindofimitation:Jacquelineusedherownbodytorepresentorstandfortheclown’smovements.

Heractionssymbolizedthoseoftheclown.Thisisnotanisolatedobservation;Piagetfindsthatthechild

oftenimitatesthings.Forexample,henotedthatLucienne,uponobservingthatherfather’sbicyclecould

bemadetomovebackandforth,performedthesamemotionsherself.Sheswayedtoandfroataboutthe

speedofthebicycle.

Piagetarguesthatsuchimitationofthingsisthesensorimotorforerunnerofmentalsymbolism.The

infant’s swayingbackand forth is thebehavioral equivalentof theolder child’smental symbolof the

bicycle.Inotherwords,fortheinfanttheactionofswayingsignifiesabicycle,whereasfortheolderchild

amental symbol performs the same function. Toward the end of the sensorimotor period, the child’s

imitation “goes underground,” figuratively speaking. Instead of imitating things on the level of overt

behavior,theolderchilddoessointernally.Forinstance,inplaceofactuallyswayingbackandforth,the

olderchildmightimitatethebicyclebymakingveryslightandalmostimperceptiblemovementsofhis

muscles.Or,insteadofformingthefingerintheshapeoftheclown’sfoot,theolderchildmighttensehis

fingermusclessoslightlythatanobserverwouldnotnotice.Moreover,thisinternalimitationisnomere

oddity.Thechild’sinternalandalmostundetectablemovementsconstitutethementalsymbol.Thechild’s

musclesperformanabbreviatedimitationofswaying,andthesebodilysensationssymbolizeforhimthe

bicycle.Whenthechild’sfingertenseseversoslightly,thisinternalimitation,whichisnotnecessarilya

visualimage,signifiestheclown.

Wehaveseen,then, thatthesensorimotorchildrepresentsthingsbyacting likethem.Theolder

child, on the other hand, performs such imitation internally, and these abbreviated bodymovements

constitutethementalsymbol.Eventuallythechildbecomessoproficientat internedimitationthatthe

movementsareextremelyabbreviatedand,therefore,almostimpossibletodetect.

Several interesting points can be made concerning the formation of the mental symbol. First,

Piaget’stheorygivesusadditionalinsightintothenatureofthechild’smentalsymbols.Wesaidearlier

thattheymightinvolveavisualcomponentandthattheyprobablydonotconsistoflinguisticfeatures.

Nowweknowthatmentalsymbolsinitiallyinvolvethechild’sactionsinanimportantway.Themental


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symbol of the bicycle consists not only of a visual image, but it also may involve bodily sensations

correspondingtothebicycle’smovements.

Second,inreferringtothesymbolasconsistingofinternalimitation,Piagetusesthetermimitation

inaverybroadsensetoaccountforvisualimagery.Considerthishypotheticalexample.Whenaperson

seesatable,hisperceptionaccommodatestoit.Hiseyesmustfollowthetable’soutline,detectitscolor,

focus to localize the table in space, and so on. In these ways, the person establishes a number of

relationshipsconcerningthetable(space,color,etc.)whichtogetherformhisperceptionofit. Inother

words, the environment does not simply impose on him the perception of the table. Instead, the

perceptionisderivedfromhisownactivity—fromaseriesofintricatemovementsofhiseyesandfrom

complex activity in the brain and nervous system. Visual perception is an activity, just as the child’s

swaying is an activity. Nextwe see the role of imitation. At a later timewhen the table is no longer

present,thepersonmayrepeatinanabbreviatedformthemovementsinvolvedinhisinitialperception

ofthetable.Thatis,hiseyesmayagainmoveastheydidwhentheytracedthetable’scontour,adjustedto

itsdistance,andsoon.Thisinternalandabbreviatedimitationoftheperceptualactivityconstitutesthe

visual image of the table. Since an image of an object is seldom as rich or as detailed as the original

perception,theimagemerelyrepresentsorsymbolizestheactualobject.Inbrief,thementalsymbolmay

involve visual imagery, and the latter may be considered the internal imitation of the originally

perceivedobject.

Third, Piaget introduces a technical vocabulary for dealing with representations. As Figure 1

shows, the semiotic or representational function involves signifiers—mental events, words, or things

whichstandforsomethingelse—andthesignified,tobedescribedshortly.Signifierssignifyorrepresent

somethingtotheinpidual.Onetypeofsignifieristhesymbol,whichmaybepersonalandidiosyncratic,

andresemblesthethingitstandsfor.Foronechild,atoymaysymbolizethebicycle;foranotherchild,the

visualimage(resemblingthebicycle’sappearance)maysuffice.Consequently,oneperson’ssymbolmay

not transmit to another person any information at all about the action or object that is represented.

Abbreviated movements, as in swaying like a bicycle, seem to be the developmental forerunners of

symbolism.Symbolsmaybemental or concrete. Concrete symbols,whichwe shall review shortly,may

involveusingoneobject(e.g.,ahandkerchief)tostandforanother(e.g.,ablanket).Mentalsymbolstake

several forms.Wehave already seen thatone typeof symbol is thevisualimage; other types include


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auditoryimages.Thesymbolinvolvesapredominanceofaccommodation.Thisissobecausethesymbol

consistsofinternalimitation,andimitationinvolvesmodifyingone’sbehaviortofitthatofamodel,orin

broader terms, tomeet the demands imposed by the social or physical environment. Another type of

signifieristhesign,whichtypicallyreferstoawordusedinconventionallanguage.(Thesigncouldalso

refer to other conventions like mathematical notation, football diagrams, etc.) A word is social, not

personal,andisarbitrarilyrelatedtothethingitstandsfor.“Bicycle,”forexample,isnotanidiosyncratic

term:mostofusagreethat“bicycle’’standsforthesameobject,andthereforeuseofthetermtransmits

considerableinformation.Also,theword“bicycle”bearsnoresemblancetotherealthing;ifourlinguistic

communitysodecreed,wecouldlegitimatelysubstitute“elephant”for“bicycle.”Insummary,signifiers

involvevarioustypesofsymbolsandsigns.

FIGURE1Schematicoutlineofthesemioticfunction.

ThecomplexityofPiaget’sterminologyshouldnotobscurethefactthattheabilitytoformmental

representations is an achievement of great magnitude. In the sensorimotor period this capacity was

lacking.Ifyouwillrecall,theonlysignifierswereconcreteattributesofthings.Forexample,themother’s

voiceorfootstepssignifiedtotheinfantthatshewouldsoonarrive.However,thisprimitivesignifier,or

“index,” was linked to the infant’s actually hearing the voice or footsteps. He had no mental

representationfortheseevents;therefore,thesignifierhadmeaningfortheinfantonlywhentheevents

actuallyoccurred.Bycontrast,theolderchildcanusementalrepresentationstostandforabsentevents

orthings.Thingsnolongerneedtobepresentforthechildtoactonthem.Inthissense,theabilityto


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representeventuallyliberatesthechildfromtheimmediatepresent.Hecanimaginethingsthatareboth

spatially and temporally separate from himself. It may therefore be said that the use of mental

representationspermitsthechildtotranscendtheconstraintsofspaceandtime.

Meaning

HavingreviewedPiaget’stheoryoftheformationofmentalsymbols,weshallnowdealwiththe

processbywhichtheyacquiremeaning.Letusconsideranapparentlysimplequestion:Towhatdoesthe

child’smentalsymbol,likeswayingbackandforth,refer?Wemayposethesamequestionwithregardto

theword:Whatdoes“bicycle”designate?Ourfirstresponsetothisquestionistosaythatboththemental

symbol and the word obviously refer to the real bicycle. But according to Piaget, thematter is more

complicatedthanthat.The“signified”(whatthesymbolorwordstandsfor,oritsmeaning)isnotthereal

object, but rather the child’s understanding or intellectual construction of the real object. To put it

differently, symbols orwords do not refer to things, but instead stand for one’s knowledge of things.

Supposeonechildusestheword“bicycle.”Forhim,abicyclehastwowheels,aseat,andhandlebars.A

bicycle is something that goes delightfully fast, and, also, it is one kind of vehicle. For another child,

however,thesignifiedmaybesomewhatdifferent.Thischildagreesthatabicyclehastwowheels,aseat,

andhandlebars,buthavingoftenfallenfrombicycles,hethereforefeelsthattheyarefrighteningand

dangerous.Further,hehasnoconceptionofthebicycleasavehicle.Notethatforboththesechildrenthe

word “bicycle” evokes some commonmeaning: twowheels, handlebars, and soon.Both children can

thereforeeasily identifywhatabicycle isandwhat it isnot. Inthis“denotative”sense,theworddoes

refer to the real object. But the children also disagree as to theword’smeaning; for one, a bicycle is

delightfulandfortheotheritisfrightening.Also,foronechilditisamemberoftheclassofbicycleswhich

inturnisincludedinthelargerclassofvehicles.Theotherchild,ontheotherhand,employsnosuch

classhierarchy. InPiaget’s terms, each childhas assimilated theword “bicycle” into adifferent set of

schemes(thesignifiedorthemeaning).Therefore,theword“bicycle,”orthechildren’spersonalmental

symbolsforit,doesnotrefertotherealthingbuttotheirunderstandingofit.

Tosummarize,internalimitation(accommodation)providesthechildwithsymbols.Thechildthen

endows these symbols and words too with meaning, assimilating them into his mental schemes.

Therefore, what the symbol or word refers to (the signified) is always personal, if not idiosyncratic,


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although in thecaseofwords there isa sufficientamountof commonsignification for communication

amonginpidualstooccur.

Symbolic Play

Afurtherexampleofanactivityimplyinguseofthesymbolicfunctionissymbolicplay.Hereisan

observation.

[At1;3(12)Jacqueline]...sawaclothwhosefringededgesvaguelyrecalledthoseofherpillow;sheseizedit,heldafoldofitinherrighthand,suckedthethumbofthesamehandandlaydownonherside,laughinghard.Shekepthereyesopen,butblinkedfromtimetotimeasifshewerealludingtoclosedeyes.(PDI,p.96)

Theobservation involves several interesting features. First, Jacqueline acted toward the cloth in

roughlythesamewayasshebehavedtowardapillow.Sheputherheadonit,suckedherthumb,andso

on.Second, Jacqueline’sbehaviorrevealedacertainplayfulness; that is,she laughedatwhatshewas

doing.Apparently,shethoughtheractionswerequitefunny.

One simple interpretation of this behavior is that the childmerely confused the clothwith the

pillow.Butthisexplanationisnotveryplausiblebecauseitfailstoexplainwhythechildlaughed.After

all,Jacquelinedidnotordinarilygiggleupongoingtobed.

Piagetinterpretsthebehaviorasacaseoftheplayfuluseofconcrete(notmental)symbols.Itisclear

fromJacqueline’slaughterandfromherattitudeofpretensethatsheknewperfectlywellthatthecloth

wasnotreallyapillow.Herplayfulness indicates thatsherealized that theclothwasasubstitute for

anotherthing.Inotherwords,theclothwasasymbolorsignifier,andwhatitsignifiedwasthepillow.

Thecloth,ofcourse,wasaconcreteobjectandnotamentalsymbol.

How did this assignment of meaning to the cloth come about? Piaget’s interpretation is that

meaningisachievedintermsofassimilation.WhileinthepastJacquelinehadperformedtheactionsof

lying down, closing the eyes, and so on only in connection with the pillow, she now extends these

schemestoanobjectwhichsheknowsisnotapillow.WecanthereforesaythatJacquelineassimilated

theclothintoschemespreviouslyappliedonlytothepillow.Itistheprocessofassimilationtoschemes

(thesignified),then,whichprovidesthemeaningforthesymbol.Moreover,Jacquelineisawareofthe


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make-believecharacterofheracts.Herplayfulnessshouldnotmakeusunderestimatetheseriousness

and importanceofheraccomplishment: shehasachievedaprimitivecomprehensionof thenatureof

symbols.Indeed,weoftenfindthatthechild’s“play”involvessignificantintellectualactivity.

ItisinterestingtonotethatPiagetfeelsthatsymbolicgamesplayanimportantroleinthechild’s

emotional lifeaswell.Thechildfrom2to4yearsis inaveryvulnerablestageofdevelopmentinthe

sensethatheisbeginningtoacquireanewsetofwaysofdealingwiththeworldaroundhim.Thechild

alsofindsthathemustconformtoasetofsocialrules,nottheleastofwhichislanguage.Thechildmust

accept the fact that words stand for things without any apparent justification. His capacity for self-

expressionvialanguageisextremelylimitedandrudimentaryandthewordsavailablefrequentlyare

inadequate to expressneeds and feelings. The childmust obey commandswhosepurposehe cannot

understand.Thechild’snaturalspontaneityisbeingcompressedintothesocialmoldofhisculture,and

heisgenerallypowerlesstoresist.

These feelingsof inadequacy lead to frustration for the child and, subsequently, to conflictwith

surroundingpersons.Symbolicplay,whichformsa largepartof thechild’sactivity inthisstage, isan

appropriatemeans of providing an adjustment to reality.With this form of interaction the child can

assimilate the external world almost directly into his own desires and needs with scarcely any

accommodation.Hecanthereforeshaperealitytohisownrequirements.Furthermore,insymbolicplay,

the child can act out the conflictual situations of real life in such a way as to ensure a successful

conclusioninwhichhecomesoutthewinner,andnot,asissometimesthecaseinreallife,theloser.In

brief,symbolicplayservesanecessarycatharticpurposeandisessentialforthechild’semotionalstability

andadjustmenttoreality.Indeed,symbolicplayoftenservesasthebasisforpsychotherapywithyoung

children.

Language

Wehavenowseentwodifferentmanifestationsofthesemioticfunction:theuseofmentalsymbols

andsymbolicplay.Wewillturnnowtoathirdaspectofthesemioticfunctionandseehowthechilduses

languageandgivesitmeaning.


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Inthesixthstageofsensorimotordevelopment,thechild’sfirstuseofwordsisnotrepresentational

inthesenseofreferringtoabsentobjects.Insteaditisintimatelyrelatedtohisongoingactions.Consider

thisexampleconcerningLaurent:

at 1;5(19) “nomore” meant going away, then throwing something on the ground, and was then used forsomethingthatwasoverturned(withoutdisappearing).Hethussaid“nomore” tohisblocks.Later “nomore”merelymeantthatsomethingwasatadistancefromhim(outsidehisfieldofprehension),andthenitreferredto the game of holding out an object for someone to throwback to him. At 1;6(23) he even said “nomore”whenhewantedsomething someonewasholding.Finally, at1;7 “nomore” became synonymouswith “beginagain.”(PDI,p.218)

Note thatLaurentdidnotuse “nomore” in a representationalway.Hedidnotmake thewords

standforanabsentthingoreventasinthesentence,“Thereisnomorewaterinthegarden.”Instead,

Laurent’suseof“nomore”wasconcreteintwosenses.First,heemployedthewordsinconnectionwith

objects that were immediately present like the overturned blocks. Second, the words were used to

expresshisimmediatedesires,aswhenhewantedsomethingapersonwasholding.Inadditiontobeing

tied toconcrete thingsoractions, thechild’s firstwordsareveryunstable.Thephrase “nomore”was

usedtorefertogoingaway,tosomethingoverturned,tosomethingatadistance,andsoon.Themeaning

of words is not constant for a young child. In fact, for him, words have little socially agreed upon

meaning; instead, they are quite personal, and in this respect they resemble idiosyncratic mental

symbols.

Thenextstepinthedevelopmentoflanguageinvolvestheuseofwordsinarepresentationalway.

Atabout2yearsofage,thechildgraduallybeginstousewordstostandforabsentthingsorevents.For

example,at1;11(11)afterreturningfromatrip,Jacquelinetoldherfatheraboutit.Shesaid,“Robertcry,

duck swim in lake, gone away” (PDI, p. 222). These events had occurred some time previously, and

Jacqueline was able to remember them. Moreover, she was capable of using words to stand for past

events. Thus, through a gradual evolution, words are no longer used by the child to refer solely to

ongoingactions,desires,orimmediatelypresentevents.

Nowthatwordshavegenerallyassumedarepresentationalcharacterandrefertoabsentthings,

we may ask whether the child uses them in the same way as the adult. For example, we saw that

Jacquelineusedthewords“duckswimin lake” torefer toevents in thepast.Despite the fact that the

wordsarerepresentational,doesthechildgivethemthesamemeaningthatanadultdoes?Anotherway


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ofputtingthequestionistoaskwhetherthechild’sconceptofduck,orthemeaningassignedtotheword

“duck,”isthesameastheadult’s.Themerefactthatthechildusestheworddoesnotnecessarilyimply

thathegivesitwhatweconsideritsordinarymeaning.Herearesomeobservationswhichmayclarifythe

issue:

at 2;7(12), seeing L. [Lucienne] in a new bathing suit, with a cap, J. [Jacqueline] asked: “What’s the baby’sname?”Hermotherexplainedthatitwasabathingcostume,butJ.pointedtoL.herselfandsaid:“Butwhat’sthenameofthat?”(indicatingL’sface)andrepeatedthequestionseveraltimes.ButassoonasL.hadherdressonagain,J.exclaimedveryseriously:“It’sLucienneagain,”asifhersisterhadchangedheridentityinchangingherclothes.(PDI,p.224)

TheobservationshowsthatJacqueline’sconceptofhersister,andtheuseoftheword“Lucienne,”

arequitedifferentfromtheadult’s.Jacqueline’sthinkingattributeslittleinpidualitytohersister.Thereis

not one Lucienne who is the same person regardless of superficial changes; instead, as a result of

wearingdifferentclothing,therealLucienneisseenastwodifferentlittlegirls.Thechildatthisagefails

torecognizethatapersonOrthingremainsthesame,orconservesitsidentity,whenitundergoesminor

variationsinappearance.

Inadditiontoperceivinginsufficientinpiduality,thechildalsoshowsotherunusualusesofwords.

OnceJacquelinewasinthegardenandwalkedonthelandlord’sflowers.Sheremarked“MespoilUncle

Alfred’sgarden”(PDI,p.224).Shehadhadearliercontactwithheruncle’sgarden,andinthepresent

caseused thephrase “UncleAlfred’s garden” to refer to the landlord’s. Inotherwords, sheusedone

phrasetorefertotwodifferentthings.Allgardensare“UncleAlfred’sgarden.”Inthecaseofhersister,

Jacquelinesawthesameinpidualunderdifferentguisesasdifferentinpiduals;inthepresentinstance

shesawdifferent“inpiduals”(gardens)asthesame“inpidual.”Clearly,inneithercasedidJacqueline’s

useofwordscorrespondtoanadult’s.Theconceptsormeaningsevokedby“Lucienne”or“UncleAlfred’s

garden”werequiteprimitive.Inasense,thechild’searlywordsresemblesymbols—theyarepersonal

andidiosyncratic.

Reasoning

Duringtheyears2to4,thechildshowsthreedifferentkindsofreasoning.Inonetype,thechildis

facedwithasimplesituationwhichhasbeenexperiencedbefore.Thechild then“reasons”about the


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situationveryconcretelyintermsofwhathadoccurredinthepast.Forexample,at2;4(16)Jacqueline

calledherfatherwhodidnotanswer.Sheconcludedfromthis:‘‘Daddydidn’thear.”Ataboutthesame

timeJacquelinesawherfathergettinghotwaterandreasoned:“Daddy’sgettinghotwater,sohe’sgoingto

shave”{PDI,p.231). Inbothcases, Jacquelinehadhadpreviousexperiencewithherfather insimilar

situations.Her“reasoning”aboutthemwas limitedmerelytosimplememoryofwhathadoccurredin

thesesituationsinthepast.Piagetfeelsthatthistypeofreasoningissimplyanapplicationofprevious

experiencetoacurrentsituationandisnottobeconfusedwiththegenuinelydeductivereasoningofthe

matureperson.

In a second kind of reasoning, the child’s desires distort thinking. For example, at 2; 10(8)

Jacquelinewantedtoeatoranges.Herparentsexplainedthatthiswasimpossiblebecausetheoranges

were still green and not yet ripe. Jacqueline “seemed to accept this, but amoment later, as shewas

drinking her chamomile tea, she said: ‘Chamomile isn’t green, it’s yellow already . . . Give me some

oranges!”’(PDI,p.231).ApparentlyJacqueline,havingastrongdesirefororanges,reasonedthatifthe

teawereyellowthentheorangesmustbeyellowtoo,andthereforeshecouldhavethemtoeat.Atthis

stage,thechildattemptstoreasontoachievesomegoal,butthoughtdistortsrealityinaccordancewith

desire.ThisissimilartoFreud’snotionofwishfulfillment.(Aswillbeevidentshortly,theteaobservation

isalsoanexampleoftransduction.)

A third type of reasoning iswhat Piaget calls “transductive.” In logic a distinction is sometimes

madebetweendeductionand induction.Deduction isusuallycharacterizedasaprocessofreasoning

fromthegeneraltotheparticular.Forinstance,ifweassumethatallmenhaveheartsofgold,andifwe

arethenshownaparticularman,wededucethathehasaheartofgold.Inductionisusuallyconsidered

a method for reasoning from the particular to the general to establish general principles from

examinationofparticularcases.Forinstance, ifwehavemeta largenumberofmenallofwhomhave

heartsofgold,wemightconcludethatallmenhaveheartsofgold.AccordingtoPiaget,theyoungchild’s

reasoning lies in between induction and deduction. The child does not go from the general to the

particular(deduction),orfromtheparticulartothegeneral(induction),butratherfromtheparticularto

theparticularwithouttouchingonthegeneral.Transductivereasoningseesarelationshipbetweentwo

ormoreconcrete(particular)itemswhenthereisnone.Forexample,onanafternoonwhenLucienne

did not take a nap, she said: “I haven’t had my nap so it isn’t afternoon” (PDI, p. 232). In this case,


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Lucienne’sthoughtproceededfromthenap(oneparticular)totheafternoon(thesecondparticular)and

concludedthattheafternoondependedonthenap,whenofcoursetherelationshipwasofadifferent

type.

Summary and Conclusions

Intheperiodfrom2to4yearsthechildachievesthecapacitytoformmentalrepresentationswhich

stand for absent things or events. To deal with things, the child no longer requires that they be

immediatelypresent;instead,thechildisabletocreateamentalsubstitutefortherealthing.Thisability

freesthechildfromtheimmediatehereandnow.Insteadofhavingtomanipulatethings,heworkswith

theirsubstitutes.Thechildformsmentalsymbolsthroughimitation.Thechildlooksatthings,handles

them,andactslikethem,andinthesewaysincorporatesagreatdealofinformationaboutthem.These

actions of the child lay the foundation formental symbolism. In fact, imitationmay be considered to

bridgethegapbetweensensorimotorandlaterintelligence.Duringthesensorimotorperiodtheinfant

developsabilitiesinimitativebehavior.Whenthechildisproficientatimitationatalaterage,hebegins

toimitateinternally,andtherebyformsthementalsymbol.InPiaget’sterminologymentalsymbolsare

signifiers.Thesymbol ispersonalandresembleswhat itrefersto.Forexample,Lucienneswayedback

andforthtorepresentabicycle.Oncementalsymbolsareformed,thechildgivesthemmeaningthrough

theprocessofassimilation.Heassimilatesthemintotheschemeswhicharealreadyavailable.Therefore,

what the symbol refers to (the signified) is always personal and intimately related to the child’s

experience.Agoodexampleoftherelationbetweenthesymbolanditsmeaningisthechild’splayfuluse

ofsymbols.Inamake-believefashion,thechildmakessomethings(symbols)standforothers.Thechild

playfullyassimilatessomeobjects intoschemesappropriate forothers.Another typeofsignifier is the

signorwordwhichisalsousedtorefertosomethingelse.Theword,however,usuallydoesnotresemble

itsreferent,buthasaconventionallyagreed-uponmeaningtofacilitatecommunication.

Duringthisperiodthechilduseswordsinseveralways.Afterapreliminarystageinwhichwords

arecloselyrelatedtoongoingactionsanddesires,thechilduseslanguagetorefertoabsentthingsand

events. The child, however, does not use words in the same way that an adult does; the meaning

assignedtowords,ortheconceptassociatedwiththem,isstillquiteprimitive.Thechild’sconceptsarein

factonlypre-concepts:theyaresometimestoogeneralandsometimestoospecific.Thechildalsoshows


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signsofan initialreasoning.Sometimes it issuccessful,butonlywhen itdoesnotgo farbeyondmere

memoryforpastevents.Atothertimesthereasoningmaybefaulty.Thisiseitherduetothetendencyfor

wishes to distort thought or to the transductive nature of the child’s thought: he reasons from the

particulartotheparticular.

These, then, are the beginnings of symbolic activity in the young child. His initial efforts are

imperfect,andfromtheadultpointofviewinvolvemany“errors.”Alongevolutionisnecessarybefore

thechildcanachievematurityinthought;logicalthinkingdoesnotemergefullyformedinthechildof2

years.

Piagetarguesthatlanguageplaysalimitedbutnotnegligibleroleintheformationofthechild’s

thought.Clearly, languagedoesnotfullyshapethechild’smentalactivities.Despitehisnewabilityat

language,thechildoftenthinksnonverbally.Heformsmentalsymbolswhicharebasedonimitationof

things andnoton theirnames. Languagedoes, however,makea contribution. For example,whenan

adult uses awordwhich refers to a class of things, the child is given a glimpse at one facet of adult

reasoning. An adult’s language forces the child, to some degree, to consider the world from a new

perspective.Nevertheless,itisprobablyfairtosaythatthechild’sthoughtdependslessonhislanguage

thanthechild’slanguagedoesonhisthought.Aswesawearlier,thechildinterpretswordsintermsof

hisownpersonalsystemofmeanings,andthechild’smeaningisnotnecessarilythesameastheadult’s.

Although the culture provides the childwith language, the latter does not immediately socialize the

child’s thought. In other words, language does not completely impose on the child the culturally

desirablewaysofthinking.Instead,thechilddistortsthelanguagetofithisownmentalstructure.The

childachievesmaturethoughtonlyafteralongprocessofdevelopmentinwhichtheroleoflanguageis

butonecontributingfactor.

THE CHILD FROM 4 TO 11 YEARS (PIAGET’S EARLY WORK)

Wehavenowreviewedtheinfant’saccomplishmentsinthesensorimotorperiod(0-2years)and

the child’s acquisition of the semiotic function (2-4 years). It is hard to emphasize sufficiently the

magnitudeof theseachievements. In thespaceofonlya fewyears, thechildhas transformedhimself

from an organism almost totally dependent on reflex and other hereditary equipment to a person


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capableof symbolic thought.During theyears to follow (after theageof4), neither sensorimotornor

symbolicactivitiesdisappear.Thechildolderthan4yearscontinuestodevelopsensorimotorschemes

applicabletoawiderangeofobjects,toimproveskillsinlanguage,andtoacquirementalrepresentations

forincreasinglylargeportionsofthesurroundingworld.Butatthesametimethechild’sdevelopment

extendsintoanumberofnewareas.

Thepresentsectionoffersanaccountofintellectualgrowthinthechildfromabout4to11years.

Recall that Piaget’s first five books cover this age span and present preliminary and tentative

conceptualizations.Laterworksoffermoreelaborateandmaturetheorizingonthesameagerange.We

willdescribeherePiaget’searlyviewsonthechildfrom4to11years;Chapter4reviewsthelaterwork.

Asweshallsee,Piaget’searlywork,althoughpreliminary,isstillquitefascinatingand,accordingtosome

criteria,ratesamonghisfinestaccomplishments.

The Use of Language

Piaget’searlyworkbeginswithaconsiderationofchildren’suseoflanguage.Attheoutsetheposes

afundamentalquestion:Whatisthefunctionofthechild’slanguage?Ourfirstresponseisprobablythat

thepurposeoflanguageiscommunication.Thechild,liketheadult,mostlikelyuseslanguagetoexpress

thoughtstoothers,andtotransmitinformation.Butalittlereflectionshouldsufficetoconvinceusthat

evenintheadult,languageisnotentirelycommunicative.Whenalone,adultsoftentalktothemselveson

amentallevel.Occasionally,theyevenspeakaloudwhennooneelseispresent.Therefore,ourinitial

hypothesisaboutthecommunicativenatureoflanguageisnotalwaystrue.

If this is so, then several questions immediately arise. How much of language—particularly

children’s language—iscommunicativeandhowmuch isnot?What is thenon-communicativevariety

like?Andwhenitisnotcommunicative,whatpurposedoeschildren’slanguageserve?Toanswerthese

andotherquestions,Piagetcarriedoutaseriesofinvestigations.Hebeganbyobservingtwo6-year-old

boys for about a month in their class at school. The children, who were from the poorer sections of

Geneva, attended a progressive class. The students could drawormakewhat they liked, couldwork

inpiduallyat“games”ofmathematicsandreading,hadthefreedomtotalkorplaytogether,andcouldgo

without permission from one room to another. As the two boys pursued their activities, Piaget and


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another observer took down in full detail the children’s speech as well as the context in which it

occurred.Piagetattemptedtoavoidinterferingwiththechildren’sactivitiesandtriednottoinfluence

their behavior in any way. The intention, of course, was to obtain a full record of the child’s use of

languageinhisnaturalschoolenvironment.Ifyouwillrecall,Piagetusedsuchnaturalisticobservation

inhisstudiesofinfancyandtheperiodfrom2to4years.Severaloftheadvantagesanddisadvantagesof

thismethodhavealreadybeendiscussedinChapter2.Onequestionthatwasnotconsiderediswhether

ornotPiaget is correct in assuming that the children’s behavior is not affectedby thepresenceof an

observer.Dochildrenactandspeakdifferentlywhenwatchedbyanadult?Unfortunately,thereislittle

empirical evidence on this issue. At themomentwe can only use our informal experience in similar

situationstohazardaguessthatafterashortperiodof timeyoungchildrengenerally learnto ignore

adultobserversandseemtobehavequitenaturally.

Afterrecordingthetwochildren’sspeech,Piagetattemptedtocategorizeeachsentencespokenby

each child. He discovered several varieties of both communicative and non-communicative language.

Non-communicativeor“egocentric”speechmaybepidedintothreetypes.Onetypeisrepetition,which

involvesthechild’smimickingsomethingshehasjustheard;forexample,“JacsaystoEz:‘Look,Ez,your

pantsare showing. ’ Pie,who is in another part of the room [andwas one of the two childrenPiaget

observed],immediatelyrepeats:‘Look,mypantsareshowing,andmyshirttoo.(LanguageandThought,LT,

p. 35). The statement clearly involved copying another’s speech since Piewas in fact quite properly

dressed.ThusPie’sutterancewasaclearcaseofrepetitionanddidnotserveacommunicativefunction.

Very often too the child is not aware that he ismerely repeatingwhat another person has said, but

believesthathisstatementisanoriginalone.AccordingtoPiaget’srecords,repetitionmadeupabout1or

2percentofthetotalnumberofstatements.

Asecondkindofegocentricspeechisthe inpidualmonologue.Thistypeoccurswhenthechild is

aloneandyettalksaloud,oftenatgreatlength.Forexample,“Levsitsdownathistablealone:7wantto

dothatdrawingthere...Iwanttodrawsomething,Ido.Ishallneedabigpieceofpapertodothat’”(LT,p.37).

Sincenooneelsewaspresentapartfromtheobserver,whobythistimepresumablynolongerdisturbed

the child, Lev’s statement clearly did not involve communication. In the case of Pie, monologue

constituted5percentofhisspeech,andforLevthefigurewas15percent.


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Perhaps themost interesting kind of egocentric speech is the collectivemonologue. This occurs

whentwoormorechildrenaretogetherandoneofthemspeaksasoliloquytowhichtheothersdonot

listen. The speakermay intend to interest the others in his remarks andmay in fact believe that the

othersarelistening.Buttheegocentricnatureofthemonologuepreventstheothersfromunderstanding

him even if they wanted to. Despite the fact that the speaker is in a group, his statements are not

communicative; he is merely talking to himself aloud. For example, when sitting with some other

childrenandapparentlyplayingwithtoysordrawing,Levsaid,“Isay,I’vegotaguntokillhimwith.Isay,

Iamthecaptainonhorseback.Isay,I’vegotahorseandagunaswell”(LT’p.41).NotethatLev’scontinual

useofthephrase“Isay”seemstoindicatethathewantedtheotherstolistentohimandthatheintended

to transmit information. But at the same time, Lev’s statement is unclear: we do not knowwhom he

intended tokillwith thegun,whowas thecaptainonhorseback,andsoon.Moreover,Lev’s remarks

wereunrelatedtoanyoneelse’sanddidnotsucceedinmakingtheotherchildrenlisten.Infact,each

child,althoughapparentlyworkingwithandspeakingtotheothers,offeredsoliloquieslikeLev’s.There

wasno“giveandtake”amongmembersofthegrouporanycontinuityinthediscussion;eachchildspoke

aboutwhat interested him at themoment, and this involvedmostly his own activities. The collective

monologue is therefore neither truly social nor communicative as it is merely the simultaneous

occurrence of at least two monologues. According to Piaget’s calculations, the collective monologue

involved23percentofLev’sspeechand30percentofPie’s.Egocentricspeechasawhole—repetition,

monologue, and collective monologue—represents 39 percent of Lev’s and 37 percent of Pie’s total

numberofsentences.

Theremainderofthechildren’sspeechiscommunicativeor“socialized.”Inthiscasethechildtakes

into consideration the point of view of the listener and attempts to transmit information to him. For

example,hetellsanotherchildcertainsimplefacts, forexample,howtooperateatoy.Orhecriticizes

anotherchild,oraskshimquestions,orinotherwaysinteractswithhim.Whileservingacommunicative

function,suchspeechneverthelessshowscertaindeficiencies.Youngchildrendonotattempttoexplain

eventstooneanother,andtheydonotspeakintermsofthecausesofevents.Also,youngchildrendonot

try to give proof or logical justification forwhat they have proposed. One reason is that they do not

considerthepossibilitythatthelistenermayhaveacontraryopinion.

AfterestablishingthesefactsinthecaseofLevandPie,Piagetthenwentontostudyalargergroup


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oftwentychildrenvaryinginagefrom4to7years.Again,themethodwasnaturalisticandinvolvedthe

recordingofthechildren’sspontaneousremarks.Ingeneral,thefindingsreplicatedthedataonLevand

Pie.Asignificantproportionofspeechwasegocentric,andthisproportionwasespecially large in the

speechoftheyoungestchildren,ataboutage4.

These, then, are the results of Piaget’s naturalistic observations. There seems to be a decline in

egocentrismandanincreaseincommunicationasthechildgetsolder.Thechild’slanguage,especiallyin

the early portion of the years from 4 to 5 or 6 years, does not entirely serve the function of

communication.Often,thechilddoesnotassumethepointofviewofthelistener;hetalksofhimself,to

himself,andbyhimself.

Howcanweexplainthenon-communicativenatureofthechild’sspeech?Whatpurposesdoesit

serve? Piaget offers a number of interesting hypotheses which he regarded as tentative, and not

conclusive.First,considerverbalrepetition,wherethechildsimplymimicswhatotherssayorrepeats

phrasesofhisown.Piaget’s interpretationisthatrepetitionis"simplythe joyofrepeatingfor itsown

sake...thepleasureofusingwords...forthesakeofplayingwiththem"(LT’p.35).Youwillnodoubt

observethatthisexplanationisanotherversionoftheprincipleoffunctionalassimilation—thetendency

torepeatschemesandtoexercisethem. Inthepresentcasethechildmimicsbothhisownwordsand

thoseofothers,justasearlierinthesensorimotorperiodherepeatedpatternsofbehavior.Consequently,

repetitionisnotmotivatedbythedesiretocommunicate,butbytheneedtoexerciseverbalschemes.

Butrepetitioncomprisesonlyasmallportionofthechild’sspeech.Letusnowturntotheinpidual

monologuewhich involves a substantial proportionof the total numberof statements. To explain the

monologue,Piagetofferstwohypotheseswhicharenotmutuallyexclusive.Onehypothesisisthatthe

inpidualmonologueservesthepurposeofwishfulfillment.Whenthechild’sactionsarenotsuccessfulin

producinganintendedresult,heuseswordstoachievehisgoal.If,forexample,hewouldliketomovea

boxbutcannotbecause it is tooheavy, thechildmighttellthebox tomove, thususingwords tobring

aboutwhathisactivitiescannotaccomplish.Thechild’slanguage,therefore,isinpartakindoffantasy,a

wordmagic.Asecondexplanationofinpidualmonologueisthatwordsandactions,forthechild,arenot

yet fully differentiated.When beginning to learn language, the 2- or 3-year-old child often calls an

immediatelypresentobjectbyitsnameorusesawordtodescribeongoingactions.Consequently,inhis


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initialexperiencewithlanguage,thething(oraction)andthewordforitaresimultaneouslypresent,

andthetwoareseenasawhole.Thewordisinasensepartofthething,andviceversa.Ittakesalong

timeforthechildtodisassociate fullythewordfromitsreferent;hemust learnthatthewordbearsa

totallyarbitraryrelationtothattowhichitrefersandthatthewordisnotapartofit.Evenintheperiod

underdiscussion(4to7years), thechildhasnotfullygraspedtherelationbetweenwordandthing.

Consequently,whenheacts—playswithtoys,draws,andsoon—hetendstosaythewordsassociated

withhisbehavior.Thus,themonologueisinasenseapartofthechild’sactionandisnotdesignedfor

thepurposeofcommunication.

Inthecaseofthecollectivemonologue,similarexplanationscanbeemployed.Sometimesthechild

inagroupmerelyrepeatswhatanothersaysbecauseoffunctionalassimilation;sometimeshisremarks

are magically intended to produce results which he otherwise cannot achieve; and, finally, his

utterancesoftenmerelyaccompanyactivitiesinwhichheisengaged.

All three types of speech—repetition, inpidual monologue, and collective monologue—may be

characterizedasegocentric.Piagetdoesnotusetheterminthesenseofselfishorself-serving.Theyoung

childischaracterizedasegocentricnotbecauseofconceitorbecauseofanattempttosatisfydesiresatthe

expenseofotherpeople,butbecauseheiscenteredabouthimself(orhisownegointhegeneralsense)

and fails to take intoaccount theother’spointofview.Whendeliveringamonologue inagroup, the

desires of the egocentric child do not necessarily clash with those of other children; rather he is

insensitivetowhattheothersneedtohear.Tocommunicate,onemustconsiderwhat informationthe

listenerdoesanddoesnothaveandwhatheisandisnotinterestedin,andthistheyoungchilddoesnot

do.

Onemay criticize the naturalistic study of the child’s language in severalways. Perhaps Piaget

foundtheuseofnon-communicativelanguagetobeextensiveonlybecauseoftheliberalatmosphereof

theschoolwheretheemphasiswasoninpidualratherthangroupactivity.Ifyouwillrecall,thechildren

wereallowed todowhat they liked,and thesituationwassodevised that thechildren learned from

inpidual play.Under these circumstances, itmight be the case that the children felt no real need for

communication,andconsequentlytheydidnotdisplaytheseabilities.


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We may, however, cite as evidence against this argument an experiment by Piaget on verbal

communication.Briefly,thetaskinvolvedanexperimenter’sgivingsomeinformationtoonechild(the

speaker)whowasthensupposedtotransmitittoanotherchild(thelistener).Piagetmadecleartothe

speakerthatthetaskwastocommunicate.Theseinstructionspresumablyorientedthechildtowardthe

goalof communicationrather than thatofplay.Therefore, theexperimentmightgive insight into the

child’sabilitytotransmitinformationwhenhefelttheneedtodoso.Theexperimentwasalsousedto

obtain information about the listener’s ability to understand the speaker. Even if the speaker were

communicative,didthelistenercomprehendwhatwassaid?However,sincethemethodsusedtoassess

thelistener’sunderstandingwereratherpoor,wewillnotconcentrateonthisaspectofthestudy.

Letusnowdescribetheexperimentingreaterdetail.Inoneportion,pairsofchildrenwereusedas

subjects. There were thirty children at ages 7 to 8 years and twenty at ages 6 to 7 years. The

experimentersentoneofthepairoutoftheroomandtoldtheotherastory.Thischild,tobereferredtoas

the speaker,was instructed to listencarefully sincehewouldhave to tell the samestory to theother

child,whomwewillcallthelistener.Thentheexperimenterreadastory,repeatedthedifficultparts,

and tried to make the speaker attend carefully. Several different stories, varying from six to nine

sentencesinlength,wereused,althoughatanyonetimethespeakerwasrequiredtotellonlyonestory

tothelistener.Next,thelistenerwasbroughtintotheroom,andthespeakertoldhimthestory.

The experimenter took down everything that was said and, in addition, questioned both the

speakerandthelistenertodeterminethedegreetowhichtheyunderstood.Aftertheexperimentwith

stories, the same pairs of children were used to investigate communication concerning mechanical

objects.Thistime,theexaminerexplainedtothespeakerhowafaucetorasyringeworks.Diagramswere

usedtomakethematterclear,andthespeakerwaspermittedtomakeuseofthediagraminexplaining

themechanicalprocess to the listener.Again, the experimenter recordedeverything that the speaker

said.

Whiletheexperimentyieldedmanyresults,weshallfocusontheverbalizationsofthespeaker.Did

children in the experiment succeed in producing communicative speech, and if not, what was their

language like? In general, the experiment on communication replicated the results of Piaget’s earlier

naturalisticobservations;thatis,inbothcasesasubstantialproportionofspeechwasnon-communicative


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or egocentric. For example, the experiment on communication showed that young children often use

pronounsanddemonstrativeadjectives—suchashe,she,it,that,this—withoutindicatingclearlytowhat

theyarereferring.Inthemidstofanexplanationofthefaucet,thespeakermightsay“Ifyoumoveitwith

thatotherthing,thenitwillgo.”Thischildfailstoconsiderthatthelistenermightnotknowwhat“it”and

“thatother thing”designate.This tendency is carried so far thatoften the speaker completely fails to

nametheobjectsinvolvedinamechanicalexplanation.Thechildisalsopooratexpressingtheorderof

events.Onechildexplaininghowafaucetworksbeganbytellinghowthewaterfallsintothebasin,and

onlylaterdidhebothertosayhowthewatergoesthroughthepipe.Or,intellingastory,thechildmight

beginwiththeendandendwiththebeginning.

Ayoungchildmayalsoexpresscausalrelationspoorly,andseldomconnectthecausewithitseffect.

Forexample,intellingastoryinwhichafairyturnedcertainchildrenintoswans,onechildsaid,“There

wasafairy,awickedfairy.Theyturnedthemselvesintoswans”(LT,pp.126-27).Notehowthechilddid

notexpressthecentralcausalrelation;itwasthefairywhocausedthechildrentobecomeswans.The

childmerelymentionedthetwoeventswithout indicatingtheirconnection.Thesecondsentencealso

illustratesthetendencytousepronounswithoutdescribingtheirreferents.Towhomdoes“they”refer?

Oftenthechildmayalsoomitlargepartsoftheexplanationorstory.Eventhoughheunderstands

andremembers theseportions (asshownbyPiaget’s laterquestioning), thechildmay fail tomention

them.Ineffectheassumesthatthelisteneralreadyknowspartsofthestoryorexplanation.Omissionsof

thiskindclearlyrevealalackofsensitivitytotheneedsofthelistener.

Another aspect of egocentric speech is manifested in the observation that the child’s story or

explanationdoesnot forma coherent and integratedwhole.The account is fragmentary; it ismerely

composedofalargenumberofspecificandunrelateditemswhicharejuxtaposedoneupontheother.

Forexample,hereisonechild’saccountofhowafaucetworks:

Thehandleisturnedonandthenthewaterruns,thelittlepipeisopenandthewaterruns.There,thereisnowaterrunning,therethehandleisturnedoff,andthenthereisnowaterrunning,andherethewaterisrunning.There,thereisnowaterrunning,andherethereiswaterrunning.(LT;p.130)

Clearlythisexplanationinvolvesamerecollectionofinpidualstatementswhicharenotintegrated

intoareasonablewhole.Oneaspectofsuchjuxtapositionisatendencyalreadydescribed:theinabilityto


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statecausedrelations.

Insummary,theprecedingfivepropertiesoftheyoungchild’sspeech—thefaultyuseofpronouns

and demonstrative adjectives, the incorrect ordering of events, the poor expression of causality, the

tendency toomit important features, and finally, juxtaposition—all are concretemanifestationsof the

child’s egocentrism—the inability to take into consideration the other person’s point of view. With

development theseegocentricmanifestationsdecreaseandspeechbecomesmore communicative.The

speakerbecomesawareoftheviewsofothersandadaptshisspeechaccordingly.

Piaget’s experiment on verbal communication also studies the understanding of the listener.

Althoughthemethodologywasquestionable,severedofPiaget’simpressionsareofinterest.Theresults

showedthat, ingeneral, the listenerdoesnotunderstandthespeakerverywell.Partof the listener’s

inabilitytounderstandisclearlyduetothespeaker’sfaultypresentation.Fewpeoplecouldcomprehend

theexplanationofthefaucetjustdescribed.ButPiagetfeelsthatpartofthelistener’sdifficultyisdueto

his own patterns of thought and not to the speaker’s egocentric speech. Even when the speaker is

relativelyclear,thelistenerdistortshisutterancesinseveralways.One,thelisteneralmostalwaysthinks

thatheunderstandswhatthespeakersays,evenwhenitisveryobscure.Thelistenerveryseldomasks

questionstoclarifyapointortoobtainadditionalinformation.Thelistenerfeelsconfidentthathehas

understoodwhen in fact he has not. Two, the speaker’s remarks evoke in the listener a kind of free

association.InPiaget’sterms,thelistenerassimilatestheremarksintohisownschemeswhichoftenbear

littlerelationtowhatthespeakerisattemptingtocommunicate.Forexample,afterlisteningtothestory

inwhichthebadfairyturnedseveralchildrenintoswans,one6-year-oldchilddistortedtheaccountin

importantways. Insteadof saying that thechildrenwere turned intoswans,hemaintained that they

weredressedinwhiteclothes.Thenheelaboratedonthispropositionuntiltheendofthestorywasno

longerrecognizable.Hetransformedonepartofthestoryand,givingfreereintohisimagination,went

onfromtheretoconstructanewtaleofhisown.Inbrief,whilethespeakerfailstotakeaccountofthe

needsofthelistener,thelisteneralsodistortswhathehears,elaboratesonit,andissatisfiedthathehas

understood,whereas,inactualfacthehasnot.

ItiseasytoseethatPiaget’sexperimentoncommunicationisdeficientinseveralways.Piagetdoes

notmakeclearthemethodsusedtoassesseitherthespeaker’sorthelistener’sunderstandingofthestory


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orexplanation.Themeasurementofcomprehensionisadifficultanddelicatematterthatrequiresmore

attentionthanPiagethasgiventoit.Piagetalsomaynothavefullyeliminatedthepossibilitythatfaulty

memory, and not egocentrism, may sometimes underlie the speaker’s lack of ability to communicate.

Perhapstheyoungchildisnotabletotellalengthystorysimplybecauseofthefailuretorememberlarge

partsofit.DespitePiaget’sattemptstocontrolforthememoryfactorbyquestioning,itisnotaltogether

cleartowhatextenthewassuccessful.

AnotherfactortobeconsideredisthatPiaget’ssubjectswerepoorchildren.Isitnotpossiblethat

lower-classchildrenhavedifferentverbalabilitiesfrommiddle-classchildren?Ifso,Piagetistooquickto

generalizehisfindingstochildreningeneral.Whiletheseandothercriticismsmayberaisedandseem

tohavevalidity,onemustrememberthatPiaget’sfirststudieswereintendedasexploratory.Theiraim

wastouncoverinterestingissuesforinvestigation,toproposepreliminaryhypotheses,andnottoreach

firmconclusions.Piaget’sstudiesoncommunicationseemtohavefulfilledhisoriginalgoals.Hisresearch

raisesinterestingquestions.Forexample,isittruethattheyoungchildcannotexpresscause-and-effect

relations, or that the listener so extensively distorts what the speaker says? Despite its deficiencies,

Piaget’sresearchisofgreathistoricalsignificance:itwasoneofthefirstattemptsinchildpsychologyto

deedwiththecrucialissueofthefunctionsofhumanlanguage.

Thusfarwehaveseenthattheyoungchildfromabout4to7yearsdisplaysasignificantamountof

egocentric speech and that the older child after about 7 years is increasingly proficient at verbal

communication. Why does egocentric speech decrease as the child gets older? Piaget proposes an

interestinghypothesis toexplain thewaningofegocentrism.Whenthechild isyoung,particularly in

infancy,adultstakegreatpainstounderstandhisthoughtsanddesires.Themothermustknowwhich

toytheinfantwantsorwhatbothershimandisnotabletorelyexclusivelyonwordstounderstandhim.

Consequently,theyoungchilddoesnotneedtocommunicateclearly;evenifhisspeechisunclear,adults

willmakeeveryefforttounderstand.Asthechildgrowsolder,however,heisthrownmoreandmore

intothecompanyofolderchildrenwhoarenotassolicitousasadults.Otherchildrendonottrysohard

topenetratetheobscuritiesofhislanguage.Moreover,theyarguewithhim;theychallengewhathesays

andforcethechildtodefendhimself.Itisundersocialpressuresofthesekindsthatthechildisgradually

forced to adopt better modes of communication. In the attempt to express himself and to justify his

arguments,thechildeventuallylearnstotakeintoaccounttheother’spointofview.Nottodosoistobe


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misunderstoodandtolosetheargument.Inthisway,then,doesegocentrismdiminish.

Clinical Method

Piaget’searlyworkwasinpartconcernedwiththecontentsofthechild’sthought.Heattemptedto

discover thespontaneous ideasof thechildatdifferentstagesofhisdevelopment.What is thechild’s

conceptionofthenatureofdreams,orwhatishisexplanationofthefactthatboatsfloatonwater?The

studyofcontentisparticularlydifficult,becauseaswehaveseenintheprevioussection,youngchildren

havegreatdifficultyincommunicatingtheirthoughts.Itisthereforecrucialfortheinvestigatorofcontent

toemploysensitiveandaccuratemethods.Piagethasdevotedcareful consideration to thechoiceofa

propermethod.Hehasrejectedthetestingapproach,assignedalimitedroletonaturalisticinvestigation,

andadoptedtheclinicalprocedure.Letusconsidereachofthesedecisionsinturn.

Theessentialfeatureofthetestingmethodisaseriesofquestionswhichareposedinthesameway

to all who take the test. If we are investigating the origin of the sun, for instance, wemight ask all

children,“Wheredidthesuncomefrom?”Itisimportantthatthequestionbeputinpreciselythesame

waytoallchildren.Infact,thereadingofthequestion(theintonation,stress,andsoon)shouldbeas

consistentaspossible.Ifachilddoesnotseemtounderstand,theexaminermayrepeatthequestion.But

this is usually themaximumof flexibility permitted: the examinermay not rephrase the question or

otherwise alter it. The purpose of a standardized administration is to guarantee that all subjects are

facedwith thesameproblems.Then if4-year-oldsgenerallygiveone typeofanswerand8-year-olds

another,theexaminermayreasonablyconcludethatthereisarealdifferencebetweentheagegroups.If,

ontheotherhand,theformofthequestioningvariedacrossagegroups,theexaminerwouldnotknow

whether the difference in answers is genuinely related to age or is due simply to the difference in

questions.Whilethetestingmethodhasimportantpsychologicaluses,Piagetfeelsthatitisnotsuitable

for his task—the discovery of content (or the discovery of structure, a problem to which Piaget also

appliestheclinicalmethod).

Thetestingmethodhasthedisadvantageofinflexibility.Ifachildgivesaninterestingresponse,the

examinercannotpursueit.Ifachildmisunderstandsthequestion,theexaminercannotclarifyit.Ifthe

child’s answer suggests an additional topic for investigation, the examiner must leave the matter


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unexplored.Inaddition,thetestproceduremaybesuggestive.Ifthechildisasked,“Wheredidthesun

comefrom?”thequestionimpliesthatthesundidhaveanorigin,andthisideamaynothaveoccurredto

thechildbefore.Consequently,hisanswermaynotrevealthecontentsofhisspontaneousthought,but

maybemerelyahastilyconsideredresponsetoaquestionencounteredforthefirsttime.And,finally,the

testmethoddoesnotusuallyallowtheexaminertoestablishthestabilityofthechild’sresponse.Ifachild

isaskedwhatthesumof2and2is,andsays“4,”hisanswermaybetentativeorfirm.Ifheisunsure,

furtherquestioningmayinducethechildtochangehismind.Ifhisbeliefisfirm,nothingwillswayhim.

Inthetestingprocedurethechildgivesananswerandthatistheendofit:atentative“4”isasgoodasa

sureone.Forthesereasons,then,Piagetrejectsthetestingapproach.

Anothermethodfortheinvestigationofspontaneouscontentisthenaturalisticprocedureasused

inPiaget’sstudyofinfancyorlanguage.Inasense,thisisanidealmethod.Supposeweobservethata

childspontaneouslyasksthequestion:“Whomadethesun?”Thestatementgivesaclearinsightintothe

contentofhisthought.Itisimmediatelyobviousthathebelievesthatsomeagent,perhapsapersonor

perhapsGod,intervenedtocreatethesun,andthatitdidnotevolvenaturally.Surelythisspontaneous

questionisfarmorevaluablethanaresponsetoastandardizedquestion.

Thenaturalisticmethod,however,issubjecttoanumberofdrawbacks.Onemayobserveachildfor

a very long time before he will say anything of interest. Suppose we are interested in the child’s

conceptionoftheoriginofthesun;itisextremelyunlikelythathewillasktherelevantquestionwhile

being observed. Consequently, the naturalisticmethod, despite its clear utility, cannot be used as the

chiefinstrumentofresearch.Atbest,naturalisticobservationcanserveonlyasubsidiaryroleintwoways.

It can suggest questions for intensive clinical examination. If, for example,wehear a child ask, “Who

madethesun?”thenwecaninterviewalargenumberofchildrentotestthegeneralityoftheassumption

underlyinghisquestion.Second,thenaturalisticobservationcanserveasacheckontheresultsofclinical

questioning.Ifinterviewingsuggeststhatchildrenbelievethatcloudsarealive,thenpatient,naturalistic

observationmayfurnishdatatosupportorrefutethishypothesis.

Piaget feels that the clinical method avoids the deficiencies of the testing and naturalistic

procedures,andinadditionoffersanumberofattractivefeatures.Theclinicalmethodishardtodescribe

since it is so flexibleandprovidesageneral framework forquestioning thechild rather thanasetor


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standardizedform.Thisaccountisthereforeintendedonlyasanoutlineoftheclinicalmethod.Thebasic

aimofthemethodistofollowthechild’sthoughtwithoutdeformingitbysuggestionsorbyimposingthe

adult’sviewsonthechild.Oneimportantfeatureisthattheexperimentertriestoadoptthelanguageof

thechildandkeepthelevelofquestionsaccessibletothechild.Termswhicharebeyondhisreachare

avoided and replaced asmuch as possible by thosewhich the child has spontaneously emitted. The

examinerusuallybeginsbyaskinganondirectivequestion.Insteadofsaying,“Whomadethesun?”or

“Howdidthesunevolve?”theexaminermightask,“Howdidthesuncomeabout?”Ifthechilddoesnot

understand,theexaminerisfreetorephrasethequestionbyasking,forexample,“Howdidthesunget

there?” After the child answers, the experimenter forms an hypothesis concerning the nature of the

child’sbeliefs.Forexample,ifthechildfirstanswered,“Itwasputthere,”theexaminermightguessthat

thechildbelievesthatapersoncreatedthesun.Subsequentquestionsareusedtotestthishypothesis.

Theexaminermightthenask:“Canyoutellmehowitwasputthere?”Ifthechildsays,“Godputitthere,”

then the examiner might follow up aspects of this response. Does the child really believe in pine

intervention,oristhisjustasuperficialmimicryofwhathehasbeentaughtinSundayschool?Toanswer

this question, the examinermay challenge the child’s belief to see how firmly he holds to it. Or the

examinermaywonderwhetherthechildmeanstosaythatthesunalreadyexistedbeforeGod“putit

there”orthatGodcreatedittoo.Furtherquestionsmustbeaskedtodecidebetweenthetwoalternatives.

Ofcourse,iftheexaminer’shypothesisisnotconfirmed,hemustallowthechild’sanswerstoleadhimto

thecorrectinterpretation.Itiseasytoseethatnotwoclinicalexaminers,eveniftheyaretestingthesame

child,willpursuethesamelineofquestioning.It isalsoclearthatclinicalquestioningisverydelicate

andsubjecttoseveralkindsoferrors.Theexaminermaytalktoomuchandtherebysuggestanswersto

thechild.Ortheexaminermaynottalkenoughandfailtoposethequestionsnecessaryfordetermining

thechild’smeaning.Piagetfeelsthatatleastayearofdailypracticeisnecessarybeforetheexaminercan

achieveproficiencyatclinicalquestioning.

Wemayraiseanumberofcriticismsoftheclinicalmethod.HowdoweknowthatPiagetisagood

clinical examiner? His books give only portions of selected clinical interviews. It is possible that the

publishedinterviewsareexceptional—fromthepointofviewofmethodandsupportforPiaget’stheory

—andthattheunpublishedprotocolsarepoorlydone.Perhapsinthelattercasetheexaminersuggested

answers to the child, asked thewrong questions, and so on. Also, wemaywonderwhether Piaget’s


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diagnoses—thejudgmentsderivedfromtheinterview—arereliable.Thatis,wouldotherpersonsagree

withtheinterpretations,orarePiaget’sdiagnosesquiteidiosyncratic?Itisalsotruethatsincetheclinical

interviewsareunstandardized,itisverydifficultforindependentinvestigatorstotestPiaget’swork.If

anotherpsychologistattemptedtorepeatPiaget’sresearchandobtaineddifferentresults,thePiagetian

criticism could always be that he failed to use the clinicalmethod properly. Another criticism that is

raised is that Piaget usually commits a large number ofmethodological sins unrelated to the clinical

method.Forexample,hedoesnotusuallyreportthenumberofsubjectsseeninaninvestigation,ortheir

exactages,ortheirsocialbackgrounds.Indescribingtheresultshepresentsonlyfragmentsofinterviews

andfailstogiveastatisticalsummaryofthechildren’sreactions.Tosummarize, theclinicalmethodis

deficient.Perhapsthechiefobjectionisthatitrequiresustotakealotonfaith:thatPiagetconductsthe

interview without suggestion, that he interprets the results properly, and so on. As we well know,

scientistsprefertotakeaslittleonfaithaspossible.

ThedeficienciesinPiaget’sresearcharereal.Yetwemustbecarefulnottoexaggeratethem;we

mustevaluatetheclinicalmethodintheoverallcontextofPiaget’swork.Piagetfeltthattheearlyportion

ofhisresearchwasessentiallyexploratory.Hisgoalwastoopenupnewareasforinvestigationandto

proposepreliminaryhypothesesforfurtherexamination.Theearlyworkwasnotintendedtoprovea

theoryortopresentdefinitiveviewsonintelligence,andPiagetfeltthatmethodsshouldbeasflexibleas

possible at the preliminary stages of research. It seemed premature to him to introduce rigorous

procedureswhenalmostnothingwasknownabout thesubjectmatter,andwhen itwasbynomeans

clearwhat the propermethods should be. If Piaget had attempted to establish every pointwith the

maximumofcertainty,thenheprobablywouldnothaveadvancedbeyondthestudyofchildren’sverbal

communication(oneofhisfirstresearchtopics).Oncethepioneeringresearchhasbeendone,thenitis

alwayspossibletochecktheresultsbymorestandardizedmethodsandrevisethetentativehypotheses.

The Content of Thought

Piaget’searlyinvestigationsofcontentareextensive.HistwobooksonthesubjectareThe Child’s

ConceptionoftheWorld(CCW)andTheChild’sConceptionofPhysicalCausality(CCPC).Theycoveralarge

numberoftopicswhichincludethechild’sbeliefsconcerningdreams,meteorology,theoriginoftrees,

thenatureofshadows,theexplanationofthesteamengine,andsoon.Toillustratethisworkweshall


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describeonlyonetopic:theoriginsofthesunandmoon.

AccordingtoPiaget’sfindingstherearethreestagesinthechild’sconceptofthesunandmoon.The

stagesoccurinsequencesomewherebetweenabout3and12years.Piagetdoesnotattempttospecify

precise age norms because there are large variations in responses. Here is an example of a stage 1

protocol,a6-year-old’sbeliefs:

Howdidthesunbegin?—Itwaswhenlifebegan.—Hastherealwaysbeenasun?—No.—Howdid itbegin?—Because it knew that life had begun.—What is itmade of?—Of fire.—But how?—Because therewas fire upthere.—Wheredidthefirecomefrom?—Fromthesky.—Howwasthe firemade in thesky?—Itwas lightedwithamatch.—Wheredid it come from, thismatch?—God threw it away. . . .Howdid themoonbegin?—Becausewebegantobealive.—Whatdidthatdo?—Itmadethemoongetbigger.—Isthemoonalive?—No...Yes.—Why?—Becausewearealive.(CCWp.258-59)

Theprotocolillustratesthreekindsofbeliefscommontochildreninthefirststageofdevelopment.

The firstbelief isanimism.Thechildbelieves that thesunandmoonarealive in thesamesense that

people are alive; that is, the sun is credited with knowing that life had begun. The second belief is

artificialism.The childasserts that the sun resulted from theactionsof anoutsideagent. Itwasnota

natural process that formed the sun, but an act of intervention on the part of God. The third belief

illustrated by the protocol contains the idea of participation. The child perceives some continuing

connection,or someparticipation,betweenhumanactivitiesand thoseof things.Hisbelief is that the

moonbeganbecausepeoplebegantobealive.Note that thisexplanation isnotartificialism,since the

childdoesnotassertthatpeoplecreatedthemoon.Hisconceptionisvague,andhemerelyassumesadim

relationbetweenpeopleandtheplanets;hebelievesthatthereissomesortofinfluenceorparticipation

betweenthem.

Thesecondstageofthechild’sconceptofthesunandmoonistransitionary.Thechildcontinuesto

believeinartificialismandanimism,butlessblatantlythanbefore.Thefollowingexcerptinvolvesan8-

year-oldchild:

Howdidthesunbegin?—Itwasabigcloudthatmadeit.—Wheredidthecloudcomefrom?—Fromthesmoke.—Andwheredidthesmokecomefrom?—Fromhouses. . . .—Howdidthecloudsmakethesunshine?—It’s alightwhichmakesitshine.—Whatlight?—Abig light, it issomeoneinHeavenwhohasset fireto it.(CCW, p.274)

Notethatatthebeginningoftheprotocolthechildinvokedonlynaturalphenomenatoexplainthe


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sun’sorigin.Thesunwasformedbycloudswhichinturnderivedfromsmoke.However,whenasked

wherethesmokecamefrom,thechildproposedanartificialistexplanation.Thesmokecamefromhouses

and,byimplication,fromfireswhichpeoplecreated.Artificialismisevenmoreapparentinthesecond

partoftheprotocolwherethechildmaintainsthatsomeoneinHeavenhascreatedalightthatmakesthe

sunshine.

Inthethirdstage,thechildgivesupnotionsofartificialism,animism,andparticipation.Whilehis

explanations are often crude and incorrect, he attributes the sun’s formation to natural processes in

whichhumanorpineagentshavenorole.Sometimes,ofcourse,thechild’saccountsarebasedonwhat

hehasbeentoldinschool.Yetsometimestheyarenot,andeventhenthechildproposesexplanations

invokingphysicalprocessesoftheplanet’sorigins.

Moral Judgment and Behavior

Piaget’s earlywork covered awide range of topics including verbal communication, concepts of

physical causality, andmoral judgment and behavior. This last topicwill be considered now. Piaget

beginshisstudyofmoralbehaviorandjudgmentwithadetailedconsiderationofchildren’sgamesof

marbles.Hedescribeshowchildrenconceiveofthegameandfollowitsrules.Atfirstglanceitmayseem

quite unusual to study morality by means of the apparently trivial game of marbles. Our intuitive

definitionofmoralityprobablyrelatestosuchmattersaslyingandstealing,andnottomeregames.But

accordingtoPiagettheessentialaspectofmoralityisthetendencytoacceptandfollowasystemofrules

which usually regulate interpersonal behavior. Our society has gradually developed norms which

control how an inpidual treats others, behaves toward property, and so on, and these regulations,

supplementedby the inpidual’sownconceptions, constitute themoral system.Oncloser inspection it

wouldseemasiftherulesgoverningthegameofmarblesfulfillallthedefiningconditionsofamoral

system. The rules control how inpiduals behave toward one another in terms of the actions which

comprisethegame,theydetermineinpidualandpropertyrights,andtheyareaculturalproductwhich

hasbeenpasseddownfromgenerationtogeneration.Thegameofmarblesalsohasauniqueadvantage

fromthepointofviewofchildpsychology.Theruleshavebeendevelopedlargelybychildren,andthe

game is played almost exclusively by children. Therefore, the child’s conception of the game and his

playingof it reflect theworkingsofhisownmindand issubject to littleadult influence.Unlikerules


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dealingwithlyingorstealing,thegameofmarblesisthechild’screation,nottheadult’s.Ifwequestion

thechildaboutthegame,hisanswersdonotsimplyparrottheteachingsofadults,butgiveagenuine

indicationofhisownthought.Butisnotthegamejustplay,somethingthatisnotatalltakenseriously,

andthatthereforebearsnorelationtomorality,whichisagravematter?Wemayanswerthiscriticismby

pointing out that the child does take the game seriously.While a game has its “fun” aspects, if one

observeschildrenplaying,onerealizesthattheyaredeeplyengrossedintheiractivities,considerthe

otherplayers’actionsofsomeimportance,andarenotentirelydisinterestedintheoutcomes.Istheadult

who“plays”thestockmarketverydifferent?

Tostudychildren’sbehaviorinthegameofmarbles,Piagetfirstacquiredathoroughknowledgeof

therulesofthegame.Thenheaskedabouttwentyboys,rangingfrom4to12or13yearsofage,toshow

himhowtoplay.(InSwitzerlandthegameofmarblesisplayedexclusivelybyboys.)Inthecourseofhis

gamewiththechild,Piagettriedtoappearasignorantaspossibleabouttherulessothatthechildwould

feel that he had to explain them. In this way Piaget was able to determine both whether the child

understoodtherules,and,ifso,whetherhefollowedthem.SometimesPiagetobservedpairsofchildren,

particularlyyoungerones,playthegamewithouthim.Piagetalsoquestionedthechildaboutthenature

of the rules. He was interested, for example, in whether the child believed that the rules might be

changedandinthechild’sconceptionoftheoriginofrules.

Letusconsiderthepracticeofrules,ormoralbehavior.Fromaboutages4to7years,anegocentric

stageoccurswherechildrendonotknoworfollowtherules,buttheyinsistthattheydo.Asanexampleof

thisstage,letusexaminethefollowing:

Piagetseparatelyexaminedtwoboyswhowereinthesameclassatschool,wholivedinthesame

houseandoftenplayedmarbleswithoneanother.Thefirstboydescribedandplayedbyasetofrules

whichwashighlyunusualandidiosyncratic.Thesecondboydidnotunderstandthefirstboy’srulesand

moreoverproposedanunusualsystemofhisown.Thus,eachoftheboys,whooftenplayed“together,”in

factfollowedhisownsystemofruleswhichborelittlerelationtotheotherchild’s.Therewaslittlenotion

of“winning,”intheadultsense,andlittlegenuinecompetitionbetweenthetwoplayers.Fortheyoung

child,“winning”means“havingagoodtime,”anditwas,therefore,quitepossibleforallplayerstowinin

thisparticulargame.Eachchildwasmerelyplayinganinpidualgameanddidnotreallyneedtheother.


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Atthesametime,thechildrenbelievedthattheywereplayinglikeotherchildrenandthattheyknew

andfollowedtherulesquitewell.

Thebehavioratmarblesissimilartothespeechofchildrenofthesameageandis,therefore,called

egocentric.Inbothcasesthechildiscenteredabouthimselfandfailstotakeintoaccountanotherperson’s

pointofview.Inthegameofmarblestheyoungchildplaysforhimselfandnotwithsomeoneelse.Hehas

hisownsetofrulesandisrelativelyuninfluencedbywhattheotherdoes.Inthecaseofspeech,thechild

talks by himself and not with someone else. He speaks for his own purposes, and hismonologue is

relatively unaffected by the other’s comments. Egocentrism is therefore a tendency common to both

speechandmoralbehavior.

Thenextstage,thatofincipientcooperation,lastsfromabout7to10or11years.Thegamebeginsto

acquire a genuinely social character, and the child has a much firmer grasp of the rules. While his

knowledgeofthegameisnotperfect,hehasmasteredthebasicrulesandattemptstolearntherest.The

childofthisstagebothcooperatesandcompeteswithhispartner.Thereiscooperationinthesensethat

thechildagreeswithhispartneronacommonsetofruleswhicharethenfollowed.(Cooperationdoes

not mean here that the two or more children assist each other to attain a common goal.) There is

competitioninthesensethateachchildtriestowinforhimself,whileatthesametimeheadherestothe

mutuallyagreed-uponframework.Nevertheless,playisnotyetfullymature.Sincethechildhasnotyet

masteredalloftherules, thegamedoesnotproceedsmoothly,andtherearedifficultiesandconflicts.

Again,thereisaparallelbetweenplayandspeech.Inbothinstances,thechildofabout7yearsofage

beginstotakeintoaccountanexternalpointofview.Inmarblesheallowsasetofrulestogovernhis

behavior,andheinteractswiththepartner.Inspeechhetriestoanticipatewhatthelistenerneedsto

know,andheacceptslinguisticconventionswhichfacilitaterealinteraction.

Thefinalstageofmoralbehavioristhatofgenuinecooperationwhichbeginsatabout11or12years

ofage.Nowthechildacquiresathoroughmasteryoftherules.Asbefore,heagreeswiththeothersonthe

waytoplaythegame,anditiswithinthiscommonframeworkthathetriestowin.Inaddition,however,

the older child shows a kind of legalistic fascinationwith the rules.He enjoys settling differences of

opinionconcerningtherules,inventingnewrules,andelaboratingonthem.Heeventriestoanticipate

allthepossiblecontingenciesthatmayarise.


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Piagettellsadelightfulanecdoteaboutthelegalistictendenciesofthisstage.Heobservedagroup

ofboysaged10and11whowerepreparing tohaveasnowball fight.Beforegettingonwith it, they

devoted a considerable amount of time topiding themselves into teams, electingofficers, devising an

elaboratesetofrulestoregulatethethrowingofsnowballs,anddecidingonasystemofpunishmentsfor

transgressors.Beforetheyhadactuallysettledonalltheselegalisticaspectsofthegame,itwastimeto

returnhome, andno snowball gamehadbeenplayed.Yet, all theplayers seemedcontentwith their

afternoon.

Wemay summarize by stating, then, that there are three major stages of the practice of rules:

egocentrism,whereeachchilddoesnotknowtherulesorhowtoapplythembutthinkshedoes;incipient

cooperation,wheremasteryoftheruleshasimprovedandchildrenbegintosharethemtocompete;and

finally,thestageofgenuinecooperation,wherechildrenknowtheruleswellandenjoyelaboratingupon

them.

Afterestablishingthechild’sknowledgeandpracticeofrules,Piagetwentontoquestionthechild

abouttheirinviolability.Heaskedthechildwhethertherulesmightbechanged,whethertheyalways

existedintheirpresentform,andhowtheyoriginated.Indeterminingthechild’sconceptionoftherules,

Piagetofcourseusedtheclinicalmethod(ashedidinestablishingknowledgeoftherules).Hefound

thattherearetwomajorstagesinnotionsconcerningtheinviolabilityofrules.Thefirststage,whichisin

turnpidedintotwoparts,lastsfromabout4or5yearstoabout9or10years.Thusitoverlapsthefirst

twostagesof thepracticeofrules(egocentrismandincipientcooperation). Inthe firstpartof the first

stage,whichweshallcalltheabsolutisticstage,thechildbelievesthatsomeauthorityoriginatedtherules

ofmarblesandthatnooneeverplayedthegamebeforethatauthorityplayedit.Moreover,theauthority

conveysontherulesasacred,unchangeablecharacter:theyareabsoluteandcannotbealtered.Hereis

partofaprotocolofa5-year-oldillustratingsomeofthesebeliefs:

Howdidyouget toknow the rules?—When Iwas quite littlemy brother showedme.MyDaddy showedmybrother.—Andhowdidyourdaddyknow?—MyDaddyjustknew.Noonetoldhim....—Tellmewhowasbornfirst, yourdaddyor your granddad?—MyDaddywas born beforemy granddad.—Who invented the game ofmarbles?—MyDaddydid.(MoralJudgment,MJ,p.55)

We see that the child believes that the rules emerged, fully formed, from his father, who is so

prestigiousthathewasbornbeforehisownfather.


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Whilebelievinginthesanctityofrules,theyoungchildfromabout4to6yearsinthefirstpartof

stage1isalsowillingtoacceptchangesintherules.Heagreestoplacethemarblesinacircle,whereasa

square is theusualconvention.Thisseemsparadoxical: thechild thinks that therulesaresacredbut

easilyconsentstotheirmodification.Piagetfeelsthatthechild’sacceptanceofchangesisonlyapparent.

Hehassuchapoorgraspofwhattherulesarethathebelievesthechangestobemerelyalternativeand

quitelegitimateversionsoftherules.Inotherwords,thechildconsentstoalterationsonlybecausehe

doesnotknowthattheyreallyarealterations.

In the latterpartof the firststage(fromabout6 to10years), thechild’sknowledgeof therules

increases,andheisconsequentlyabletorecognizearealchangeintheruleswhenitisproposed.Now

herefusestoacceptthesealterationsandassertsthattherulesareimmutable.Forexample,Piagetasked

oneboyof6yearstoinventanewgame,andherefused,saying“I’veneverinventedgames.”Then,after

Piagetsuggestedanewgameofmarblestohim,theboyplayeditforatime.Butwhenasked,“Couldthis

gameeverbecomeafairgame?”theboyresponded“No,becauseit’snotthesame[astheusualgameof

marbles]”(MJ,P-60).

If you will recall, many of the children who are in stage 1 of the conception of rules are

simultaneouslyinstage1ofthepracticeofrules(egocentrism).Thismeansthatatthesametimethatthe

childbelievestherulestobesacredandimmutable,healsodoesnotknowthemtoowellanddoesnot

followthem.Againweseemtobefacedwithaparadox:howcanheplacesomuchfaithinthesamerules

that he consistently breaks? To understand this apparent contradiction,wemust consider the child’s

acquisitionofrules.Usuallyhelearnsthemfromanolderchildwhomheconsiderssimilartoadults,and

whomhethereforeimbueswiththesamerespectandauthoritythathegivestoadults.InPiaget’sterms,

there is a relationship of constraint or unilateral respect between older and younger children; the

former’sauthority isunconditionallyacceptedso that theyoungerchildassigns to therules thesame

authoritythatheconsiderstheolderchildtohave.Sincetheadultandtheolderchildareconsidered

infallible,soaretheruleswhichtheypropagate.Inaddition,theyoungchildisegocentric.Aswesawin

the case of language, he cannot take thepoint of viewof others. Since he iswrappedup in his own

concerns,hecannotunderstandthevalueofruleswhichprotecttheinterestsofothers.Itisnotsomuch

thatheisselfish;ratherhedoesnotperceivethelegitimateneedsthatotherpersonshave.Sincethisis

so,hedoesnotunderstandthepurposeofrules.Forhimtheyaremerelyexternalthingswhichcannotbe


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changed.

Wecansay,then,thattheyoungchildimbuesruleswithabsoluterespectsincetheyderivefroma

prestigiouspersonandthatheseestherulesasexternalobjectswhichcannotbechangedbecausehis

egocentrismpreventshimfromunderstandingthepurposeofrules.

Piagetthennotesthatallofthefactorsmentioned—therelationofunilateralrespect,egocentrism,

theconceptionoftherulesasauthoritativeandexternal—preventtheyoungchildfromparticipationin

theformationofrules.Sincetheyoungchildcannotassumetheolderchild’spointofview,howcanhe

cooperate indeveloping fairrules?Because theyoungchilddoesnotparticipate inmaking therules,

theyremainquiteexternaltohim.Therulesarenotreallyhis;theyareakindofforeignbodyimposed

onhim.Itshouldcomeasnosurprisethattheydonoteffectivelytransformhisbehavior.Inotherwords,

becausethechildhasnotcooperatedindevisingtherules,hedoesnotunderstandthemand,therefore,

isnotabletofollowthem.

Inthesecondstageoftheconceptionofrules,beginningatabout10or11years,thechildbelieves

that the rules can be changed, that they originated through human invention, and that they are

maintainedonlybymutualconsentamongequals.Consequently,thechildwillagreetoamodificationof

thegamesolongasalloftheotherplayersagree,andsolongasthechangeisafairone.Sincehehimself

participatesasanequalintheinventionofnewrules,hefeelsobligatedtofollowthemanddoesso.

Toexplaintheshiftfromtheabsolutisticmoralityoftheyoungerchildtotheflexibilityoftheolder

child,Piagetproposesasociallearningtheory.HebeginsbynotingthatasthechildinWesternsociety

growsolder,hebecomesprogressivelyfreeofparentalandotheradultsupervision.Duringthefirstfive

yearsorsooflife,thechildisverycloselytiedtohisparents.Afterthatpointhegoestoschool,spendsan

increasingamountoftimewithpeers,andgenerallyassumesgreaterresponsibilityforhisownlife.As

theseeventstakeplace,thechildgraduallylearnstomakedecisionsforhimselfanddoesnotnecessarily

acceptasauthoritativetheviewsofotherpersonswhoarenowconsideredhisequals.Inotherwords,the

child escapes from the attitude of unilateral respect toward elders and begins to adopt a position of

mutualrespect.Asaresultofthisdevelopmenthedoesnotunquestioninglyacceptrulesasbindingand

immutable.Becausehenowseeshimselfastheequalofothers,hedesirestoassistintheformationand


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modificationofthemoralcode.

Anotherandrelatedfactorinfluencingthedeclineoftheabsolutisticconceptofrulesisthechild’s

increasingcontactwithpergentpointsofview.As thechildwidenshissphereofcontactsbeyondthe

immediatefamily,hediscoversthatthereareperseandconflictingopinionsandcustoms.Hefindsthat

not everyone accepts the views promulgated by his parents. This conflict betweenwhat he has been

taughtandwhatotherpeoplebelieve forces thechild toreassesshisownpositionand toresolve the

differencesinopinion.Inattemptingtodoso,thechildreasonsaboutrulesandcomestotheconclusion

thattheymust,tosomeextent,bearbitraryand,therefore,changeable.

Tosummarize,ashegrowsolderthechildevolvesfromapositionofsubmissiontoadultstooneof

equality. He also is confronted with beliefs contradictory to those he has been taught. Both these

experiencesinfluencethechildtoseerulesashavingahuman,andhencefallible,origin,andtoagreeto

participateintheirformationandalteration.Sincethechildnowhasahandintheformationofrules,

theynolongerexistasaforeignentityimposedonhisconscience;theynolongerexistasacodewhich

maybeunquestionablyrespected,occasionallyobeyed,andseldomunderstood.Thechildnowchooses

tofollowruleswhicharehisownoratleastfreelyagreedupon.

Piagetgoesontoexaminethedevelopmentofjudgmentsconcerningexplicitlymoralsituations.To

study this he told children stories which posed a moral dilemma and asked them to resolve it. For

example,ifachildstolesomeapples,whatwouldhispunishmentbe?InthiswayPiagetattemptedto

discover the child’s conception of justice, punishment, lying, and similar matters. To illustrate these

investigations,wewillfocusontheconceptionofgoodnessandnaughtiness.

Piagetpresentedhissubjectswithaseriesofstoriesoftwotypes.Inonestory,thecentralcharacter

performed an actwhich unintentionally resulted in considerable damage; in the other, he caused a

negligibleamountofdamageasaresultofadeliberatelyimproperact.Thesubject’staskwastodecide

whowasgoodandwhowasnaughty.

Hereisanexampleofthefirsttype:

AlittleboywhowascalledAugustusoncenoticedthathisfather’s inkpotwasempty.Onedaythathisfatherwasawayhethoughtoffillingtheinkpotsoastohelphisfather,andsothatheshouldfinditfullwhenhecame


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home.Butwhilehewasopeningtheinkbottlehemadeabigblotonthetablecloth.(MJ,p.122)

Thecorrespondingstoryinvolvingnegligibledamageisasfollows:

TherewasalittleboycalledJulian.HisfatherhadgoneoutandJulianthoughtitwouldbefuntoplaywithhisfather’sinkpot.Firstheplayedwiththepen,andthenhemadealittleblotonthetablecloth.(MJ,p.122)

After telling eachpair of stories, Piaget askedwhether the two childrenwere equally guilty, or

whichofthetwowasthenaughtierandwhy.Heusedtheclinicalmethodtoprobethechild’sresponses.

The results were that until the age of 10, children give two kinds of answers. One of the answers

maintainsthatthecharacter’sguiltisdeterminedbythenatureofhismotives.Theboywhowantedto

helphisfatherbutcausedagreatdealofdamageislessguiltythantheboywhoengagedinanimproper

actwhichresultedinnegligibledamage.Piagetcallsthisa“subjective”conceptionofresponsibilitysince

thechildtakesintoaccountthemotives(thesubjectivestate)ofthecharacter inthestory.Thesecond

typeofjudgmentfoundinthisstage(andfound,moreover,inmanyofthesamechildrenwhosometimes

giveasubjectiveanswer)islessmature.Thisanswermaintainsthatthecharacter’sguiltisdetermined

notbyhismotives,butbythesheeramountofdamagehehascaused.Theboywhowantedtohelphis

fatherisneverthelessguiltybecausehemadealargestain,whereastheboyplayingwiththepenisnot

guiltysincehisstainwassosmall.Considerthisprotocol,fromagirlof7years:

Whichisthemostnaughty?—Theonewhomadethebigblot.—Why?—Becauseitwasbig.—Whydidhemakeabigblot?—Tobehelpful.—Andwhydidtheotheronemakealittleblot?—Becausehewasalwaystouchingthings.Hemadealittleblot.—Thenwhichofthemisthenaughtiest?—Theonewhomadeabigblot. (MJ,p.126)

Itisevidentfromtheprotocolthatthechildwasperfectlyawareofeachcharacter’sintentions,and

yet ignored them.Whatdeterminesguilt isnot intentionbutquantityofdamage.Piagetcharacterizes

sucharesponseasacaseofmoralrealism.Thejudgmentis“realistic”inthesensethatthecriterionof

guiltisnotsubjective(theintention)butmaterialor“real”(theamountofdamage).Thechildconsiders

onlythefactsofdamage,notthesubjectivestateofmotive.Also,thechild’sjudgmentobservestheletter

andnotthespiritofthelaw.Therule(inthiscase,“Thoushaltnotspillink”)isanabsolute,sothatany

actionwhichconformstoitisgood,andanywhichdoesnotisbad.

Piagetfindsthattheyoungchild’smoralrealismispervasive.Considerthedefinitionofalie.One

6-year-oldgaveatypicalresponseinsaying:“It’swhenyousaynaughtywords”(MJ,p.141).Hewenton


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toagreethat“fool”isaliebecauseitisawordyoushouldnotsay.Weseethenthatthechild’sdefinition

is“realistic”:alieisabadthinganddoesnotatallrefertotheintentiontodeceive.Asecondexample

concernsyoungchildren’scomparisonofthemagnitudeoflies.TostudythissortofjudgmentPiagetread

thechildrentwostories.Inonestoryaboywasfrightenedbyadogandtoldhismotherthatthedogwas

“asbigasacow.”Inasecondstoryaboydeliberatelydeceivedhismotherabouthisschoolgrades.Young

childrenoftenmaintainedthatthestoryaboutthedogwasagreaterliethanthestoryaboutthegrades.

Thereasonwasthatseeingadogthesizeofacowwasalessprobableeventthangettinggoodgrades.In

thecaseofthedogthereisamuchgreaterdiscrepancybetweenactualfacts(therealsizeofthedog)and

thelie(thedogbeingaslargeasacow)thaninthecaseofgrades,wherethelie(agoodgrade)seems

almostaslikelyasthefact(abadgrade).Inotherwords,seeingadogaslargeasacowisfarlesslikelyto

occur than having good grades and, therefore, appears to be a bigger lie. Intention to deceive is

irrelevant,andtheimportantcriterionhastodowiththeprobabilityofoccurrenceoftheevents.Thusthe

youngchild’s judgmentof liesisas“realistic”ashisdecisionconcerninggoodnessandnaughtiness.It

focusesontheexternalormaterialaspectofthequestionandfailstotakeintoaccounttheintentionalor

subjectiveaspect.

Whydoesasignificantproportionoftheyoungchild’sresponsesinvolvemoralrealism?Partofthe

reasonisprobablythatparentsaresometimes“realistic”themselves.Someadultspunishthechildmore

forbreakingfifteencupsunintentionallythanforpurposelydestroyingonecup.Butthisisnotthewhole

story.Parentspunishastatement intendedtodeceive(areal lie)morethanamereexaggeration(for

example,thedogasbigasacow).Thechild,however,thinksthattheexaggerationisnaughtierthanthe

intentiontodeceive,soitseemsthatthechild’sjudgmentdoesnotsimplyreflectthepunishmentswhich

hehasactuallyreceivedfromadults.Itisapparent,then,thattwoadditionalfactorsareinvolved.One

factor is therelationofunilateral respect.Since theparent is respected, soarehisrules. If theparent

forbidsthebreakingofcups,thentheactofdoingsoisbadregardlessofintention.Anotherfactoristhe

child’segocentricpatternsofthought.Sincehecannotassumepointsofviewdifferentfromhisown,he

cannotseetheother’sneedfortruth,andconsequently,heisnotawareofthefactthathis“lies,”inwhich

hehimselfoftenappearstobelieve,aredeceivingthelistener.Unilateralrespectandegocentrism,then,

contributetomoralrealismjustastheydototheconceptofrulesasinviolableandsacred.

Thechildgraduallyabandonsmoralrealisminfavorofamore“subjective”approach.Injudgments


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ofgoodnessandnaughtinesshefocusesonmotivation,notextentofdamage.Injudgmentsoflyinghe

considerstheintentiontodeceive,notjustthelikelihoodthattheeventcouldhaveoccurred.Aswasthe

case in the conceptionof rules, the child’sprogress isdue largely tohisnew independence from the

family,tohisincreasedinteractionwithothers,tohiscontactwithpergentviews,andtosimilarfactors.

We may make severed comments concerning moral behavior and judgment. First, Piaget

emphasizes that thevariousstagesoverlap, that thesamechildmaybe inbothstagessimultaneously

dependinguponthecontentofaparticularsituation,andthatprimitive formsofmoral judgmentare

oftencharacteristicofadultsaswellaschildren.Neitherthestagesnorthecourseoftheirdevelopment

areclear-cut,andPiagetdoesnotwishtogiveanimpressionoforderlinesswherelittleistobefound.

Second,Piaget’s social learning theory—thatprimitivemoral judgmentderives in fact fromunilateral

respectandmatureconceptionsfromcooperationandsimilarfactors—isspeculativebecausethereisno

direct evidence linking adult constraint with moral realism. Nevertheless, the theory points in

interesting directions. The effect of the social environment on intellectual processes has hardly been

considered.Undoubtedlythetheorywillrequireclarificationandelaboration,particularlywithregardto

thereciprocaleffectwhichseemstoexistbetweencooperationandthediminutionofegocentrism.Does

the child take the other’s point of viewmainly because the two persons interact, or do they interact

mainlybecausetheycaneachtaketheother’spointofview?Or,asseemsmoreplausible,coulditbethat

thereisacomplexrelationshipbetweencooperationandthepassingofegocentrism?

AthirdcommentisthatPiaget’stheory,likeFreud’s,issomewhatpessimistic.AccordingtoFreudit

is inevitable for both social and biological reasons that the childwill experience anOedipal conflict,

whichwillresultintheadoptionofaharshandauthoritariansuperegoorconscience.ForPiaget,too,it

seemsinevitablethattheyoungchildwilldisplayegocentricthoughtandthathewillstandinarelation

ofunilateralrespecttotheadult.Egocentrismdefinescertainpropertiesofthoughtobservedinyoung

childrenwhichappeartobeunavoidableandwhichmustbeovercomebeforethechildcanreachamore

mature level of cognitive functioning. Unilateral respect is inevitable too; even if the parent tries, he

cannotcreateatotalatmosphereofmutualrespect.Theparentmustarbitrarilyimposeuponthechild

someregulationsbecausethechildcannotunderstandtheircomplexrationale.Sinceegocentrismand

unilateralrespectareinevitable,soistheirproduct,moralrealism.


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AfourthcommentisthatPiagethasnotyetfullydemonstratedthatthemoraljudgmentselicitedby

his questioning on stories correspond to moral judgments in "real life." Piaget’s arguments may be

convincing—forexample,thatchildrentakethegameofmarblesseriously—butnoamountofargument

canresolvetheissue.Whatisrequiredisnaturalisticstudy.Weneedtoseewhethermoralrealism,for

example,isindeedfoundinchildren’smoraljudgmentsinthenaturalsituation.

A fifth comment concerning moral behavior and judgment is that Piaget’s work has certainly

fulfilleditsoriginalpurpose:tostimulatefurtherexperimentationandtheorizing.Moraljudgmenthas

been a popular topic for research, and in the main, independent investigators’ findings have been

consonantwiththoseofPiaget.1

Reasoning

Piaget’searlyworktoucheduponthechild’sreasoning,too.Theresearchagainwaspreliminary,

andasweshallseeinChapter4,helaterintensivelyelaborateduponthesametopics.Atthispointwe

willconsiderseveraltypesofreasoning:syncretism,juxtaposition,andordinalandpart-wholerelations.

InoneofhisstudiesPiagetpresentedthirty-five9-year-oldboysandgirlswithaseriesofproverbs

andacollectionofexplanatorysentences.Thechild’staskwastoconnecteachproverbwiththeproper

explanatorysentence.Forexample,oneproverbis,“Drunkenoncewillgetdrunkagain.”Thesentence

which expressed the same idea is, “It is difficult to break old habits,” and not, “Some people are

continuallydrunk.”Piagetalsoquestionedeachchildconcerningthereasonsforhischoice.

One8-year-oldchildsaidthatthesentencecorrespondingto“Whenthecat’sawaythemicecan

play”is“Somepeoplegetveryexcitedbutneverdoanything.”WhenPiagetaskedhisjustification,he

responded:

Becausethewordsareaboutthesame. . . . Itmeansthatsomepeoplegetveryexcited,butafterwardstheydonothing, theyare too tired.Thereare somepeoplewhoget excited. It’s likewhen cats runafterhensorchicks.Theycomeandrestintheshadeandgotosleep.Therearelotsofpeoplewhorunaboutagreatdeal,whogettooexcited.Thenafterwardstheyarewornoutandgotobed.(LT,p.149)

Thechild’sprocessofreasoningiscertainlyveryconfused.Onewaywemaycharacterizeit is in

termsof syncretism, a tendency to connect a series of separate ideas into one confusedwhole. In the


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present case the child tries to tie together an absent cat with excited people. The child assigns to

disparatethingsasimilaritywhichisalmostunfathomabletotheadult.Howdoesthetendencytoward

syncretismwork?AccordingtoPiaget,whenthechildreadstheproverbheconstructsaninterpretation

ofit.Thisinterpretationmaybeonlylooselyrelatedtotherealmeaningoftheproverbbecausethechild,

ineffect,freeassociateswhenhehearsthewords.

Inthecaseofthesubjectwhoseprotocolwasjustdescribed,subsequentquestioningrevealedthat

heinterpretedtheproverbasmeaning“Thecatrunsafterthemice.”Thechildthensearchedamongthe

alternativesentencestofindtheonecorrespondingtotheproverb.Hisinterpretationorunderstanding

guidedthisprocess,sothatheviewedthesentencesintermsofhisinterpretationoftheoriginalproverb.

InPiaget’sterminology,thechildassimilatesthesentencesintotheschemewhichoriginallycontributed

towardhisunderstanding.Thesubjectcitedthusperceivedasimilaritybetweenhisunderstandingof,

“Thecatrunsafterthemice,”andthesentence,“Peoplegetexcited.”Then,afterthechildhasinterpreted

aproverbandseenarelationbetweentheinterpretationandasentence,hesaysthatthesentenceand

theproverbhavethesamemeaning.Bymeansofanintermediary—theschemewhichenabledhimto

understand in the first place—he has conglomerated two apparently disparate items. In a sense,

syncretismisacaseofassimilationgonewild.Thechilddoesnotaccommodatetotherealmeaningofthe

proverb;rather,heassimilatesitintohisownscheme,andthenhegoesoninthesamewaytoassimilate

thesentenceintothisschemetoo.

Nowwewill consider thephenomenonof juxtaposition. If youwill recall, in his study of verbal

communicationPiaget found thatyoung children seldomexpress causal relations. Indescribing some

mechanicaldevice,thechildmerelysaysthataandboccurred;hedoesnotsaythatacausedb.Insteadof

beingrelatedonetotheother,thetwoeventsaremerelyjuxtaposed,thatis,placedoneaftertheother.

Toinvestigatethismattermoredirectly,Piagetperformedanexperimentonfortychildrenfromabout6

to10 years of age.He gave each child an incomplete sentence endingwith theword “because,” and

askedhimtocompleteit.Forexample,hemightask,“Watergetshotbecause...”.Ifthechildanswered,

“thefirewasturnedon,”thenPiagetmightcontinuebyasking,“Andthefirewasturnedonbecause..

.’’.In thisway, he attempted todetermine if children coulduse thenotionof causalitywhen they are

almost directly asked to do so. The responses to the sentences and to clinical questioning revealed a

frequentinabilitytoexpresscausalrelations.Herearesomeexamples:2


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themanfellfromhisbicycle,becausehebrokehisarm....Ihadabath,becauseafterwardsIwasclean....I’velostmypenbecauseI’mnotwriting....Hefelloffhisbike,becausehefellandthenhehurthimself. (JudgmentandReasoning,JR,pp.17-18)

At leasttwoexplanationsofthechild’sresponsesarepossible.Accordingtooneexplanation, the

child’sanswersexpresssophisticatedrelationships.Thesentence“Ihadabath,becauseafterwardsIwas

clean”means“WecantellthatIhadabathbecauseafterwardsIwasclean”or“Mycleanlinessimplies

that I had taken a bath.” A second interpretation of the same sentence is that the child has a poor

understandingofcausality:hereversescauseandeffectandmerelyjuxtaposesoneeventaftertheother.

Which explanation is correct? A number of factors seem to support the second interpretation,

juxtaposition.Inhisnaturalspeechthechildseldomusestheword“because”orothersimilarwordsto

expressrelations,causalorotherwise,betweenevents.Also,someoftheanswerstoPiaget’stestdonot

revealsophisticatedrelationshipsofthetypeproposedbythefirsthypothesis.Anexampleis,"Hefelloff

hisbike,becausehefellandthenhehurthimself."Thisstatementdoesnotdirectlyconnectfallingwith

injury;thetwoeventsaremerelyjuxtaposed.Themoreaccurateinterpretationofthechild’sresponses

seemstobethattheyrevealafailuretoperceivecausality(letalonemoresophisticatedrelations)and

indicateatendencymerelytoplaceeventsoneaftertheotherwithoutspecifyingtherelationsamong

them.

Juxtaposition can also be seen in another anddifferent context, namely, the child’s drawing. In

depictingabicycle,forinstance,thechilddrawsmanyofthepartsbutdoesnotsynthesizethemintoa

properwhole.Hemaydrawthechainbutnotconnectittothewheel;hemaydrawtheseatbutnotattach

ittotheframe.Weseethatthechildconsidersonlyisolatedeventsandignorestherelationsbetween

them.

Sincesyncretismandjuxtapositionseemtobeopposites,theirsimultaneousexistenceintheyoung

childposesaparadox.Howcanthesamechildbothignorethepartsinfavorofthewhole(syncretism)

and ignore thewhole in favorof theparts (juxtaposition)?Piaget attempts to resolve theparadoxby

arguing that both juxtaposition and syncretism are expressions of a common mode of thought—the

inabilitytothinkaboutseveredaspectsofasituationsimultaneously.Juxtapositioninvolvesfailingtosee

anyrelationamongthepartsofawhole,andtheresultisthattheyareseenasdiscreteandunrelatedto

eachother.Thechildisthusunabletothinksimultaneouslyaboutthepartsasseparatethingsandabout


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therelationswhichunite them.Similarly, in theuseofsyncretism, thechildperceivesawholeor the

commonrelationships,butfailstorecognizethedifferenceswithinthewhole.Healsohasfocusedonone

aspect of the situation at the expense of the other. In other words, since the child cannot focus

simultaneouslybothonthedifferencesamongthingsandontheircommonrelationships,heisapttosee

either a succession of unrelated events (juxtaposition) or a conglomerated whole (syncretism). Both

typesofdistortionsresultfromthesamedeficiencyinthought.

InyetanotherinvestigationPiagetstudiedrelationalthinking.Hepresentedanumberofchildren

withthisproblem:“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichis

thedarkest,Edith,Suzanne,orLili?”(JR.,p.87).TheproblemineffectinvolveswhatPiagetwaslaterto

callordinalrelationships. Supposewe know thatb is a smellier number than c and thatb is a larger

numberthana.Whichisthelargestnumber?Theanswer,ofcourse,isc.IfwesubstituteLilifora,Edith

forb,andSuzanneforc,and“haslighterhairthan’’ for“isasmallernumberthan,”thenwehavethe

sameprobleminthetwocases:bothdealwiththeunderstandingofrelationsofordering,whetherthese

beintermsoflightnessofcolor,sizeofnumber,andsoon.Bothproblemspresentthechildwithpartial

informationconcerningtheordering(e.g.,thatb<candb>a)andaskhimtodeducetheentireordering

(thata<b<c).Piagetfoundthatchildrenevenasoldas13yearsfoundtheproblemtobeverydifficult.

Forexample,a9-year-oldsaid:“Youcan’ttell,becauseitsaysthatEdithisthefairestandthedarkest”(JR,

p. 88). Piaget again explains their difficulty in terms of an inability to consider severed aspects of a

situationsimultaneously.Itisbecausethechildcannotatthesametimefocusonb<candb>athathe

failstodeducea<b<corthatSuzanneisthedarkestofthelot.

Another investigation yielded remarkably similar results. The study dealt explicitly with the

relationsoftheparttothewhole.Theaimwastodiscoverwhetherthechildbelievedthatthepartwas

includedin thewhole.Thequestionswerephrasedintermsoftherelationsbetweencities(theparts)

andcountries(thewhole).Hereisanexample:

Stu(7;8)saysthat“GenevaisinSwitzerland”andthat“Switzerlandisbigger[thanGeneva],"ButGenevansarenot Swiss. “Then where must you come from to be Swiss?”—“From Switzerland.” We draw a circlerepresenting Switzerland, and ask Stu to put the cantons in their places. . . . Stu inscribeswithin the circlethreeorfoursmallerones—Geneva,Vaud,etc.,buthestillmaintainsthatGenevansarenotSwisspeople.TheSwissaretheinhabitantsofthebigcircle.(JR,p.123)


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Notethatattheoutsetthechildseemstomaintainthatthecityispartofalargerwhole(“Genevais

inSwitzerland”).Butwhenheisquestionedaboutthematter,hedeniesthatGenevansareSwissorthat

the part is in fact included in the whole. The child again sees part andwhole separately: they are

unrelatedentities.

We see in summarizing that Piaget’s studies of reasoning find that the child has a tendency to

grouptogethervariousdifferenteventsintoalooseandconfusedwhole(syncretism),thathesometimes

fails to see the relations among separate events (juxtaposition), that he fails to understand ordinal

relations, and that he cannot dealwith the relations between a part and thewhole ofwhich it is a

member.Allthesetypesofreasoningrevealacommondeficiency:aninabilitytothinksimultaneously

aboutseveralaspectsofasituation.

Piagetmakesanextremelyinterestinggeneralcommentabouthisinvestigations.Hepostulatesthat

hisfindings,sincetheyaretheresultsofquestioningchildren,holdtrueonthe“planeofverbalthought”

butnotonthe“planeofaction.”That is,whilechildrenmayfailaproblemwhenitssolutionrequires

verbalexpression,theymaybequiteabletodealwiththesamedilemmaonapractical,behaviorallevel.

Whilethechildfirstsolvesproblemsontheplaneofaction,hethenmustrelearnhissolutionsonthe

planeofverbalthought.Inasense,actionismoreadvancedthanverbalthought(forthechildfrom7to

11years);thelatterlagsbehindtheformer.Piagettermsthelagaverticaldécalage.Theverticalityrefers

toanascendingagescale:whatthechildlearnsatage7ontheplaneofaction,hemustrestructureatage

11ontheplaneofverbalthought.“Décalage”referstothegaporlag.

GENERAL SUMMARY AND CONCLUSIONS

Piaget’s early work is greatly varied. The first studies deal with the child’s use of language.

Naturalisticobservationrevealsthatchildrenyoungerthantheageof7yearsoftenfailtousespeechasa

vehiclefortransmittinginformationtooneanother,andinsteadfrequentlyrepeatanother’sremarksor

engage in inpidual or collective monologues. An experiment confirms these findings: when young

childrenaregiventheexplicittaskofconveyinginformationtoanotherchild,theyfailtocommunicate.

Theydonot consider the informationalneedsof the listener.Moreover, the listenerdistortswhat the

speakersaysbygivingitidiosyncraticinterpretations.


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InotherinvestigationsPiagetusestheclinicalmethod.Herejectsthetestingapproachbecauseofits

rigidityandrejectsthenaturalisticapproachbecauseofitsfailuretoyieldasufficientamountofrelevant

information.Theclinicalapproach,hefeels,ismoreflexibleand,therefore,isespeciallywellsuitedto

theexploratoryaimsof initialstagesofresearch.Heusestheclinicalmethodto investigatethechild’s

conceptionoftheworld,andfindsthatthechildexhibitsseveralprimitivethoughtpatterns.Animism is

thetendencytoconsidernaturaleventstobealiveinthesamesenseashumanbeingsare.Artificialism is

the tendency tobelieve thatsomeagent—humanorpine—creatednaturalevents.Participation is the

vagueideathathumanactionsandnaturalprocessesinteractandarerelated.

Afurtherstudy,againusingtheclinicalmethodinpart,dealswithmoraljudgmentandbehavior.

Childrenbelowtheageof7yearsfailtofollowtherulesofagamewhileatthesametimebelievethatthe

rulesaresacredandinviolable.Olderchildrendisplaybothagreatertendencytofollowtherulesandto

believe that theycanbechanged. Inexplicitlymoral situations,youngchildrenbelieve thatguiltand

moral responsibility are determined not by intention but by the amount of damage produced. These

“realistic”moraltendenciesareseeninthecaseoflyingaswell,anddeclinewithage.

Instudiesofreasoning,Piagetfindsthattheyoungchild’sthoughtischaracterizedbysyncretism,

thetendencytogrouptogetherintoaconfusedwholeseveralapparentlyunrelatedthingsorevents,and

byjuxtaposition,thefailuretoseetherealconnectionsamongseveralthingsorevents,andthefailureto

understand either part-whole or ordinal relations. All these tendencies reflect a common pattern of

thought:theinabilitytoconsiderseveralaspectsofasituationsimultaneously.

Piagetemploysasociallearningtheorytoexplainthechild’sdevelopmentparticularlyintheareas

oflanguageandmoraljudgment.Hepostulates,forexample,thatthechild’sprimitivemoraljudgmentis

theresultofegocentricthoughttendenciesandtherelationofunilateralrespecttowardtheadult.The

child’smoraljudgmentbecomesmorematurewhenheadoptsapositionofmutualrespecttowardadults

andcomesintocontactwithnewsocialinstitutionsandpointsofview.

ThereareseveralcommentswemaymakeconcerningPiaget’searlyresearch.First,whatarethe

relations among the various findings? The young child is egocentric in communication, has an

absolutisticconceptofrules,isrealisticinhismoraljudgment,andinhisreasoningdisplayssyncretism


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andjuxtaposition.Thesevariedtermsatfirstmayseemtorefertodifferentandunrelatedphenomena.

Onemightthinkthatmoralrealismandsyncretism,forinstance,refertodifferentpatternsofthought,

andthatthereisnocommonalitybetweenthem.ButPiagetfeelsthatsuchaviewismistaken:thereis

indeed a strong similarity amongmany of the young child’s reactions to the problems posed by the

variousinvestigations.

The common pattern underlying these apparently perse reactions is the inability to deal with

severalaspectsofasituationsimultaneously.Thisisduetotheegocentricnatureofthechild’sthoughtor

theincapacitytoshiftattentionfromonetoanotheraspectofasituation.Inthecaseofspeech,theyoung

childcannotconsiderboththeother’spointofviewandhisownatonce,andthereforecenterssolelyon

hisownpointofview.Inthecaseofrules,theyoungchildfailstoconsiderbothhisowninterestsandthe

needs of others. Consequently, he often breaks the rules. He sees the origin of rules from a limited

perspective, too. Emanating from a person whom he regards as prestigious, they must likewise be

prestigious.Thechildfailstoconsiderboththeparent’sprestigeandhisreasonsfordevisingtherules.In

thecaseofmoraljudgment,thechildcannotconsiderbothdegreeofdamageandintention,andhebases

hisjudgmententirelyontheformer.Asfarasreasoningisconcerned,wehavealreadyseenhowboth

syncretismandjuxtapositionareexpressionsofasingletendency,namely,thatoffocusingonalimited

aspectoftheproblem.Thesamemaybesaidoftheunderstandingofordinalandpart-wholerelations.In

theformer,thechildconsidersonlycertainpartsofrelationsbutnotothers;inthelatter,hefocuseson

thepartbutnotthewhole,orviceversa.

As thechildgrowsolderandcomes into contactwithopposingpointsofviewandvariedsocial

institutions,his thoughtgoes throughaprocessofdecentration. Inspeech,heconsidersbothwhathe

wantstoexpressandthelistener’sneeds.Ingames,heconsiderstheother’sinterestsaswellashisown

and is, therefore, willing to follow and modify the rules. In moral judgment, he considers both the

outcomesofaperson’sbehavioranditsintent.Andinreasoning,hetriestoconsiderthecomplexitiesof

problems—boththedifferencesandsimilaritiesamongthesamesetofevents.Thus,thechilddecenters

histhoughtjustasinthesensorimotorperiodtheinfantdecenteredhisbehavior.Thenewbornactsasif

theworld is centered about himself andmust learn to behave inmore adaptiveways. Similarly, the

young child thinks from a limited perspective andmust widen it. Both infant and young childmust

decenter—theformer,hisactionandthelatter,histhought.


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Inadditiontocharacterizingtheyoungchild’sthoughtintermsofcentration,Piagetoccasionally

described it inFreudian terms.Freuddescribedseveralprimitivementaloperationsusually found in

certainkindsofmentalillnessandinthedeepestlayersofthenormalperson’sunconscious.Freudfelt

thatthistypeofthinking,called“autisticthought,”displayscertainregularities.Forinstance,itshowsa

tendencytofusedisparatethingsintooneimage.Thus,inadreamwemayperceiveacharacterwhoisa

“condensation”oftwodistinctpersons.InhisearlyworkPiagetproposedthatthethoughtofthechildis

intermediatebetweenautisticandadultthinking.Forexample,thechild’ssyncretismissimilarto,but

more mature than, the tendency toward condensation. While at the beginning of his career Piaget

borrowedafewideasfrompsychoanalysis,hewasneveradiscipleofFreudbutalwaysanindependent

investigator.Astimewenton,hislimiteddependenceonFreuddiminishedfurtherwiththeresultthat

Piaget’slaterworkistotallydevoidofFreudianconcepts.

Piaget not only abandoned Freudian ideas, but became dissatisfiedwith the clinicalmethod as

administered at that time.He came to feel that it relied tooheavily on language. The child thinks in

nonverbalwaystoo,andtheexclusivelyverbalclinicalmethodwasnotalwayseffectiveintappingthese

thoughtprocesses.Consequently,heturnedtosomewhatdifferentmethodswhichwewilldescribein

thenextchapter.

Despitetheirmethodologicaldeficiencies,Piaget’searlyinvestigationsmaybeconsideredamong

themost interesting of his achievements. Themajor part of the early studies dealt with socially and

practicallyrelevantphenomena: thechild’sability to communicate information, to followrules, and to

makemoraljudgments.Allthesemattersareobviouslyimportantforthechild’spracticalsuccessinthe

worldandforhisinteractionswithothers.

Bycontrast,Piaget’s laterworkdeals,asweshallsee,withmoreabstractphenomena:thechild’s

understanding of number or classification. These have less obvious relevance to the child’s ordinary

activities.Probably,hisabilitytounderstandthecardinalityofnumbermakeslessofadifferencetohis

daily life than his ability to communicate to other children. Also, in his early books, Piaget showed a

strong interest in the role of social factors indevelopment. Later research, aswe shall see, convinced

Piagetthatotherfactorsofequalimportancewereinvolved.Withtimehisinterestshavetendedtofocus

onthesefactorsratherthanonthesocialenvironment.


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Finally,wemaynote that the explanatory conceptswhich evolved fromPiaget’s earlywork are

vague. They are stated in ordinary language and are often not entirely clear. Much confusion, for

example, has arisen over the concept of egocentrism. But as we have stated repeatedly, Piaget fully

recognized that his early conceptswere only preliminary and tentative, not final and conclusive.He

hoped that his earlyworkwould stimulate research by others, and that he himself could clarify his

conceptsatalatertime.Thefirstofhisexpectationshasbeenfulfilled:therehasbeenmuchresearchon

moral judgment, for example. We will see in the next chapter how Piaget elaborated and even

formalizedsomeofhisearlyandtentativenotions,includingordinalandpart-wholerelations.

Notes

1Forareviewofthisliterature,seeT.Lickona,ed.,MoralDevelopmentandBehavior(NewYork:Holt,RinehartandWinston,1976).

2Thesentencetobecompletedisinromantype,andthechild’sanswerisinitalic.


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4 The Years 2 through 11:

Piaget’s Later Work

ThischapterdealswithaspectsofPiaget’slaterwork(fromapproximately1940onward)onthe

childfromabout2to11years.AswasshowninChapter1,thisportionofPiaget’sresearchandtheoryis

voluminous and covers suchmatters as the child’s conception of chance, space, geometry,movement,

number,andother topics.Sincewecannotreviewall the laterworkhere,weshall focusonwhatwe

consider tobebasic issues and conceptswhich reappear in andapply to almost all ofPiaget’s recent

writings.We will consider (1) the revised clinical method, (2) the child’s classification of objects or

events, (3) the ability to place them in ordinal relations, (4) the concept of number (particularly its

conservationovertransformations),(5)thenatureofmental imagery,(6)thedevelopmentofmemory

andconsciousness,and(7)somegeneralcharacteristicsofthought.

THE REVISED CLINICAL METHOD

WesawinChapter3thatPiaget’soriginalclinicalmethodwashighlydependentonverbalizations.

Theexaminerposedthequestionsinwords,andthechildwasrequiredtogivetheanswersinthesame

way.Theexaminer’squestionsusuallydidnotrefertothingsoreventsthatwereimmediatelypresent,

andtheproblemsdidnotalwaysinvolveconcreteobjects

whichthechildcouldmanipulateorevensee.Forexample,theexaminermightdepictachildwho

had unwittingly broken some cups andmight then ask the subject being questioned for a judgment

concerningthechild’snaughtinessandthepunishmenttobemetedout.Insuchasituationasthis,the

subjectisrequiredtodoseveralthings.Hemustinterprettheexaminer’sdescriptionsoastopicturethe

scenetohimself;hemustmakeaspecialefforttocomprehendcertaincrucialaspectsofthequestion,like

theword“naughty”;andhemustexpresshisjudgmentinwords.

Aftersomeexperiencewiththismethod,Piagetcametofeelthatitwasinadequatebecauseitrelied

too heavily on language. The childmight not understand everything said to him, particularly if the


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wordsdidnotalwaysrefertoconcreteobjects.Evenifthechilddidunderstand,perhapshecouldnot

adequately express in words the full extent of his knowledge. Consequently, Piaget modified his

procedures, and the result iswhatwe shall call “the revised clinicalmethod” (sometimes called the

“method of critical exploration”). The new method involves several features. First, the examiner’s

questionsrefer toconcreteobjectsoreventswhichthechildhasbeforehim.No longermust thechild

imaginethesethingsmerelyonthebasisofaverbaldescription.Second,aneffortismadetoletthechild

expresshisanswerbymanipulatingtheobjects,andnotsolelyexpresshimselfthroughlanguage.

For example, let us suppose that the examinerwishes to knowwhether the child can form two

distinctclasses.Toinvestigatethematterhemightpresentthechildwithanarrayofcirclesandsquares

allmixedtogetherinnoorder,andaskhimtoputtogethertheonesthatbelongtogether,orsortouttwo

distinctpiles.Whatthechilddoeswiththeobjects—whatsortofpileshemakes—andnotwhathesays

aboutthem,constitutestheprimarydataofthestudy.Ifafterencouragementachildstillcannotforma

pileofcirclesseparatefromapileofsquares,thentheexaminermightconcludethathedoesnothavethe

classificationskillsunderinvestigation.Whilecompletelynonverbaltestsaredesirable,itisoftenhardto

inventthem.ThisisespeciallytrueforPiaget,sinceheusuallyinvestigatesthechild’sunderstandingof

abstractconceptsthatarenoteasilymanifestedinthebehavioralmanipulationofconcretematerials.The

revisedclinicalmethod, therefore,mustoftendepend for itsdataon thechild’sverbal responses.But

evenwhenthisisnecessary,thechild’sanswersrefertoaproblemstatedintermsofconcretematerials

whicharepresent.

Third, Piaget introduced the use of counterarguments or countersuggestions. These involve

presentingthechildwithapointofviewthatcontradictshisown,andaskinghimwhathethinksofthe

opposingview.Thepurposeofthesecounterargumentsistodeterminethestabilityandauthenticityof

thechild’sthinking.Childrenwhohavemasteredaconceptwillresistthecountersuggestion;thosewho

havenottendtobeswayedbythecontradictoryargument.

Afourthfeatureoftherevisedclinicalmethodisnotnew:theexaminer’squestioningisflexible.

Ratherthanemployastandardizedlistofquestions,hemodifiesthemoraddsnewonesasthesituation

demands.Asbefore,Piagetstillfeelsthatthereisnopointeitherinaskingachildaquestionthathedoes

notunderstandorinfailingtoclarifyananswer.


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To summarize, the revised clinical method involves posing questions concerning concrete

materials; allowing the child to “answer” by manipulating the materials, if this is at all possible;

introducing counterarguments; and, as in the earlier clinicalmethod, statingquestions andpursuing

answersinaflexibleandunstandardizedway.Whetherornottherevisedclinicalproceduregivesan

accurateassessmentofthechild’sabilitiesisamatterfordebate.Ingeneral,mostpsychologists(outsideof

Geneva) do not use this method in research, mainly on the grounds that it is not sufficiently

standardized.Wethink that thisattitude ismistaken,especiallysince thereareverygoodreasons for

avoiding standardization.1 In any event, the revised clinical method is less exclusively verbal than

Piaget’searlierprocedureandattemptstogiveanaccurateassessmentofthechild’sthoughtprocesses

whichinlargemeasuremaybenonverbal.

CLASSIFICATION

Piaget has used the revised clinical method to study classification in the child. The preceding

chaptershavealreadytouchedonthisandrelatedmatters,anditmaybeusefultoreviewsomeofthe

materialhere.Wesawthatthereisaprimitivesortofmotorclassificationinthesensorimotorperiod(0to

about2years)whentheinfantappliestoobjectsintheenvironmentabbreviationsoffamiliarschemes.

Forexample,Luciennesawatoyparrothangingabovehercribandkickedherfeetveryslightly.Thiswas

anabbreviationofaschemewhichshecouldquiteeasilyhaveappliedtothepresentsituation.Itseemed

asifheractionclassifiedtheparrotasa“thingtobeswung.”Moreover,theabbreviationshowsthatthe

behaviorwasbecominginternalized.Eventuallyitcouldbereplacedbythethought:“That’stheparrot;

that’s something I can swing.” But the abbreviated schemes are not yet instances of legitimate

classification.Onereasonisthattheschemesapplytoindividualobjectsoveraperiodoftimeandnottoa

collectionofobjects.Forexample,Luciennekickedfromtimetotimewhenevershesawparrotsandthus

indicatedrecognition.Butthis

recognitiondoesnotimplythatsheconsideredtheparrotstobelongtoaclass.Matureclassification,

on the other hand, involves the conception of a collection of things, whether they are immediately

presentorimagined.AsecondreasonwhyitisnotpossibletocreditLuciennewithclassificationhasto

do with inclusion relations, which will be expanded on shortly. Briefly, this refers to the ability to

constructahierarchicalclassification,suchthattoyparrotsareasubclassofalarger,moreinclusiveclass


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liketoysingeneral.

From about 2 to 4 years the child begins to classify collections of objects in away that is quite

primitive. He uses the preconcept. Sometimes he fails to see that one individual member of a class

remains the same individual despite slight perceptual changes, and sometimes he thinks that two

different members of the same class are the same individual. Between 5 and 10 years, the child’s

classificationisstillfaultyinseveralways.Thereisthephenomenonofjuxtaposition,theinabilitytosee

thatseveralobjectsareindeedmembersofthesameclass.Thereisalsosyncretism,thetendencytogroup

togetheranumberofdisparateeventsintoanill-definedandillogicalwhole.

As was pointed out, Piaget’s investigations of the preconcept, syncretism, and juxtaposition,

conductedinthe1920sand1930swerepreliminaryandtentative.First,thereexistedmethodological

defects:thedatawerealmostexclusivelyverbalsothatPiaget’sinterpretationwasbasedlargelyonwhat

the child said. Second, Piaget’s concepts—syncretism, juxtaposition, the preconcept—were somewhat

vagueandneededelaboration. Inthe1950sPiagetreturnedtothestudyofclassificationinthechild

fromabout2to12years.Theseinvestigationsmakeuseoftherevisedclinicalmethod;theyalsomodify

thenotionsofpreconcept,syncretism,and juxtapositionandsuggestnewwaysofconceptualizingthe

child’sclassificatoryactivities.

Some Properties of a Class

BeforeexaminingPiaget’sresearchintoclassification,wemustclearlyunderstandwhathemeans

byaclass.Supposewehavebeforeusanumberofobjectsallmixedtogether.Thearraycontainsalarge

red triangle, a small blue circle, a large pink circle, and a small black triangle. All the objects are

discriminablydifferentonefromtheother.Thatis,thereisnodifficultyinperceivingthatanyoneobject

isdifferentfromanyoftheothers.Forexample,thelargeredtriangleisveryobviouslylargerandredder

thanthesmallblacktriangle.Suppose,too,thatwewishtoplacetheseobjectsintotwodifferentclasses.

Onewayofdoingthisistoputinoneseparatepilethelargeredtriangleandthesmallblacktriangle.In

thesecondpilewouldgothesmallbluecircleandthelargepinkcircle.Iftheoriginalarraycontained

additionaltriangularobjects,regardlessoftheir


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sizeorcolor,theywouldofcoursegointhefirstpile.Similarlyallothercircularobjectswouldgoin

thesecondpile.Thetwopileseachrepresentaclass.Ofcourse,wemightclassifytheobjectsinanother

way.Wecouldputinonepilethetwosmallobjects(regardlessoftheircolororshape)andinthesecond

pilethetwolargeobjects.Thereareusuallymanydifferentclassesthatonemayformfromagivenarray

ofobjects.

Piagetmakesanumberofpointsabouttheclassesformedfromtheoriginalarray(forpurposesof

illustrationconsiderjustourfirstexample,theclassoftrianglesandtheclassofcircles):

1.Noobjectisamemberofbothclassessimultaneously.Forexample,thelargeredtriangleisintheclassoftrianglesandnotalsointheclassofcircles.Thus,theclassesaremutuallyexclusiveordisjoint.Thisholdseven if therearemore than twoclasses formed. (Forexample, wemight divide some animal pictures into the classes of lions, tigers, andelephants,allofwhicharedisjoint.)

2.Allmembersofaclasssharesomesimilarity.Forexample,thesmallbluecircleandthelargepinkcirclebothsharethepropertyofcircularity.Circularityisthedefiningproperty,thecrucialattribute,oftheclass;thatis,weincludeintheclassofcirclesanyobjectwhichiscircular.Anotherwayofputtingitistosaythatcircularityistheintensionoftheclass.Thedefiningpropertyorintensionoftheotherclassistriangularity.

3.Eachclassmaybedescribedintermsofalistofitsmembers.Insteadofdescribingaclassintermsofitsdefiningpropertyorintension(forexample,theclassoftriangularobjects),wemay simply list theobjects in the class (forexample, large red triangleandsmallblack triangle). Sucha list is theextensionof the class.Note that the listmay involveconcreteobjects(likelarge,bluecircles)orabstractideas,events,actions,andsoon(likethelistofthepartsofspeech).

4. The defining property of a class determineswhat objects are placed in it. Anotherway ofstatingthisisthatintensiondefinesextension,orthe“fieldofapplication”ofaconcept.Forexample,ifweknowthatoneclassistobeformedonthebasisoftriangularityandanotheronthebasisofcircularity,wecanpredictthecontentofthelistofobjectsineachclass.

Thesearesomefundamentalpropertiesofclasses,asPiagetdefinesthem.(Thereareothercrucial

attributestoo,likeinclusionrelations,whichwewilldiscusslater.)Piagetthenaskswhetherthechild

classifiesobjectsinaccordancewiththeseproperties.Whenaskedtogroupobjects,doesthechildform


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mutuallyexclusiveclasses?Dohisclasseshavedefiningpropertieswhichdeterminethelistofobjectsin

eachclass?

Piaget discovers three stages of development. The first two—both of which we may call

preoperational—occur roughlyduring theyears2 to7.The third stage—thatofconcrete operations—

occursroughlyfromtheyears7to11.

Stage 1

To investigate classification,Piagetperformedanumberof experimentswhichused the revised

clinicalmethod.Inonestudy,hetestedanumberofchildrenfromabout2to5yearsofage.Theywere

presentedwith flat geometric shapes ofwood and of plastic. The shapes included squares, triangles,

rings,andhalf-rings,allofwhichwereinseveralcolors.Theshapesweremixedtogetherandthechild

wastold:“Puttogetherthingsthatarealike.”Sometimesadditionalinstructionsweregiven:“Putthemso

thatthey’reallthesame”or“Putthemhereifthey’rethesame,andthenoverthereifthey’redifferent

fromthisonebutthesameaseachother”(EarlyGrowthofLogic,EGL,p.21).

Thechildrendisplayedseveralmethodsofgroupingtheobjects.Onemethod iscalledthesmall

partialalignment.Withthismethodthechildusesonlysomeoftheobjectsintheoriginalarrayandputs

them together in severalways apparentlywithout any overall guiding plan. For example, one child

beganbyputtingsixhalf-rings(semicircles)ofvariouscolors inastraight line; thensheputayellow

triangle on top of a blue square; later she put a red square in between two blue triangles; then put

squaresandtrianglesinnoparticularorder,inastraightline.Thereareseveralpointstonoteaboutthis

performance. Sometimes similarities among objects determine the collection. For example, the subject

whoseperformancewas just describedbeganwith a line of half-rings. At other times the same child

groupedthingsonthebasisofnodetectablesimilarity;thatis,sheputayellowtriangleonabluesquare,

oraredsquarebetweentwobluetriangles.Inbothofthesecases,thereisnosimilarityofeithercoloror

form.

Itisclearthatsmallpartiedalignmentsarenottrueclassesforseveralreasons.Oneofthemisthat

intension does not define extension; that is, no consistent defining property determined which


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geometric formswereput invariouscollections.Thechilddoesnotoperateunderanoverallguiding

plan like a system of rules (defining properties) which organize theway in which he arranges the

objects.

Otherchildrenofthisageusethegeometricfigurestoconstructaninterestingformorpicture.One

childarrangedanumberofcirclesandsquarestorepresentalongverticalobjectandthenproclaimedit

tobetheEiffelTower;anotherchildplacedanumberofhalf-ringsinbetweenseveredsquares,allina

horizontalline,anddescribedtheresultasabridge.Piagetcallstheseproductionscomplexobjects.Itis

obviousthatlikethesmallpartialalignments,andlikesomeothertypesofcollectionsnotdescribedhere,

thecomplexobject isnotatrueclass.Figuresarenotplaced inthecomplexobjectbecausetheyshare

somedefiningproperty;rather,extensionisdeterminedsolelybytherequirementsofthepictureunder

construction.

Inanotherinvestigation,Piagetpresentedchildrenofthesameagewithnongeometricfiguresfor

classification—little toyswhich included people, houses, animals, and so on. Once again, the results

showedaninabilitytoformclasses.Onechildputtwodollsinacradle,thentwowheelbarrowstogether,

thenahorse.Whentheexamineraskedthechild forall theobjects likeahorse,shegavehimall the

animalsandthenababyandtwotrees.Thisexampleillustratesthefactthatalthoughtheyoungchild

may perceive similarities among the objects, these do not fully determine what objects go into the

collection. That is, the child saw that all animalswere in some respect similar and gave them to the

examinerwhenaskedforobjectslikethehorse.Ifthechildhadstoppedthere,shemighthaveformeda

classwhichwasbasedonthedefiningpropertyof“animalness.”However,shewentontothrowinthe

babyand two trees.The similarity (intension) that she firstperceiveddidnot fullydeterminewhich

objectswere to be grouped together (extension). It is as if the child forgot about the initial defining

property(animalness)andthenswitchedtosomeother.

Wemaymakeseveral commentson these investigations.First, theymakeclear thenatureof the

revisedclinicalmethod.Theexaminergivesthechildconcreteobjectstoworkwith.Thetaskinstructions

andquestionsarestillverbal,ofcourse,buttheyrefertorealthingsthatthechildcanmanipulate.The

childisrequiredtosayverylittle.Mostofhisresponsesarenotverbalbutbehavioral.Hedoesnothaveto

saythatalloftheanimalsdoordonotgotogether;rather,hecanputthemtogetherorfailtodoso.


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Second,althoughtherevisedclinicalmethod isan improvementoverwhatwasusedbefore,we

wonderwhetherthetaskwasentirelycleartothechild.Theinstructions(e.g.,“Puttogetherthingsthat

arealike”)seemrathervagueandsusceptibletomanyinterpretations.Wesuspectthatdifferentmethods

of presenting the task to the child might produce entirely different results. Piaget considered this

objectionandtriedanessentiallynonverbalmethod.Hebegantoclassifytheobjectshimselfandasked

thechildtodothesamething.Theresultagainwasnottrueclassification,but“complexobjects,”andso

on.Whilethismethodwasnotsuccessful,itdoesnotexhaustthepossibilities.Otherinvestigatorshave

exploreddifferentprocedures,withsomesuccess.2

Stage 2

Childrenfromabout5to7yearsproducecollectionsthatseemtoberealclasses.Whenpresented

withthesituationdescribedearlier,onechildproducedtwolargecollections,onewhichcontainedall

thepolygonsand theother the curvilinear forms.Moreover, eachof these collectionswas subdivided

further. Thepolygons, for instance, contained separatepiles of squares, triangles, and so on, and the

curvilinearformsinvolvedseparatecollectionsofcircles,half-rings,andsoon.Thus,thechildnotonly

seemstoformclasses,butarrangesthemhierarchically,asinFigure2.Therearetwogeneralcollections

(polygons and curvilinear forms) at the top of the hierarchy, and these both branch out into several

subcollections below (squares, triangles, etc.). The child’s activities may be characterized in several

additionalways.(1)Heplacesintheappropriatecollectionalloftheobjectswhichwereintheinitial

array.Theyoungerchilddidnotdo this;he leftsomeobjectsunclassified. (2) Intension fullydefines

extension.Thatis,ifthechilddefinesacollectiononthebasisofthedefiningpropertyofcircularity,all

circlesgointothatpile,andnoneisplacedinanyotherpile.(3)Atagivenlevelofthehierarchy,similar

definingpropertiesareusedtodeterminecollections.Forexample,atthelowerlevelofthehierarchyin

Figure2,allthecollectionsaredefinedintermsofgeometricform—squares,triangles,andsoon.Itisnot

thecasethatsomecollectionsaredefinedbyformandsomebycolor.Tosummarize,itwouldseemthat

thechildfromabout5to7yearsproducesratherelaboratehierarchicalcollectionswhichdeservetobe

calledtrueclasses.


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FIGURE2Classificationofgeometricobjects.

Piaget feels, however, that the child of this stage fails to comprehend one crucial aspect of the

hierarchyhehasconstructed.Thechilddoesnotunderstandkeyrelationsamongthedifferentlevelsof

thehierarchy.Thisistheproblemofclassinclusionwhichwewillnowillustrate.Supposewearegivena

randomly organized array of blue and red squares and black and white circles. We construct an

arrangement(seeFigure3)suchthattherearetwomajorcollections(squaresversuscircles)andwithin

eachofthesetherearetwofurthersubdivisions(blueversusredsquaresandblackversuswhitecircles).

Thus,thereisahierarchywhosehigherlevelisdefinedbyshapeandwhoselowerlevelisdefinedby

color.Consider for themomentonlyone-halfof thehierarchy,namely, thesquareswhicharedivided

intoblueandred.Ifweunderstandinclusionrelations,thenwecanmakestatementsofthissort:(1)All

ofthesquaresareeitherblueorred.(2)Therearemoresquaresthantherearebluesquares.(3)There

aremoresquaresthanthereareredsquares.(4)Iftheredsquaresaretakenawayfromthesquares,then

theblueonesareleft.(5)Ifthebluesquaresaretakenawayfromthesquares,thentheredonesareleft.

(6)Allthebluesaresquares,butonlysomeofthesquaresareblue.These,then,aresomeofthepossible

statementsaboutinclusionrelations—therelationsofthepartstothewhole,ofthewholetotheparts,

andthepartstotheparts.Theymayseemveryobvious,butsodomanyotherprincipleswhichchildren

failtounderstand.


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FIGURE3Classificationofsquaresandcircles.

Piaget investigated the understanding of inclusion relations in children of various ages. Let us

considernowthechildfromabout5to7years.Piagetpresentedeachofhissubjectswithanumberof

picturesof flowersandotherthings.Thechildwasfirstrequiredtogroupthepicturesinanywayhe

wished, and then he was asked a number of questions concerning inclusion relations. The results

concerning spontaneous classification replicatedwhatwas found earlier: the child from5 to 7 years

constructscollectionswhichseemtoinvolveahierarchy.Onechildformedtwolargecollections:flowers

versusotherthings;thenhefurthersubdividedtheflowersintoprimulasversusotherkindsofflowers.

IntermsofFigure4,thechildseemedtohaveconstructedthetoptwolevelsofthehierarchy.(Hedidnot

makeafurthersubdivisionintermsofyellowversusotherprimulas.)Itwouldseemthattheconstruction

ofsuchahierarchyimpliestheunderstandingofinclusionrelations.Ifthesubjectdividedtheflowers

intoprimulasversusotherkinds,musthenotunderstand that therearemore flowers than thereare

primulas? The results of Piaget’s questioning, however, point to different conclusions. Consider this

protocolofachildaged6years2months:

A little girl takes all the yellow primulas andmakes a bunch of them, or else shemakes a bunch of all theprimulas.Whichwaydoesshehavethebiggerbunch?—Theonewith theyellowprimulaswillbebigger. [Hethencountedtheyellowprimulasandtheotherprimulasandfoundthattherewerefourofeachkind]Oh no,it’sthesamething....—Andwhichwillbebigger:abunchmadeupoftheprimulasoroneofalltheflowers?—They’reboththesame.(EGL,p.102)


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FIGURE4Classificationofflowersandotherthings.

Although this child had earlier constructed a hierarchical arrangement of the materials, he

maintainedthattheyellowprimulasdidnotformasmallercollectionthantheprimulasasawholeand

thattheprimulasdidnotformasmallercollectionthantheflowersasawhole.Bothoftheseanswers,of

course,arequitewrong.Inbothcases,thepartissmallerthanthewholefromwhichitderives.

What is the explanation for the child’s inability to comprehend inclusion relations? Piaget

postulates that once the child has divided a whole into two subgroupings, he cannot then think

simultaneouslyintermsofthelargercollectionandthesubdivisionswhichhehasconstructedfromit.

For example, suppose a child divides a collection of flowers (thewhole) into primulas versus other

flowers(subdivisionsofthewhole).Whenheisasked“Aretheremoreprimulasormoreflowers?”he

mustconsiderboththeoriginalcollection(flowers)andoneofhissubdivisions(primulas)atthesame

time.Hemustcomparethe“size”ofoneagainstthatoftheother.Undertheseconditions,hefocusesor

centersonthecollectionhecansee(theprimulas)andignorestheoriginalcollection(alloftheflowers),

whichisnolongerpresent in its initialstate(acollectionoftheprimulasandotherflowersallmixed

together).Andsincehecentersonthepart,ignoringthewhole,hisanswerstoinclusionquestionsare

oftenwrong.

Stage 3

Childrenfromabout7to11yearsofagearebothcapableofconstructinghierarchicalclassifications


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andofcomprehendinginclusion.Forexample,afterconstructingahierarchy,onechildof9yearsand2

monthswasasked:

Whichwouldmakeabiggerbunch:oneofalltheprimulasoroneofalltheyellowprimulas?—Alltheprimulas,ofcourse,You’dbetakingtheyellowonesaswell.—Andalltheprimulasoralltheflowers?—Ifyoutakealltheflowers,youtaketheprimulastoo.(EGL,p.109)

Thisprotocolmakesquiteclearthechild’sabilitytothinksimultaneouslyintermsofthewholeand

itsparts(e.g.,“Ifyoutakealltheflowers,youtaketheprimulastoo”).Whilehephysicallyseparatesthe

flowersintoprimulasandotherkinds,thechildisabletoreasonbothabouttheoriginalwholeandits

part at the same time.His thought hasdecentered from exclusive preoccupationwith the part or the

whole.

Piagetalsofoundthatwhenthechildofthisagewasaskedthesamequestionsabouthypothetical

objects,thesubjectoftenfailedtogivecorrectanswers.Apparently,thechild’sclassificationisconcrete:

he understands the inclusion relations of a group of real objects, but fails to comprehend the same

relationswhenimaginaryclassesareinvolved.Thegapbetweenhypotheticalandconcretereasoningis

anotherexampleofverticaldécalage.

Wemaysummarizebystatingthatthechildfrom7to11hasreachedthemostadvancedstageas

farastheclassificationofconcreteobjectsisconcerned:hecanconstructahierarchicalarrangementand

understand the relations among the levels of the hierarchy. Piaget then proposes that this

accomplishmentcanbedescribedintermsofalogicomathematicalmodel.Letusexplorethisidea.

Rationale for the Use of a Logicomathematical Model

WehaveseenthatPiagetattemptstodescribethebasicprocessesunderlyingtheclassificationof

objectsor events.Heproposes that the stage1 child (2 to4or5years) fails to constructhierarchical

arrangementspartlybecauseafterashortwhileheforgetsthedefiningproperty(intension)whichhe

hasusedtoformacollection.Thestage2child(5to7years)canconstructahierarchybecauseofthe

ability to use a defining property to determinewhich objects go in a collection, but at the same time

cannot understand inclusion relations because of the inability to simultaneously consider several

immediatelypresentcollectionsandthelargeronefromwhichtheywerederived.Thestage3child(7to


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11years)cancorrectlyanswerquestionsconcerninginclusionbecauseofhisabilitytothinkoforiginal

classesandtheirderivativesatthesametime.

Thusfar,wehavedescribedthesebasicprocesses(theabilitytothinksimultaneouslyofsubclasses

andlargerclasses)intermsoftheordinarylanguage.Manypsychologistsbelievethatthisistheproper

procedure;butothers,includingPiaget,feelthatdescriptionsofstructureshouldbephrased,asmuchas

possible,inaformallanguagelikemathematics.

Letusconsiderfirst,however,someaspectsoftheuseofthecommonlanguage.Mostpsychological

theorieshavebeenstatedinthisway.Freud,forexample,wroteexclusivelyinGermanandnotinlogic

nor mathematics, and no doubt there is not a single formula in the entire corpus of psychoanalytic

doctrine.AnotherexamplefromanotherpointonthepsychologicalspectrumisTolman,anexperimental

psychologist,whoproducedhistheoriesoflearninginordinaryEnglishandmadeuseofonlyafew(and

nonessential) symbols.TolmanandFreudarehardly isolatedexamples.Today, too, themajorpartof

psychological theorizing is done in English, or Russian, and so forth. Several advantages are usually

claimedforthisprocedure.Theordinarylanguagemaybericherandsubtlerthanformallanguages,and

alsoitisgenerallyeasiertoreadthanmathematicsorlogic.

However,anotherapproachtothisproblemispossible.Piagetfeelsthatforscientificpurposesthe

ordinary language is fundamentally ambiguous and must be supplemented by formal approaches.

Anyoneevenslightly familiarwith thehistoryofpsychologyknows thatmost, ifnotall,psychological

theories stated in the common languagehavebeenvagueandeasily susceptible tomisinterpretation.

Even today there aremany fruitless arguments over themeaningofwords like “concept” or “ego” or

“learning.”Asanexample,letusconsidertheword“thought,”whichwehaveusedwithoutdefinition

quitefrequently.Nodoubt“thought”meansquitedifferentthingstodifferentreaders.Tosomeitmay

mean “ideas,” and to some “consciousness”; to others it may mean “mental effort,” “meditation,”

“concentration,”“opinion,”andsoforth.Isitanywonderthatagivenpsychologicaltheorywhichuses

words like this will elicit a variety of interpretations and, hence, considerable argument and

misunderstanding?PerhapsaprimeexampleofthedifficultyisPiaget’sownuseofverbaltheoriesinhis

earlywork.Considerableconfusionstillsurroundstheterms“egocentrism,”“moralrealism,”andsoforth.


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Piaget feels, then, that the ordinary language produces obscure and ambiguous psychological

theorizing, andmust therefore be supplemented, if not replaced, by othermodes of description. The

physical sciences have convincingly shown that mathematics is an extremely powerful tool for

communicating certain precise ideas. Piaget—along with increasingly large numbers of other

psychologists—feelsthatitwouldbefruitfulforpsychologytoadoptasimilarapproach,andhehimself

has attempted to do so in the case of classification and othermatters. Let us now explore his formal

descriptionofthestructureofclassification.

FIGURE5Classificationhierarchy.

Grouping I

The formal description called a Grouping3 begins with this situation: we have a classification

hierarchyofthesortconstructedbythe7-to11-year-oldchildreninPiaget’sexperiments(seeFigure5).

Thisiswhatwestartwith(thatis,itisagiven)andtheGroupingdescribeswhatthechildcandowith

thehierarchy.Atthetopofthehierarchythatthechildhasconstructedarethetwoclasses,flowerswhich

weshallsymbolizeas(C)andotherthings(C').Onthemiddlelevelofthehierarchywefindprimulas

(B)andotherflowers(B').Onthelowestlevelthereareyellowprimulas(A)andprimulasofothercolors

(A').Eachoftheclasses(A,A',B,B',C,C')isanelementofthesystem.Thereisonebinaryoperatorthatmay

beappliedtotheelements,namely,combining.Wewillsymbolizecombiningby+,althoughthereader

shouldbeawarethatcombiningclassesisnotpreciselyequivalenttoaddingnumbers.Theoperator+is

binarysinceitcanbeappliedtoonlytwoelementsatatime.Justaswecanaddonlytwonumbersatany


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onetime,sowecanonlycombinetwoclassesatatime.

Given theelements and thebinaryoperator, the fiveproperties describe theways inwhich the

operatormaybeappliedtotheelements.

Thefirstpropertyiscomposition(usuallyreferredtoinmathematicsasclosure)whichstatesthat

whenwecombineanytwoelementsofthesystemtheresultwillbeanotherelementofthesystem.For

example,ifwecombinetheyellowprimulaswiththeprimulasofothercolors,wegetthegeneralclassof

primulas.ThismaybewrittenasA+A'=B.Orifwecombinetheyellowprimulaswithalltheprimulas,

wegetall theprimulas.WemaywritethisasA+B=B.Thispropertydescribesaspectsofthechild’s

abilitytounderstandahierarchy.Forexample,hecanmentallyconstructalargerclassbycombiningits

subclasses.

Thesecondpropertyisassociativity,whichmaybestbeillustratedinaconcretemanner.Suppose

we want to combine three classes such as yellow primulas, primulas, and flowers (A, B, and C,

respectively). Remember thatwe cannot just add all three of them together simultaneously since the

operator (combining) is binary; that is, it can be applied to only two elements at a time. Given this

limitation,thereareatleasttwowaysofaddingA,B,andC.Wemightfirstcombinetheyellowprimulas

andtheprimulasandgetprimulas.Thatis,wedoA+B=B.Thenwemightcombinethisresult(B)with

flowers-in-general(C)andgetflowers-in-general.Thus,wedoB+C=C.Tosummarize,wefirstperform

A+B=BandthenB+C=CsothatourfinalresultisC.Anotherwayofstatingthisis(A+B)+C=C.

There is yet a second way of combining the classes. We could start by combining the yellow

primulas(A)withthecombinationofprimulasandflowersingeneral(B+C)andfinishwiththesame

result:flowers-in-general,(C).ThuswecanwriteA+(B+C)=C.Notethatthefinedresultofperforming

theoperationbyeithermethodisC,sothatthetwomethodsmaybeconsideredequivalent.Wemaywrite

thisequivalenceas(A+B)+C=A+(B+C).Thisequationexpressesthefactthatthechildcancombine

classesindifferentordersandcanrealizethattheresultsareequivalent.

The third property is identity, which states that there is a special element in the system (the

“nothing” element), that produces no changewhen combinedwith any of the other elements. If we

combine the nothing elementwith the yellowprimulas the resultwill be the yellowprimulas. Ifwe


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symbolize nothing by 0, thenwe have A + 0 = A.More concretely, if we do not combine the yellow

primulaswithanyoftheotherclasses,then,ofcourse,westillhavetheyellowprimulas.

Thefourthpropertyisnegationorinverse,whichstatesthatforanyelement(class)inthesystem,

thereisanotherelement(theinverse)thatproducesthenothingelementwhencombinedwiththefirst

element.Thatis,ifweaddtotheclassofyellowprimulasitsinverse,thenweareleftwithnothing.The

inverseisequivalenttotheoperationoftakingawaythesameclass.Ifwestartwithyellowprimulasand

combinewiththisclassitsinverse,weareineffecttakingawaytheyellowprimulaswiththeresultthat

weareleftwithnothing.WecanwritethisasA+(-A)=0orA-A=0.Theinverserulemightapplytoa

trainofthoughtlikethis:“SupposeIcombinetheyellowprimulaswithalloftheotherprimulas.ThenI

havealloftheprimulas.ButifItakeaway[inverseornegation]alloftheotherprimulas,thenIamleft

again just with the yellow primulas. ’ ’ Note how this train of thought is reversible. First, the other

primulasareadded,butlatertheyaretakenaway,sothatthethinkerisonceagainatthepointwherehe

started.Negation,then,isonekindofreversibility.

Theinversealsomaybeusedtoexpressaspectsofclassinclusion.Supposewestartwiththeclassof

primulas (B) and take away (or add the inverse of) the primulas which are not yellow (A'). This

operationleavesuswiththeyellowprimulas(A).WemaywritethisasA=B+(-A')orA=B-A'.Thistype

ofreasoningunderliesthechild’sabilitytosaythattherearemoreprimulasthanyellowones,thatthe

yellowprimulasareincluded intheclassofprimulas,orthattheyellowprimulasareonlysomeofthe

primulas.

Thefifthpropertyactuallyencompassesseveralaspects.Oneofthemisrelatedtospecialidentity

elements.Supposewecombinetheclassofyellowprimulaswithitself.Theresultisyellowprimulas.We

maywritethisasA+A=A.Inthisequation,Afunctionsasanidentityelementlike0.AddingAtoAislike

adding0toA:theresult,A,isunchanged.Piagetcallsthistautology.Anotheraspectisresorption.Ifwe

combinetheclassofyellowprimulaswiththeclassofprimulas,theresultisprimulas.Wemaywritethis

asA+B=B.Here,too,Afunctionsasanidentityelement.AddingAtoBislikeadding0toB;theresult,B,

isunchanged.Inasense,thisisanotherwayoflookingatinclusionrelations.Theyellowprimulasmust

be includedintheclassofprimulas(ormustbesomeoftheprimulas)sinceaddingtheformertothe

latterdoesnotchangethelatter.


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These,then,aresomeoftheaspectsofGroupingIandareintendedasaformaldescriptionofthe

processes underlying the child’s classification. The model involves elements (classes), the binary

operatorofcombining,andfivepropertiesgoverningtheapplicationoftheoperatortotheelements.

Discussion of Grouping I

AfewgeneralremarksshouldbemadeconcerningGroupingI.First,Piaget’suseofmathematicsis

notatallmeanttoimplythatthechildunderstandsthelogicomathematicalmodelinanyexplicitsense.It

is obvious thatmost children have never heard of the special identity element, let aloneGrouping I.

Clearly,thechildisnotamathematicianatthislevel.Infact,heoftencannotdescribeinanyclearway,

mathematicalorotherwise,hisprocedureforsolvingaparticularproblem.Hisreportisoftenincoherent.

Piagetusesthelogicomathematicalmodel,therefore,nottocharacterizethechild’sconsciousness,butto

describetheprocessesunderlyinghisclassification.

Second,GroupingIisnotmetricallyquantitativeinthesensethatitdoesnotinvolvenumbers.The

operations involve classes whichmay be of any size. It does notmatter whether there are 5 yellow

primulasand6whiteones,or5,000yellowprimulasand300whiteones.Inbothcasestherearemore

primulasthantherearewhiteprimulas,andsoforth.

Third,wemayexpandonourearlierpointthattheGroupingisintendedtodescribethestructure

ofthechild’sclassification.Piagetisnotinterestedintheminordetailsofthechild’sperformance;thatis,

whetherheisclassifyingflowersorfishorwhetherhefirstputtheflowersinanarrangementandthen

theanimals.Piaget insteadattempts tocapture theessenceof thechild’sactivitiesand to identify the

processesunderlyingthem.TheGroupingisPiaget’swayofdescribingtheseprocessesinaclearway.

Therefore,theGroupingisnotsimplyaprotocol listingeverythingthatthechilddoes. It is insteadan

abstractionwhichdescribesbasicprocessesliketheabilitytocombinementallytwosmallerclassesintoa

largerone,ortotakeawayoneclassfromanother.

The grouping also is a comprehensive and integrated structure. It is comprehensive since it

describes the processes underlying basic classification activities. The Grouping describes the

potentialities of the child, and not necessarilywhat he does in any one task at any one time. Let us


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suppose that a child constructs a hierarchy of classes. In doing so hemay notmake use of inclusion

relations.Inthiscase,theGroupingdoesnotsomuchdescribewhatthechildactuallydoes,butwhathe

iscapableofdoingundertheproperconditions.

Also,theGroupingisanintegratedsysteminthesensethateachofthepropertiesdoesnotstand

alonebut isrelated toallof theothers.Onthemathematical level, this iseasy tosee.Thepropertyof

associativitydescribestheorderinwhichelementsmaybecombined,butthepropertyofcompositionor

closure is needed to interpret the result of the associative combination. In other words, associativity

showsthattwodifferentordersofcombiningelementsareequivalent,andcompositionrevealsthatboth

oftheseordersofcombinationresultinanotherelementwhichmustbeinthesystem.Thus,theproperty

ofassociativitywouldbemeaninglesswithoutthepropertyofcomposition.Wecannothaveoneproperty

withouttheother.ThisfeatureoftheGroupingis,ofcourse,intendedtoreflectanimportantaspectofthe

child’s activities: the child’s successful classification (including the understanding of inclusion)

presupposes an interrelatedwhole, a structure of mental operations. For example, suppose the child

recognizesthattherearemoreprimulasthanyellowprimulas.Thisachievement impliesanumberof

interrelatedmentalacts.

Thechildmustbeawarethattheprimulas(whicharenolongerpresentinasinglecollection)are

thecombinationofyellowprimulasandprimulasofother colors (A+A'=B).Thechildmustalsobe

aware thatwhenyellowprimulasare takenaway from theprimulas, there remainprimulasofother

colors(B-A=A').These, then,aresomeoftheoperationsunderlyingthechild’sanswertoaquestion

concerninginclusion.Whenthechildcorrectlyanswersthequestion,hemaynotfirstactuallyperformall

theseoperations.However,theyareimplicitinhisanswer;hecouldnotanswercorrectlyifitwerenot

possibleforhimtoperformalltheoperationsinvolvedintheclassificationsystem.Tosummarize,any

particularresponsethatthechildmakestoaclassificationproblemcannotbeconsideredinisolation.His

responsepresupposesacomplexstructure,and it is thiswhichPiagetdescribesas theGrouping.The

Grouping,inotherwords,describesthementaloperationswhichmakeitpossibleforthechildto“really”

understandclassification.

Fourth, the Grouping explains and predicts behavior. Insofar as the Grouping describes the

processes underlying the child’s classification, it may be said to explain performance. The Grouping


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statesthatthechildcancombinetwoclassestogetalargerone.Thisoperation,amongothers,underlies

thechild’sabilitytounderstandinclusionrelationsandinthissenseexplainsit.InsofarastheGrouping

isgeneral itmaybesaidtopredictbehavior.TheGrouping isnot limitedtotheobjectsPiagetusedto

studyclassification.BecausetheGroupingprovidesadescriptionofstructure,itgoesbeyondthedetails

ofanyparticularproblemandallowsustopredictwhatthechild’sperformanceislikeonothersimilar

tasks.

Fifth,PiagethasdescribedseveralotherGroupingsallofwhichareintendedtorefertothechild’s

ability(from7to11)todealwithconcreteobjectsorthoughtaboutthem.Therefore,stage3istermed

concreteoperational.

Sixth,towardtheendofhislife,PiagetbegantofeelthattheGroupingmodelisnotfullyadequate

as an account of the concrete operations. While the facts concerning children’s performance on the

classificationtasks(andothersaswell)remainaswellestablishedasever,theGroupingmodelsuffers

fromseveraldeficiencies.“[TheGrouping]model...hasgeneratedlittleenthusiasmfromlogiciansand

mathematiciansbecauseof itsunavoidable limitations . . . and consequent ‘lackof elegance’ ” (Piaget,

1977b).(Indeed,onemightevengofurtherandclaimthatthelogicofthemodelisnotonlyinelegant,

butnotentirelycoherent.)“[TheGroupingmodel]...wastoocloselylinkedtothetraditionalmodelof

extensional logic and truth tables” (Piaget, 1980, p. 5, quoted in Beilin, 1985). In view of these

limitations, Piaget felt it is necessary to develop new formal models to characterize the essence of

concrete operational thought. “Abetterway, I nowbelieve, of capturing thenatural growthof logical

thinkinginthechildistopursueakindoflogicofmeanings”(Piaget,quotedinBeilin,1985b).While

Piagetdidnothave the time todevelopsuchmodels indetail,hebegan theeffortby introducing the

notion of “correspondences,” which we describe in our discussion of pre-operational strengths. It is

importanttorealize,asBeilinpointsout,“thatPiagetwasnotirrevocablycommittedtoaparticularlogic

or abstract model; consequently, following Piaget’s example, others are free to [select] the logical or

mathematicalmodelsthatbestexplainthedataofcognitivedevelopment”(Beilin,1985,p.112).

Inbrief,Piagetbelievedthatwhilethinkingisbestdescribedintermsof logicalmodels,hisown

effortsinthisareawerenotentirelysuccessful.Henceitisnecessarytoexpandthetheorybydeveloping

newmodels.AsPiagetclaimed,hehimselfwasthechief“revisionist”ofPiagetiantheory.


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Piaget’searlywork(inthe1920sand1930s)dealtwithclassificationinapreliminaryway.Inthe

1950shereturned to theproblem,using therevisedclinicalmethod.Hepresented2- to11-year-old

childrenwithanarrayofobjectstobeclassified.Thefindingswerethatinstage1(2to5years)thechild

fails to use consistently a clear rule or defining property to sort the objects into different classes. He

insteadconstructsgraphiccollectionswhicharesmallpartialalignmentsorinterestingforms.Instage2

(5 to 7 years), the child sorts the objects by a reasonable defining property and even constructs a

hierarchical classification, but fails to comprehend inclusion relations. Stages 1 and 2 are termed

preoperational.Instage3,whichisconcreteoperational(7to11years),thechildhasamaturenotionof

class, particularly when real objects are involved. The child sorts them by defining properties,

understands the relations between class and subclass, and so forth. To describe clearly the processes

underlyingthechild’sactivities,PiagetproposesalogicomathematicalmodelwhichhecallsGroupingI.

ThisGroupinginvolvessomeelements,abinaryoperator,andfivepropertiesrelatingtheoperatortothe

elements.Also,theGroupingisnotmetricallyquantitativeinthesensethatitdoesnotmatterhowbigor

small(innumericalterms)arethevariousclassesinvolved.Thechild,ofcourseisnotconsciousofthe

Grouping; rather theGrouping is intended todescribe thebasic structuresofhis activities. Inhis last

years,Piagetrecognizedtheshortcomingsof theGroupingmodelandproposedthedevelopmentofa

new“logicofmeanings.”

Piagetstressesthattheagenormsdescribingclassificationareonlyapproximate.Aparticularchild

maypassfromstage1tostage2at6yearsandnotnecessarilyat4or5years.Onechildmayspendthree

years in stage 1while another childmay spend four years in the same stage. Piaget doesmaintain,

however,thatthesequenceofdevelopmentisinvariant.Thechildmustfirstbecharacterizedbystage1

before he can advance to stage 2 and then to stage 3. Piaget also points out that a child may not

necessarilybe inthesamestageofdevelopmentwithrespecttodifferentareasofcognition.That is,a

childmaybeinstage1withrespecttoclassification,andinstage2ofnumberdevelopment.Thus,achild

maybeslightlymoreadvancedinsomecategoriesofthoughtthaninothers.

Oneimportantissueregardingclassification,andindeedalltheconceptsstudiedbyPiaget,isthe

generalityofthefindingsforchildrenindifferentcultures.Recently,muchcross-culturalworkhasbeen


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carriedouttodeterminewhetherchildrenindifferentculturesemploythetypesofreasoningdescribed

byPiaget, andwhether the sequenceof stages is invariant across cultures, asPiagetproposes.Opper

(1971;andinDasen,1977)hasexaminedanumberofPiagetianconcepts,includingclassification,in

rural and urban children in two Southeast Asian countries, Thailand andMalaysia. Likemany other

investigators(forareview,seeDasen,1977),Opperfindsthatalthoughtheagesmayvary,thesequence

ofdevelopmentisthesameindifferentcultures:first,Thaichildrenarecharacterizedbystage1,then

stage2,andsoon.

Moreover, Opper finds that Thai andMalaysian children present responses similar to those of

Swisschildren.Forexample,whenaMalaysiangirlinstage2ofclassificationwasaskedwhetherthere

aremorerosesorflowersinabunchofsevenrosesandtwoorchids,sheresponded,“Therearemore

roses than flowers.” The examiner said, “Show me the flowers.” The child then pointed to the two

orchids.

AThaiboy,inthesamestage,waspresentedwithsevenrosesandtwolotus.He,too,maintained

thattherearemorerosesthanflowers.Moreroses.—Morethanwhat?—Morethanflowers.—Whatarethe

flowers?—Roses.—Are there any others?—There are.—What?—Lotus.—So in this bunch, which is

more,rosesorflowers?—Moreroses.—Thanwhat?—Thanlotus.

Turningtothestage3child,wealsofindthesameresponsesastheSwisschildren.Forexample,a

Malaysiangirlsaid:Therearemoreflowersbecauseifit’sroses,it’sonlythese[pointingtoroses],butthe

flowersareplus thesealso [pointing to orchids].We see then that inmany casesThai andMalaysian

children’sargumentsarevirtuallyidenticaltothoseofSwisschildren.

How can we evaluate Piaget’s work on classification? On the one hand, Piaget has been very

successfulatwhathehasattemptedtodo.Anumberofindependentinvestigatorshaveconfirmedthat

stage1classificationtakesunusualforms(e.g.,Vigotsky,1962),thatyoungchildrenexperiencegenuine

difficulty with class inclusion (Klahr andWallace, 1972), and that the course of development with

respecttoclassificationisgenerallyasPiagethasdescribed(Kofsky,1966).Ontheotherhand,itshould

bepointedoutthatPiaget’sapproachtoclassificationisofaveryspecificsort.Hefocusesmainlyonthe

hierarchicalstructureofclasses,forexample,classinclusion.Heisnotparticularlyconcernedwithother


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aspectsof conceptswhichnowseemtobequite important.ThusNeisser (1967)haspointedout that

everyday concepts are often vague and difficult to define, and Rosch (1973) has developed a new

approachfocusingonnonlogicalaspectsofchildren’sconcepts.Thedefiningpropertyorintensionofa

classisoftenquitevague,aparticularobjectmayfitintoseveralclassessimultaneously,theboundaries

betweenclassesmaybe fuzzy,and itmaynotbepossible to formasimplehierarchy. Inbrief,Piaget’s

approachfocusesononlyoneofmanyimportantaspectsofclasses.

RELATIONS

In Chapters 2 and 3 we have already reviewed several aspects of relations, a problem (like

classification)withwhichPiagethasbeenconcernedsincehisearliestworkinpsychology.Wesawthat

in the sensorimotor period the infant displays precursors of relations. He can broadly discriminate

withinthedimensionsofnumerosity,intensityofmusculareffort,andloudnessofsounds(amongother

dimensions).Inthecaseofnumerosity,youwillrecallthatLaurentsaid“papa”whenPiagetsaid“papa,”

thatLaurentsaid“bababa”whenPiagetsaid“papa-papa,”andthatLaurentsaid“papapapa”inresponse

to “papapapapapapa.” Laurent’s imitation, although not exact, nevertheless implies an ability to

discriminateorhearthedifferenceamongseveralsoundswhichdifferedinnumberofrepetitionsofone

syllable.Similarly,inthecaseofmusculareffort,Laurentappearedabletodetectthedifferenceamong

thevariationsinvigorwithwhichheswungachain,andalsohewasabletodiscriminateamongsounds

ofdifferentdegreesofloudness.Thus,theinfantcandifferentiategradationswithindifferentkindsof

stimuli:somethingsarelouderthanothers,ormorenumerous,orbigger,andsoforth.Hecanperceive

differencesinvariousaspectsofhisworld.Theabilitytomakesuchdiscriminationsisaprerequisitefor

reasoningaboutdifferences.

Piaget’s early research on the child from about 5 to 10 years investigated reasoning about

differences, but not the perception of differences. He presented children with this verbal problem

(amongothers):“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichisthe

darkest,Edith,Suzanne,orLili?”{JudgmentandReasoning,p.87).Theresultsshowedthatchildrenfrom

5to10yearsareunabletodealwithproblemsofthissort,calledtransitivity,ataverballevel.

Asinthecaseofclassification,Piagetreturnedtotheproblemofrelationsinhislaterwork.Using


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therevisedclinicalmethod,heperformedseveralinterestingstudiesonordinalrelations,whichwewill

nowcharacterizebriefly.

Some Properties of Ordinal Relations

Piaget’sdefinitionofordinalrelationsinvolvesseveralfeatures.Supposewehaveseveralnumbers,

suchas17,65,25,3,and1,0OI.Itispossibletoarrangetheminorderofincreasingsize.Wemayusethe

symbol<tostandfor“isasmallernumberthan”andwrite3<17<25<65<1,0OI.Thesequenceisan

orderingofthenumberswiththesmallestbeingfirst,thenextsmallestsecond,andsoforth.Notethatthe

absolutesizeofthenumbersmakesnodifference.Thesecondnumberdoesnothavetobeexactlyone

morethanthefirstorexactlytwiceasbigasthefirst.Thelastnumber,solongasitislargerthan65,may

beofanysizewhatsoever.Also,wedonotneedtohavezeroas thebeginningof theseries.Theonly

requirements forordering thenumbersare that theyaredifferent fromoneanother, thatat leastone

numberissmallerthantherest,thatanotherislargerthanalltherest,andthatanynumberinbetween

thesmallestandthelargestisbothlargerthantheoneimmediatelyprecedingitintheseriesandsmaller

than the one immediately following it. Of course, orderings are not limited to numbers.Wemay also

ordersoundsonthedimensionofloudness.Supposesoundaisverysoft,bismuchlouderthana,andc

isslightlymoreloudthanb.Thenwehavea<b<c,where<means“issofterthan.”Againtheprecise

degreeofloudnessdoesnotaffecttheordering.

Piaget’s work deals with such matters as the child’s ability to construct orderings or ordinal

relationsandtomanipulatetheminvariousways.Thesestudies,involvingchildrenfromabout4to8

yearsofage,usuallydetectthreedistinctstagesofdevelopment:stage1lastingfromabout4to5,stage2

fromabout5to6,andstage3fromabout7andabove.Thefirsttwostagesarepreoperational,andthelast

isconcreteoperational.Whiletheagenormsareapproximate,thesequenceiscrucial.

Stage 1

Onestudywasconcernedwiththeabilitytoconstructanorderingofacollectionoftenstickswhich

differedonly insize.Wewillcall theshortestof thesticks(about9centimeters in length)A, thenext

largerB,andsoonthroughJ,thelargest(about16centimetersinlength).AdifferedfromBbyabout.8


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centimeters,andthisalsowastrueofBandC,andsoon.Piagetpresentedthechildwiththesticksina

randomlyorganizedarrayandaskedhimtoselectthesmallestofthelot.Afterthiswasdone,Piagetgave

aninstructionlikethis:“Nowtrytoputfirstthesmallest,thenonealittlebitbigger,thenanotheralittle

bitbigger,andsoon”(Child’sConceptionofNumber,CCN,pp.124-25). Inanotherstudythechildwas

askedtomakeastaircasefromthesticks.

Whenconfrontedwiththisproblem,childreninstage1showedseveredreactions,noneofwhich

wassuccessful. Somechildrenproducedrandomarrangementsof the sticks, likeH,E,B, J, and so on.

Otherchildrenmanagedtoorderafewofthesticks,butnotallofthem.AnexampleofthisreactionisA,B,

C,D,H,F,E,andsoon.

Anotherstrategywastoplacethelargersticksinonecollectionandthesmallersticksinasecond

collection.Withineachofthesecollections,however,thestickswereinarandomorder.Amoreadvanced

reactionalsoappearedwhichmaybeconsideredatransitiontothenextstage.Thechildstartedwith

somestick,likeB,apparentlyselectedatrandom;thenhetookanotherstick,likeH,andmadethetopofit

extendslightlyabovethetopofB;athirdstick,forexample,A,wasmadetoextendslightlybeyondthe

topofB;andsoforth.Theresultwasthatthetopsofthesticksformanordering;Hisslightlyhigherthan

B,andAslightlyhigherthanH,andsoforth,asinFigure6.Butthebottomsofthesticksalsodifferedina

randomway,andfailedtolieonastraightlineastheyshould.Thus,thechildconstructsanordering,but

onlybyignoringthelengthofeachstick.Thisprocedurefreeshimfromthenecessityofcomparingeach

stickwiththeoneimmediatelyprecedingitandwiththeonetofollow.Onewayofcharacterizingthese

activitiesistosaythatthechildfocuses(centers)ononeaspectoftheproblem(puttingthetopsinorder)

butignoresanother,equallyimportantaspect(arrangingthebottomsinastraightline).Tosummarize,

thechildatthisstagefrequentlycannotformasystematicorderingofanynumberofobjectsalthoughhe

issometimesabletoorderafewofthem.


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FIGURE6Orderingofsticks.

Stage 2

Presentedwiththesameproblem,childreninthesecondstagegenerallysucceedinconstructing

theordinalarrangementofsticks,sothatA<B<C<D<E<F<G<H<I<J.Butthechilddoesnotbuildthe

orderingswithout difficulty. Sometimes he begins by ignoring the bottomsof the sticks, as in stage 1.

Sometimeshemakesmanyerrors,likeA<D<B,andsoon,andtakesalongtimetorecognizeandcorrect

them.Thechildcontinuallyrearrangeshisordering,andshiftsthesticksfromonepositiontoanother.

Essentiallythechild’sprocedureisoneoftrialanderror,lackinganoverallplanorguidingprinciple.

Forexample,ifhehaschosenAasthesmallest,hemightthenchooseanothersmallone,like

D,andlineitupnexttoA.Thenhemightchooseanothersmallone,likeC,andplaceitnexttoDand

seethatitissmallerthanD.Sincethisisso,hemightrearrangethesticksplacingCafterAbutbeforeD.

AfterbeginningwithA,thechildfailstolookforastickthatislongerthanAbutsmallerthanalltheones

remaining. If this rule is followed, then each step of the ordering can be constructed without any

difficulty.However, thechildat this stagedoesnotemploysucha logicalprocedure.He fails tomake

systematic comparisons between a given stick and the one immediately preceding it and all those


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following.

This tendencywas furtherrevealedby theadditionofonemoreproblem.Afterconstructing the

orderingAthroughJ,thechildrenweregivenanewcollectionoftensticks,a,b,c,d,e,f,g,h,i,j.Eachof

thesenewstickscouldfitinbetweenapairofsticksofthefirstseries.Thatis,ifthenewsetofstickswere

orderedcorrectlyalongwiththefirstset,thearrangementwouldbeA<a<B<b<C<c<D<d<E<e<F<

f<G<g<H<h<I<i<J<j.Thechild’staskwastodopreciselythis;tofitthenewsticksintotheordering

alreadyconstructed(AthroughJ),soastomakeanewordinalarrangementinvolvingalltwentysticks.

Childrenofthisstagehadgreatdifficultywiththeproblem.Infact,manyfailedtosolveit.Partof

one child’s orderingwasC e d D, and another producedH g G I h j c, and so forth. Other children

succeededinproducingthecorrectordering,butonlyafterconsiderabletrialanderror.

Thesedifficultiesseemduetoseveralfactors.Onefactorappearstobethatthechildperceivesthe

originalseriesasawholeandfindsithardtobreakuptheseriesintosmallerunits.Also,childrenofthis

stagedonotapproachtheproblemwithaguidingprinciple.Theyfailtousearulelike,“Startwiththe

smallestofa-j)insertitinbetweenthepairofthesmalleststicksinA-J)thentakethesmallestofb-jand

insertitbetweenthesmallestpairofsticksinB-J)andsoforth.”Notonlydidthechildrenfailtousearule

likethis,buttheyalsohaddifficultyindecidingthatagivenelementofa-jwasatthesametimebigger

thanonestickinA-JandsmallerthanthenextlargerstickinA-J.Toplacedproperly,thechildmustsee

thatd<EandthatD<d.Hemustcoordinate thesetworelationsbutfailstodosoconsistently.That is,

somechildrenwouldtakeeand,seeingthatitwaslargerthanB,wouldplaceitrightafterB.Theyfailed

toconsiderwhetherewasatthesametimesmallerthanC,andthereforemadeanerror.

Afterinvestigatingthechild’sabilitytoconstructanorderingandplacenewelementsinit,Piaget

wenton to study the child’s ability to construct equivalencesbetween two separateorderings (which

involveequalnumbersofelements).Toillustratethis,letustakeaclasswithfifteenboysandfifteengirls

andordereachofthesegroupsintermsofheight.Wefindtheshortestboy,thenext-to-shortestboy,and

soon,andwedothesameforgirls.Wecanseethatthetwoorderingsareequivalentinsomewaysand

differentinothers.Somedifferencesarethattheheightoftheshortestboymaybe48inches,whereasthe

height of the shortest girl is 44 inches. Also, the second shortest boymay be 4 inches taller than the


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shortestone,whereasthesecondshortestgirlisonly1inchtallerthantheshortestgirl.Despitethese

realdifferences,thereareimportantsimilaritiesbetweenthetwoorderings.Theboywhois48inches

tallandthegirlwhois44inchestall,despitetheirdifferenceinheight,areequivalentintermsoftheir

positionintheordering.Theyareboththeshortest.Thesameholdstrue,ofcourse,forthetallestboyand

girl,thenexttotallest,andsoforth.

Piagetthenraisesthe issueofwhethertheyoungchildcanrecognizetheequivalencesbetween

twodistinctorderings.Doesheunderstandthattwoobjects,whiledifferinginheight,forexample,canat

thesametimebeequivalentintermsoftheirrelativepositioninanordering?Tostudythematterhefirst

presentedchildrenwithtendolls,A-J,whichwerepresentedinarandomdisplayandwhichcouldbe

arrangedinorderofheight;andwithtensticks,A'-J',alsorandomlyarranged,whichcouldbeorderedin

size.Thesticksweresmallerthanthedolls,andthedifferencesbetweenadjacentpairsofstickswere

smallerthanbetweenpairsofdolls.Thechildwastoldthatthedollsaregoingforawalkandthateachof

themmust have the proper stick. The intention of the instructions, of course,was to get the child to

produceanorderingofthedollsandofthesticksandtomakeeachmemberofoneorderingcorrespond

totheappropriatememberoftheotherordering.Thus,dollAshouldhavestickA',dollBshouldhave

stickB',andsoon.Piagetcallsthisprocesstheplacingoforderingsintoone-to-onecorrespondence.

Theresultsshowedthatchildrenofthisstagecanproduceaone-to-onecorrespondenceofdolls

andsticks,butonlyinatrial-and-errorfashion.Themostcommonprocedureistoorderthedolls(bytrial

anderror)andthentoorderthesticks(bytrialanderror).Onlyaftertwoseparateorderingshavebeen

constructedaretheelementsofeachputintoone-to-onecorrespondence.Thatis,thechildfirstidentifies

thelargestdoll,thenexttolargestdoll,andcompletestheorderingofdolls;thenhegoesontoorderthe

sticks.Itisonlyafterthisisdonethatthechildplacesthelargeststickwiththelargestdoll,thenextto

largest stick with the next to largest doll, and so forth. While this procedure works, it is somewhat

cumbersome.Aneasiermethodistobeginbyidentifyingthelargest(orsmallest)dollandthelargest(or

smallest)stickandimmediatelyplacingthetwotogether.Thesecondstepistochoosethe largestdoll

andstickofallthoseremainingandtoplacethemtogether,andsoforth.Inanyevent,thechildinthis

stage does succeed in setting the two orders into one-to-one correspondence. He seems to have

establishedthattheorderingsareequivalent.


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FIGURE7Theequivalenceofrelativeposition(dollsandsticks).

The next problem concerns the stability of the equivalence established by one-to-one

correspondence.Letussupposethatthesticksareplacedveryclosetogetherwiththeirorderpreserved

(asinFigure7).Theshorteststickisclosesttothethirdtallestdoll,thesecondstickisclosesttothefourth

tallestdoll,andso forth.Doesthechildrecognizethat thesecondtalleststick isstill equivalent to the

secondtallestdoll,eventhoughtheformerisnowclosesttothefourthtallestdoll?Thatis,doesthechild

conservetheequivalenceofrelativepositionwhentheovertone-to-onecorrespondenceisdestroyed?

Piaget presented this and similar problems to a number of children. He placed the sticks close

togetherandaskedwhichstick“goeswith”whichdoll.Piagetdiscoveredseveredmethodsofattacking

theproblem.Themostprimitivereactionistoassertthatadollisequivalenttothestickclosesttoit.Thus,

thesecondlargeststickandfourthlargestdollareconsideredtobelongtogethersimplybecauseoneis

belowtheother.Thechild’sjudgmentisdominatedbyspatialrelations.Otherchildrentrytosolvethe

problembycounting,buttheyfailtodosoproperly.Forexample,onechildsaidthatthefourthlargest

stickwasequivalenttothethirdlargestdoll.Thereasonforhismistakewasthathenoticedthatthere


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werethreesticksprecedingthefourthlargeststick;hethencountedoutthreedolls,stoppedthere,and

identifiedthethirddollwiththefourthstick.Thismethodisquitefrequentamongchildrenofthisstage;

thatis,theyfindadollcorrespondingtothenthstick,countingtheprecedingn-1sticks,thencountthe

dolls,stoppingatthen-1thelement.Thechildconfusesthepositiontobefound(say,stick4)withthe

numberofprecedingelements(3).

Stage 3

Afterabouttheageof6-7years,thechildissuccessfulinallofthetaskswehavedescribed.When

askedtoconstructasingleorderingofsticksdifferinginsize,thechilddoessoquiteeasily.Theordering

isguidedbyanoverallplan.Thechildusuallybeginswiththesmallest(orsometimes,withthelargest),

then thenext smallest, and so forth, in sequenceuntil theordering is complete.This strategymaybe

characterizedasstartingwiththesmallestandcontinuingtotakethesmallestofeverythingthatisleft,

untilthestickshavebeenexhausted.Whenaskedtoplaceadditionalsticks(a-j)intheirproperpositions

within the ordering (A-J) already constructed, the child does so with almost no errors. The process

underlyingthisachievementisthecomparisonofoneofthenewsticks(say,d)withtwointheoriginal

orderingsimultaneously.That is, toascertaind'sproperposition, thechilddeterminesthat it isat the

sametimebiggerthanDbutsmallerthanE.Tophrasethematterdifferently,hecoordinatestwoinverse

relations—biggerandsmallerthan.

Inasimilarwaytheconcreteoperationalchildeasilyplacestwoseparateorderingsintoone-to-one

correspondence.Onechildimmediatelyputthebiggestdollwiththebiggestball(ballsweresometimes

usedinplaceofsticks),thenexttobiggestdollwiththenexttobiggestball,andsoforth.Hisstrategywas

to identify thebiggestdollandballofall thoseremainingand toplace the twotogetheratonce.This

procedureismoreeconomicalthanthatoftheyoungerchildwhofirstordersthedolls,thentheballs,

and finallybegins toput them together.When thisone-to-onecorrespondence isdestroyed, thechild

conservestheequivalenceofrelativeposition.Herealizesthatthesmallestdollisstillequivalenttothe

smallestballandnottotheballtowhichithappenstobeclosestinspace.

Insummarizingthematerialontheconcreteoperationalchild,then,wecanstatethatheisadeptat

understanding and manipulating ordinal relations. However, as in the case of classification, one


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limitation applies: he can deal with relations on a concrete level only; that is, when real objects or

thoughtsaboutthemareinvolved.Nevertheless,histhoughtisfarmoreadvancedthanthatofthechild

in stages 1 and 2. The child can construct orderings, put two such orderings into one-to-one

correspondence,andconservetheresultingequivalences.Asinthecaseofclassification,theprocesses

underlying the child’s ability tomanipulate relations form integrated and comprehensive structures.

Each of his mental operations cannot be understood without reference to the others of which he is

capable. These processesmust be interpreted in terms of complex systemsof operations. To describe

thesesystems,Piagethasdevelopedseverallogicomathematicalmodels,similartoGroupingI(although

they,of course,deadwithrelations,notclasses).Also,Piagethas investigatedseveralotheraspectsof

ordinalrelations,suchastransitivity(ifa>bandb>c,thena>c),whichwewillnotcoverhere.

NUMBER

Theabilitytounderstandclassesandrelations,accordingtoPiaget,isbasictomatureconceptsin

many areas. The several groupings which describe the processes underlying the older child’s

performance in problems of classes and relationsmay also be used to characterize concepts of space,

chance,geometry,andsoforth.Sincewecannotreviewall theseconcepts,wewillconcentrateonone

thatisparticularlyinterestingandthathasreceivedconsiderableattentionintheAmericanandBritish

researchliterature,namely,theconceptof(whole)number.

First,wemustunderstandwhatPiagetdoesanddoesnotmeanbytheconceptofnumber.Hedoes

notmean and isnot interested in computational abilities as taught in the first few grades of school.

Whetherthechildcanadd2and2,orsubtract3from5,isnottheissue.ThereasonforPiaget’slackof

interest in thesematters is that simple addition and subtraction of whole numbers, aswell as other

manipulationsof them,canbecarriedoutentirelybyroteandwithoutunderstanding.Thechildcan

simply memorize the addition and subtraction tables and fail to comprehend the basic concepts

underlyingthem.Piagetdoesnotdenythatitisusefultomemorizethefactsofadditionandsubtraction;

for purposes of computation, we all find it helpful to do so. He asserts, however, that for mature

understanding of number, such rotememorization is not sufficient andmust be accompanied by the

masteryofcertainbasicideas.


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Amongthese ideasareone-to-onecorrespondenceandconservation.Letus firstconsiderone-to-

onecorrespondence.SupposewearepresentedwithacollectionorsetofdiscreteobjectsasinFigure8.

Thesizeoftheobjects,theircolor,andsofortharecompletelyirrelevant.Allthatisrequiredisthattheset

contain a finite number of discrete objects. We are then given a box of objects and are required to

construct from it another setwhich has the same number property as the first set. It does notmatter

whethertheobjectsinthesecondset(whichwewillcallsetB)arethesamecolor,size,andsoonasthose

inthefirstset(setA).WhethersetAcontainselephantsandsetBcontainsgeraniumsisirrelevant.The

onlyrequirementisthattheyhavethesamenumber.OnewayofconstructingasetBsothatitwillhave

thesamenumberpropertyasAisbycountingtheobjectsinA(say,therearefive)andthentakeoutofthe

boxthesamenumberofobjects.Thisprocedure,whichofcourseisquiteadequate,probablyoccursfirstto

adults.Butsupposewecannotcount.SupposewedonotknowthenumberofobjectsinsetA.Evenwith

theselimitationsthereisasimplewayofconstructinganewset,B,whichwillhavethesamenumber

propertyasA.ThismethodmerelyinvolvesputtingnexttoeachmemberofsetAone,andonlyone,new

object.Thesenewobjects,aftertheone-to-onecorrespondencehasbeenestablished,formaset,B,with

thesamenumberasA.Ofcoursewedonotreallyhavetophysicallyplaceeachnewobjectnexttoonein

A;wecannotetheone-to-onecorrespondencementally.That is,wecan“saytoourselves,”“Thisnew

object corresponds to the first in the lineof setA,” and soon.The important idea is not thephysical

placingtogetherofthesets,butthepairingofonememberinsetAwithoneinsetB,howeverthisisdone.

FIGURE8Collectionofobjects.

Althoughverysimple, the ideaofone-to-onecorrespondence isbasicandpowerful,andmaybe

usedinavarietyofsituations.Ifwewanttodeterminewhethertherearethesamenumberofseatsas

peopleinanauditorium,allwehavetodoisaskeveryonetositdown(withnooneallowedtositon


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anyoneelse’s lap!). Ifall thepeopleare inseats(inone-to-onecorrespondencewith theseats)and if

noneoftheseatsisempty,thenthenumbers(whatevertheymaybe)ofpeopleandseatsareequal.If

therearepeoplestanding,thenthisdefinestherelationofmorepeoplethanseats.Ifthereareempty

seats, then this defines the relation of more seats than people. In brief, one-to-one correspondence

establishesthatanytwosets—regardlessofthenatureoftheobjectscomprisingthem—areequivalentin

number.Countingorotherproceduresarenotneeded.Lackofone-to-onecorrespondenceestablishes

thatonesetislargerthantheother(andonesmallerthantheother).

FIGURE9Conservationofnumber.

ThesecondbasicideawhichPiagetinvestigatesisconservation.Supposethatwehaveestablished

thatsetsAandBareequalinnumber,asinFigure9A.Thatis,wehaveputsetAinaline,andbeloweach

memberofsetAwehaveputanewobject.The lineofthenewobjects issetB.Supposethatwethen

compress themembers of set B, as in Figure 9B, so that the perceptual one-to-one correspondence is

destroyed.NoweachmemberofsetBisnotdirectlybelowadifferentmemberofsetA.Theproblemis

whetherthetwosetswhichnowdifferinphysicalarrangementstillareequalinnumber.Inotherwords,

istheequivalenceestablishedinFigure9AconservedwhentherearrangementshowninFigure9Bis

performed?Toadults,thismayseemlikeafoolishquestion.Ofcourse,theequalityofnumbershasnot

changed!Buttheproblemiswhetherchildrenacceptthissimpleandbasicidea,too.Iftheydonot,then

theirworldofnumbermustbeverychaoticindeed.Ifquantityisseentochangewhenevermerephysical

arrangement isaltered, thenthechild fails toappreciatecertainbasicconstanciesor invariants in the

environment.

Piagethasconductedanumberof investigationsonthechild’sunderstandingofthesetwobasic

ideas: one-to-one correspondence and conservation of the equivalence of twonumbers.He finds that


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youngchildrenfailtounderstandthesetwonotionsandthataperiodofdevelopmentisrequiredbefore

thechildachievesthementaloperationsnecessaryforthoroughcomprehensionofnumber.Letusnow

reviewtheexperiments.

Stage 1

Tostudytheabilitytoconstructsetsofequivalentnumber,Piagetpresentedchildrenwithavariety

ofproblems.The simplestof these involvedplacingbefore the childa rowof sixor sevenpenniesor

buttonsorsweets,andsoon.Theexaminerthenaskedthechildtopickoutthe“samenumber”or“as

many” from a large collection of similar objects. Thus the childwas given set A andwas required to

constructasecondset,B,whichwasequivalentinnumber.Thechildrenwere,ofcourse,nottoldhowto

constructsetB.Hereisaprotocoldescribinghowastage1child,4yearsand7monthsofage,dealtwith

theproblem.Piagethadplacedsixsweetsinarowandtoldthechildthattheybelongedtohisfriend

Roger:

“Putasmanysweetshereastherearethere.Those...areforRoger.Youaretotakeasmanyashehas.”(Hemade a compact row of about ten,whichwas shorter than themodel.)—“Are they the same?”—“Not yet”(addingsome).—“Andnow?”—"Yes.”—“Why?”—“Becausethey’relikethat”(indicatingthelength).(CCN,p.75)

FIGURE10Failuretoconstructequalsets.

The example makes clear the predominant tendency of this stage. The child does not use the

methodofone-to-onecorrespondence.Instead,hethinksthatthetwosetsareequivalentinnumberif

theyhavethesamelengths.InPiaget’sterms,thechildcentersononedimension—thelength—ofsetA

(Roger’ssweetsorthemodel)andbaseshisconstructionofsetBsolelyintermsofthatonedimension.

TheresultispicturedinFigure10.Thelengthsofthetworowsareequal,buttheirnumbersarenot.The

newrowisdenser;thatis,therearesmallerspacesbetweenthesweets,thanRoger’srow,butthechild

ignoresthisfactandconcentratesonlyonthelengths.Sincehefailstocoordinatethetwodimensionsof

lengthanddensityatthesametime,hecannotconstructsetsequivalent innumberexceptwhenvery


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smallnumbersareinvolved,orexceptbyaccident.

In another investigation, Piaget tried tomake the child understand the principle of one-to-one

correspondence,andthenperformedtheconservationexperiment.Inthisstudy,setAwasarowoften

vasesandsetBconsistedofflowers.Onechild,4yearsand4monthsofage,

put13flowersclosetogetherinarowopposite10vasesrathermorespacedout,althoughhehadcountedthevases from 1 to 10. Since the rowswere the same length, he thought that the flowers and vaseswere “thesame.”—“Thenyoucanputtheflowersintothevases?”—“Yes.”—Hedidso,andfoundhehad3flowers[left]over.(CCN,p.50)

Thechild,then,initiallyconstructedsetBsoastomakeitthesamelengthassetAandthoughtthat

thetwosetswerethereforeequalinnumber.Theexaminerthenmadethechildconstructaone-to-one

correspondencebetweentheflowersandvases;thatis,thechildputeachflowerinavase.Theresult

was ten flowers in ten vases (or two sets equivalent in number), and the three extra flowers were

discarded. The question now iswhether the child realizes that the two sets are really equivalent in

number.Doesthechildconservetheequivalencedespiteamerephysicalrearrangementoftheobjects?

Tofindout,Piagetcontinuedtheexperimentwiththesamechild.

The flowerswere taken out andbunched together in front of the vases. [That is, they formed a shorter rowthan did the vases.] “Is there the same number of vases and flowers?”—“No.”—“Where are there more?”—“There are more vases.”—“If we put the flowers back into the vases, will there be one flower in eachvase?”—“Yes.”—“Why?”—“Becausethereareenough.”(Thevaseswereclosedupandtheflowersspacedout.)—“Andnow?”—“Therearemoreflowers.”(CCN,p.50)

Notethatafterthechildhadhimselfestablishedaone-to-onecorrespondencebetweentheflowers

andvases,hefailedtoconservethenumericalequivalenceofthetwosets.Whentheflowerswereput

intoashorterrowthanthevases,thechildbelievedthatthenumberswerenolongerequalandthatnow

thereweremorevases.Hemaintainedthiseventhoughherealizedthattheone-to-onecorrespondence

couldbereestablished;that is, that theflowerscouldbereturnedtothevases.Thenwhentherowof

vaseswasmadeshorterthanthatoftheflowers,hechangedhismindonceagain.Heassertedthatnow

thereweremore flowers. Clearly, this child centered on the lengths of the rows and used only this

informationtomakejudgmentsofequivalenceorlackofequivalenceofnumber.Whentherowswerethe

samelength(aswhentheflowerswereinthevases),hesaidthattheywereequalinnumber.Whenthe

rowsdifferedinlength,hebelievedthatthelongerlinehadthegreaternumber.


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Piagetalsoinvestigatedtheroleofcounting,questioningthewayinwhichcountingthetwosets

affectsthechild’sjudgment.Onechild,5yearsand3monthsofage,failedtheconservationproblem.He

saidthatsetA(sixglasses)wasgreaterthansetB(sixbottles)becauseonewaslongerthantheother.

Thentheexaminersaid:

“Can you count?”—“Yes.”—“Howmany glasses are there?”— “Six.”—“And how many bottles?”—“Six.”—“Sothere’sthesamenumberofglassesandbottles?”—“Therearemorewhereit’sbigger[thatis,longer].”(CCN, p.45)

This examination shows thatwhile the child can count, the act ismeaningless in deedingwith

conservation.Althoughhecanreciteastringofnumbers,hedoesnotcomprehendwhattheysignify.The

fact that he counted six bottles and also six glasses does not imply to him that the sets are equal in

number. For him, equality of number is determined solely by equality of lengths, and counting is an

extraneousandirrelevantact,whichdoesnotassureeithertheequivalenceofsetsoritsconservation.4

Stage 2

The child of this stage easily constructs two sets equivalent innumber, but fails to conserve the

equivalencewhenthesetsarerearranged.Per,achildof5years,7months,

hadnodifficultyinmakingarowof6sweetscorrespondingtothemodel.[Piagetuses“model”torefertosetA, the row to be copied, and “copy” to refer to set B.] The model was then closed up: “I’ve got more.”—“Why?”—“Becauseit’salongerline.”(Theprocesswasreversed.)—Nowtherearemorethere,becauseit’sa big line.” But a moment later, Per said the opposite: “Are there more here [referring to the longerrow]?”—“No.”—“Why not?”—“Because it’s long.”—“And there [the shorter row]?”—“There are more there,becausethere’salittlebundle”[Thechildmeantthattheshorterrowwasdenser].—“Thenaretheremoreinalittlebundlethaninabigline?”—“Yes.”AfterthisPerwentbacktousinglengthasthecriterion,madethetworowsthesamelengthagainandsaid:“Nowthey’reboththesame.”(CCN,p.79)

Theprotocolshowsthatthechildofthisstageeasilyconstructsasetequalinnumbertoanother.He

also establishes the equivalence by the method of one-to-one correspondence. That is, in order to

constructsetB,heplacesanewsweetjustbeloweachinsetA.Buttheone-to-onecorrespondenceisnot

fullyunderstood;itisjust“perceptual.”WhensetBismadeshorterthansetA,thechildfailstoconserve

the equivalencewhich he so easily constructed. The protocol also shows that the child is ambivalent

about thecriteriaused toestablishequalityor inequalityofnumber.Sometimeshemaintains that the

longerrowhasmorebecauseitislonger;atothertimeshebelievesthattheshorterrowhasmorebecause


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it is denser. In Piaget’s terms the child sometimes centers on the lengths (ignoring densities) and

sometimes centers on the densities (ignoring lengths). This tendency is an improvement over what

occursinthepreviousstage,sincetheyoungerchild(instage1)consistentlycentersononlyoneofthe

twodimensions,usuallylength,anddoesnotconsidertheother,usuallydensity,atall.Bycontrast,the

childinstage2haswidenedthesphereofhiscentrations.Henotices,albeitatdifferenttimes,thatboth

dimensionsmayberelevantandusestheinformationfromeitherofthesedimensionsseparatelytomake

ajudgment.Thisuseofpartialinformationiscalledregulations.Wewillseenexthowthechildinthe

periodofconcreteoperationscoordinatesthetwodimensions.

Stage 3

The results of this stage are easy to describe. The child can now construct a set numerically

equivalenttoanothersetandcanconservetheirequivalencedespitechangesinphysicalarrangement.

Hereisaprotocolillustratingthisstage:

“Takethesamenumberofpenniesastherearethere[therewere6 insetA],Hemadearowof6underthemodel,butputhismuchclosertogethersothattherewasnospatialcorrespondencebetweentherows.Bothendsof themodel extendedbeyond thoseof the copy. “Haveyougot the samenumber?”—"Yes.”—“Are youandthatboy[referringtothehypotheticalownerofsetA]justasrichasoneanother?”—“Yes.”—(The penniesof the model were then closed up and his own were spaced out.)—“And now?”— “Thesame.”—“Exactly?”—“Yes.”—“Whyaretheythesame?”—“Becauseyou’veputthemclosertogether.”(CCN,p.82)

Thisprotocolcontainsseveralinterestingfeatures.OnefeatureisthatinmakingsetBequaltosetA,

theconcreteoperationalchilddoesnotbothertoplaceeachelementinBdirectlyundereachelementin

A.Hedoesnotneedtorelyontheperceptionofspatialproximitybetweentheelementsofeachset.How

thendoesheconstructnumericallyequivalentsets?Onemethod,ofcourse,issimplytocountthenumber

ofobjectsinsetA,andthenmerelycountoutthesamenumberforsetB.Probablysomechildrenusedthis

method,butPiagetconcludedfromhisclinicalexaminationsthatotherchildrendidnotusecounting.

Theyseemedtousethemethodofone-to-onecorrespondence,butinamoresophisticatedwaythanthe

youngerchild.Theconcreteoperationalchild’stechniquemaybedescribedasfollows:toconstructsetB

equaltosetA,heputsoutonepennyforthefirstpennyinsetA,andsoforth.Itdoesnotmatterwherehe

putsthemembersofsetB.TheonlycrucialrequirementisthathematcheachmemberinsetAwithone

andonlyonememberinsetB(anonspatialone-to-onecorrespondence).Thechildmustnotforgettoput


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outapennyforeachmemberofsetA(thatis,hecannotskipanymemberofsetA)andmustnotputout

morethanonepennyforeachmemberofsetA(thatis,hemustnotcountanymemberofsetAtwice).

Theprocessofestablishingsetsequalinnumbermaybedescribedintermsofclassesandrelations.

Asfarasrelationsareconcerned,thechildusesthemethodofvicariantordering.SupposethatsetA(the

model)isalineofpennies,andthechildmustconstructasetB(thecopy)fromalargesupplyofcandies.

Hebeginsbypointingatthepennyontheextremeleftandputsoutasweet.Thenhepointstothesecond

pennyfromtheleft,putsoutasweetforit,andcontinuesuntilthelineofpennieshasbeenexhausted.

Thisprocessofpointingtoonepennyatatime,beingcarefultocounteachpennyonceandonlyonce,is

anordering. It isequivalent tosaying: “Thispennycomes first, thisonesecond, thisone thirdandso

forth.Inaway,theorderingofpenniesislikearrangingaseriesofsticksordollsinorderofheight.There

is a first stick, a second stick, and so forth, just as there is a firstpennyanda secondone.Therefore,

something like the ability to construct ordinal relations underlies the child’s construction of sets

equivalentinnumber.

Despite theevident similarity, the twoprocesses—constructingordinal relations (as inordering

thesticks)andvicariantordering(thepennies)—arenotidentical.Inthecaseofthesticks,thereisone

andonlyoneshorteststickwhichmustcomefirst intheseries,oneandonlyonesecondshorteststick

whichmustcomesecondintheseries,andsoforth.Inthecaseofthepennies,itdoesnotmatterwhich

pennyisconsideredfirstintheseries,whichcomessecond,andsoon.Onecouldstartcountingatthe

extremeleft,attheextremeright,inthemiddleorwhereveronepleased,justsolongasoneiscarefulnot

toomitpointingtoeachofthepenniesandnottopointtoanyofthemmorethanonce.Theorderingof

penniesiscalled“vicariant”forthisveryreason:theorderinwhichthepenniesarecounteddoesnot

matter.

Other aspects of relations are involved too.When putting out one and only one sweet for each

penny,thechildiscoordinatingtwoorderings.Thisissimilartotheproblemofdollsandsticks.Justasthe

childcangivetotheshortestdolltheshorteststick,tothesecondshortestdollthesecondshorteststick,

andsoforth,socanheplacethefirstsweetwiththefirstpenny,thesecondsweetwiththesecondpenny,

andsoforth.Ofcourse,theone-to-onecorrespondenceofpenniesandsweetsisvicariant,whereasthe

one-to-onecorrespondenceofdollsandsticksisnot.Inthelatterinstance,thereisoneandonlyonestick


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(theshortest)whichgoeswiththeshortestdoll,andsoforth.Inthecaseofpenniesandsweets,itdoes

notmatterwhichsweetisplacedintocorrespondencewithanypenny,solongasoneandonlyonesweet

isusedforeachpenny.

Theconstructionofequivalentsetsalsoinvolvesclassification.Tothechild,thepenniesinsetA,for

instance,areinsomewaysallthesameandinsomewaysdifferentfromoneanother.Theyaredifferent

inthatacertainpennyiscountedfirst,anotheronesecond,andsoforth.Theyarethesameinthatitdoes

notmatterwhichiscountedfirst,whichsecond,andsoforth.Inotherwords,itisonlythechild’sactof

pointingtoeachinturnthatdifferentiatesthepennies;otherwise,theyareallequivalent.Insofaraseach

ofthepenniesisanelementequivalenttoalltherest,theyareallmembersofthesameclass.Thesameis

true,ofcourse,ofthesweetsinsetB.

Thus far we have seen how the child’s ability to construct sets equivalent in number may be

analyzedintoanumberofcomponentskills.Underlyingthechild’sovertperformance(e.g.,placingona

table seven sweets corresponding to seven pennies) are a number of concrete operations: vicariant

ordering, one-to-one correspondence of two vicariant orderings, and classification. Some of the

operations involveclassesandothers relations.Thus,number isaunionof classesandrelations.The

operationsareconcretesincethechildcanapplythemonlytoimmediatelypresentobjectsorthoughts

about them.Theyareoperations since theyare actionswhich the childperformsmentally andwhich

have the added property of being reversible. This means that for each particular mental action, for

instanceaddition, thechildcanperformitsoppositeaction, in thiscasesubtraction,which leaveshim

wherehestarted.Asoperations,theymayalsobedescribedintermsofoverallstructuresorsystems,that

is,intermsoftheGroupings,anexampleofwhichwehavegiveninthecaseofclassification.5

Inthestageofconcreteoperations,thechildcanalsoconservenumber.Afterconstructingtwosets

equivalent in number, the child recognizes that the sets remain equivalent despite mere physical

rearrangementofthesets.Ifthesevensweetsarecompressedtomakeashortlinewhilethelineofseven

penniesremainsthesame,thetwosetsareneverthelessstillequalinnumber.Theequivalencehasbeen

conserved.

Whatenablestheconcreteoperationalchildtoconservewhilethepreoperational(stages1and2)


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childfailstodoso?Recallthemechanismunderlyingthepreoperationalchild’sfailure:centration.The

youngerchildcentersononlyalimitedamountoftheinformationavailable.Whentherowofsweetsis

compressed,henoticesonlythatthelineofpenniesisnowlongerthanthelineofsweets.Heignoresthe

fact that the line of sweets is denser (has smaller spaces between adjacent elements), and bases his

judgmentonlyonthelengths.Thepreoperationalchildknowsthatempiricalreversibilityispossible:he

realizesthatifthesweetswerereturnedtotheiroriginalpositions,therewouldbeonesweetforeach

penny.Thisknowledgedoesnothelp,however;despite it, he feels that thenumberof a set changes

whenitsappearanceisaltered.Perceptualfactorshavetoostrongaholdonthechildatthisstage.They

arenotyetsufficientlycontrolledbymentalactionswhichcancompensateformisleadinginformation.

Bycontrast,theconcreteoperationalchilddecentershisattention.Heattendstoboththerelevant

dimensionsandusesthisinformationinseveralways.

1.Henoticesthatthelineofpennieshasbecomelongerthanthelineofsweetsandthatthelineofsweetshasbecomedenserthanthelineofpennies.Moreover,hecoordinatesthetwodimensions. He mentally manipulates the visual data available to him. This mentalactivity leads him to realize that while the length of the line of pennies increases(relativetothesweets)byacertainamount,thedensityofthelineofsweetsincreasesbyanequivalentamount.Inotherwords,thechildconceivesthatthepennies’increaseinlengthisbalancedby,orcompensatedfor,bythesweets’increaseindensity:thereisarelation of reciprocity or compensation between length and density. In effect, oneincreasecancelsouttheotherwiththeresultthatthesetsremainequivalentinnumber.Thisreciprocityisoneformofreversibility.Sincetheincreaseinlengthcounteractstheincreaseindensity,theresultisareturn,orareversal,totheoriginalsituation,whichisequalnumber.

2.Theconcreteoperationalchildalsocomestousetheoperationofnegation.Wehavealreadyseenthatwhentherowofsweetsiscompressed,theconcreteoperationalchildrealizesthatthesweets’ increaseindensityisreciprocatedbythepennies’ increaseinlength,and that, as a result of these reciprocal transformations, the number of the two setsremains equivalent. The concrete operational child is also able to imagine that thesechangescanbeannulledornegated.Hereasonsthattheactionofcontractingthesweetscanbenegatedbytheinverseactionofspreadingthemout.Theoneactionisannulledby theother. Suchannulmentornegation isanother formof reversibility; that is, thechild mentally reverses the action of contracting the row of sweets. As a result heattributesequalnumberstothetwosets.Notethatthestage3childbothreversestheactofcontractingandrecognizesthatthefinalresultistheoriginalarrangementofsweets


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andpennies.Thestage2child,whoiscapableofempiricalreversibility,recognizesthatthesweetscanbereturnedtotheiroriginalpositionbutdoesnotfocusonorappreciatetheactofrearrangement.Heattendstostates,nottransformations.

3. The concrete operational child sometimes uses an identity argument, reasoning that thenumbersmustbethesamesincethesameobjectsareinvolved:nothinghasbeenaddedortakenaway.

Thestage3child’s thought isconcrete inaspecialsensewhichSinclair(1971),oneof themost

importantGenevaninvestigators,expressesquiteclearly:“Concreteoperations...doesnotmeanthatthe

childcanthinklogicallyonlyifhecanatthesametimemanipulateobjects....Concrete,inthePiagetian

sense,meansthatthechildcanthinkinalogicallycoherentmanneraboutobjectsthatdoexistandhave

realproperties,andaboutactionsthatarepossible;hecanperformthementaloperationsinvolvedboth

whenaskedpurelyverbalquestionsandwhenmanipulatingobjects....Theactualpresenceofobjectsis

nointrinsiccondition”(pp.5-6).

Tosummarize, thestage3child,havingenteredtheperiodofconcreteoperations,canconstruct

two sets equivalent in number, and can conserve this equivalence despite changes in appearance.

Underlyingtheseachievementsareanumberof thoughtprocesses.Theability toconstructequivalent

setsrequiresvicariantorderingandclassification.Theabilitytoconserve,whichisacquiredasaresultof

thedecentrationofthechild’sattention,issupportedbythreetypesofoperationswhicharesometimes

explicitlyexpressedinthechild’sjustificationofhisresponse:reciprocity,negation,andidentity.These

areaspectsofconcreteoperations,whichmaybedescribedbythegroupings.Thechilddoesnotalways

performallofthethoughtprocesseswhenpresentedwithaproblemofconstructingequalsets,nordoes

herefertoallthreeargumentswhenaskedforajustificationofconservation.Hemightonlyrefertoone

or perhaps two of them. The child is, however, capable of performing all the concrete operations,

althoughhemaynot alwaysdo so. In fact, after a periodof time the concrete operational child takes

conservation for granted.He immediately recognizes that number is conserved anddoes not need to

proveconservationtohimselfbymeansofnegationorreciprocity.Whenaskedwhynumberisconserved,

hethinksthatthequestionissillyandthatthefactofconservationisself-evident.Forhim,conservation

has become amatter of logical necessity. This is evidence that the child has acquired an underlying

structureofmentaloperations inwhicheach isdependentupon theotherandnone isperformed in


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isolation.Thestage3child’sthoughtisconcreteinthespecialsensethathecanthinkcoherentlyabout

anddealwithrealobjectsbutnothypotheticalentities.

In conclusion, Piaget’s work on number has been extraordinarily productive. It has stimulated

volumes of research on children’s number, and many of Piaget’s findings have been successfully

replicated,eveninnon-Westernsocieties(seeDasen,1977).AsweshallfindinChapter6,theworkhas

alsohadimplicationsforeducationalcurricula.Likemanymajorcontributionstopsychology,thework

has aroused a good deal of controversy, and several alternative views have been proposed (see, for

example,GelmanandGallistel,1978;andGinsburg,1982).

CONSERVATION

Thus far, we have described only the conservation of number—that is, the child’s ability to

recognize that thenumericalequivalencebetween twosets remainsunchangeddespitealterationsof

physical arrangement. Piaget has also investigated severed other conservations which include

continuous quantity, substance, weight, and volume. The conservation of continuous quantity may be

definedbythissituation.Thechildispresentedwithtwoidenticalbeakers(AandB),eachfilledwith

equalamountsofliquid(seeFigure11),andisaskedwhetherthetwoglassescontainthesameamount

ornotthesameamounttodrink.Afterheagreestotheequivalenceofquantities,theliquidispouredby

either the experimenter or the child from one of the two identical beakers (say, B) into a third,

dissimilarlyshapedbeaker(C).Thecolumnoftheliquidinthethirdclass(andtheglassitself)isboth

shorterandwiderthanthatintheremainingoriginalglass(A).Thechildisnowaskedwhetherthetwo

beakers(nowAandC)containequalamounts.Ifheassertsthattheydo,heisaskedtoexplainwhy.The

liquid inC is then returned to theoriginalbeakerB, and the child is againasked ifA andB contain

identicalamounts.Themanipulationisrepeated,thistimewithaglass(D)whichistallerandthinner

thantheoriginalbeakers.Finally,theliquidofeitherAorBispouredintoaset(E)ofaboutthreeorfour

smallerglassesandthesamequestionsareaskedofthechild.Ifthechildcontinuouslyassertsineach

casethattheamountthathasbeenpouredfromBintothedifferentbeakersisalwaysthesameasthe

amountremaining in theoriginalbeaker(A), thenhehasconservedcontinuousquantity.That is, the

childrecognizesthatmerelypouringtheliquidfromBtoCorDorE,doesnotincreaseordecreasethe

quantity;the“amount”ofliquidremainsthesame(orisconserved)whetheritisinBorinC.Sincethe


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quantitiesAandBwereequal,andsincepouringtheliquidofBintoCdoesnotchangeitsquantity,then

thequantitiesinAandCmustalsobeequal.Ifthechilddoesnotconsistentlyassertthisequality,thenhe

hasfailedtoconserve.

FIGURE11Conservationofcontinuousquantities.

Inthecaseofconservationofsubstance,thechildispresentedwithtwoidenticalballsofPlasticine

(orclay,etc.).HeisfirstaskedwhetherthereisthesameamountofPlasticineinbothballs.Ifhedoesnot

think so, he is asked to take away or add some clay tomake them identical. Then, the experimenter

changesoneoftheballstoasausageshape,whilethechildwatches.Thechildmustnowdecidewhether

ornottheballandthesausagehaveequalamountsofsubstance.As inthe liquidsituation, theball is

changed into a varietyofdifferent shapes. If the child consistently asserts that thebelli and thenew

shapesdohaveequalamountsofsubstance,thenhehasconservedsubstanceandhasrecognizedthat

merelychangingtheshapedoesnotaltertheamountofmatterinvolved.

To test theconservation ofweight, the experimenter again presents the childwith two identical

ballsofPlasticineandplacesthemonabalance.Thechildseesthatthetwoballsweighthesame.Then

theyareremovedfromthebalanceandoneballistransformedintotheshapeofasausage.Thechildis

askedtoanticipatetheresultsofplacingtheballandthesausageonthetwosidesofthebalance.Will

theystillremainbalancedorwillonesidebeheavierthantheother?Thequestioniswhetherthechild

recognizesthatweightisconserveddespitechangesinshape.Hereagainaseriesofchangesaremadeto

oneoftheballsandthequestionastotheidentityofweightisrepeated.

Inthecaseofconservationofvolume,twoballsofPlasticineareplacedintwoidenticalbeakers,each

filledwithequalquantitiesofliquid.Thechildseesthattheballsdisplaceanequalvolumeofliquidin


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bothbeakers.Or,inthechild’sterms,theliquidgoesupanequaldistanceinbothcases.Thentheballs

areremovedfromthebeakers,andoneballischangedintotheshapeofasausage.Thequestionnowis

whetherthechildrecognizesthatbothballandsausagecontinuetodisplaceequalvolumes,orwhether

thewatergoesupanequalamountinbothcases.

All theseconservationsaresimilar.Theyinvolvea firstphase inwhichthechildmustrecognize

thattwoamounts—liquidquantity,substance,weight,orvolume—areequal.Mostchildrenabovetheage

of 4 years are quite successful in this task. All the conservations also involve a visible transformation

whichmaybedonebyeitherthechildortheexperimenter.Whilethechildwatches,orasaresultofhis

ownactions,theliquidispouredfromonebeakertoanother,ortheballischangedintoasausage.Itis

quiteapparentthatnoliquidorPlasticineisaddedortakenaway.It isalsoapparentthatthingsnow

lookdifferent.Thecolumnofliquidisshorterandwider,andtheballisnowasausage.And,finally,all

theconservationsinvolveasecondphaseinwhichthechildmustonceagainjudgewhethertheamounts

inquestion are still the same.Of course, they are equivalent, and the issue iswhether the childwill

recognizethisorbemisledbytheobservedchangesinappearance.

Piaget’sgeneral findingsare that there isasequenceofdevelopmentwithregard toeachof the

conservations.Childrenbeginbyfailingtoconserveandrequireaperiodofdevelopmentbeforetheyare

able to succeedat the task.Forexample, in the caseof continuousquantities, childrenarenotable to

conserveuntilabouttheageof6or7years.Inthefirstphaseoftheproblem(twoidenticalbeakers,each

filledwithequalamountsofliquid),theyoungestchildren,around4or5yearsofage,correctlyconclude

that theamountsof liquidareequal.Since thechildhaseitherpouredout the liquid into thesecond

beaker,orhastoldtheexperimenterwhentostoppouring,thisisnotsurprising.Ifaskedtojustifythe

identity,thechildwillsaythatthewatercomesuptothesamelevelineachglasssothattheamountsare

equal.Whentheliquidinonebeakerispouredintoathirdglasswhichisdifferentinshapefromthefirst

two,thechildnowmaintainsthattheamountsarenolongerequal.Oneglasshasmoretodrinkthanthe

other.Askedtoexplainhisanswer,hesaysthattheglasswiththetallercolumnofliquidhasthegreater

amount.Thisjudgmentofamountsistiedexclusivelytotheheightsofthecolumnsofliquid:whenthe

heightsare the same (as inphase1), the child thinks that theamountsare the same;when theyare

different(asinphase2),thentheamountsmustbedifferenttoo.


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Instage2,thechildof5or6yearsvacillatesinhisresponsestotheconservationproblem.Whilehe

usuallyfailstoconserve,hisapproachtotheproblemvariesfromtimetotime.Inthesecondphaseofthe

experiment(whenonebeaker isshorterandwiderthantheother), thechildsometimessaysthatthe

tallerbeakerhasmore todrink,andsometimesmaintains that thewideronehas thegreateramount.

Unlikethestage1child,hedoesnotconcentrateexclusivelyontheheightsofthecolumnsofliquid,but

sometimesbaseshisjudgmentsonthewidthsaswell.

Instage3,thechildiscapableofconservation.Whenaskedwhytheamountsdonotchangeafter

thepouring,hegivesatleastoneofseveralreasons.OneisthatiftheliquidinCwerereturnedtoits

originalcontainer,B, thenthetwoinitialbeakers,AandB,wouldcontain identicalcolumnsof liquid.

Thisisthenegationargument.Asecondreasonistheidentityargument:it’sthesamewater.Youhaven’t

addedanyortakenanyaway.Athirdargument,involvingcompensationorreciprocity, isthatthethird

glass,C,isshorterthantheoriginalbeaker,A,butwhatClostinheightwascompensatedbyC’sgainin

width;therefore,theamountinCmustbeequaltotheamountinA.

Towardtheendofhislife,Piagetreturnedtotheproblemofconservationandstressedtheroleof

commutability. Inoneexperiment,Piaget (1979)presentedchildrenwithaconservationofsubstance

problemofthefollowingtype.Aballofclayispresentedandthenapieceisremoved.Thechildisasked

iftheballhasthesameamount,andsaysno,sincesomethinghasbeentakenaway.Thepiecethathad

beenremovedfromonesideoftheballwasplacedontheothersideandthechildwasagainaskedifthe

ballhasthesameamountnow(withthepieceaddedtotheotherside)asdidtheoriginalball.Piaget

findsthatundertheseconditions,childrenassertconservationataveryyoungage.Theysayessentially

that“It’sthesamething,youtookitawayandthenputitbackandit’salwaysthesame”(p.21).Inother

words,thechildrenhaveunderstood“thatthereisdisplacement,andthatwhenonedisplaces,whatis

addedatoneplacehasbeentakenawayfromanotherplace”(p.21).ThisPiagetcalls“commutability”

andclaimsthatitisoneimportantfactorinconservation.Commutabilitybearsasimilaritytothenotionof

compensation.

In the case of conservation of substance, weight, and volume, a similar progression to that of

quantityappears.Inthefirststage,thechildfailstoconserveapparentlybecauseofaconcentrationon

onlyoneofthestimulusdimensionsinvolved.Thatis,inthecaseofweighthemaysaythatthesausageis


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heavier than the ball because the former is longer. In the second stage, he again fails to conserve,

although now he vacillates between the two dimensions involved. For instance, he may sometimes

believethattheballisheavierbecauseitiswiderandatothertimesassertthatthesausageisheavier

because it is longer. In the third stage, the child conserves, for reasons similar to those cited for

continuousquantities.

Whilealltheconservationsfollowasimilarcourseofdevelopment,thereisastrikingirregularityas

well—thephenomenonofhorizontaldécalage.Thisreferstothefact,whichhasbeenwellsubstantiated,

thatthechildmasterstheconservationofdiscontinuousquantityandsubstanceataboutage6or7;does

notachievestage3oftheconservationofweightuntilage9or10;doesnotunderstandtheconservation

ofvolumeuntilapproximately11or12.Ineachcasetheargumentsusedarethesame,sometimeseven

involvingthesamewords.Buthavingmasteredconservationinonesubstantivearea,likesubstance,the

child is not able to generalize immediately to another area like that of weight. First, he acquires

conservationofdiscontinuousquantityandsubstance,andthenweight,andthenvolume.Thedécalage,

orlackofimmediatetransfer,illustrateshowconcreteisthethoughtofthechildduringtheagesofabout

7to11years.Hisreasoningistiedtoparticularsituationsandobjects;hismentaloperationsinonearea

maynotbeappliedtoanother,nomatterhowusefulthismightbe.

GENERAL CHARACTERISTICS OF THOUGHT

Wehavereviewedthedevelopmentofvariousaspectsofthought:classes,relations,number,and

conservation.Itwouldseemusefulatthistimetotakeabroaderlookatsomegeneralcharacteristicsof

cognitivedevelopment.

Underlying Patterns of Thought

There are striking regularities in the child’s cognitive development. In each of the two major

periodsofdevelopmentdiscussedinthischapter(preoperationalandconcreteoperational),thechild

usesdistinctivepatternsofthoughttoapproachdifferentsubstantiveproblems.Thereappeartobesome

generalpatternswhichcharacterize the thoughtof thepreoperational childandsomeotherpatterns

manifestedintheconcreteoperationalchild’scognition.


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Consider,first,thechildfromabout4to7yearsinthepreoperationalperiod.(Rememberthatthis

age designation is only approximate, since a child as old as 9 or 10 years typically shows a

preoperationalapproachtotheconservationofvolume.)Onegeneralcharacteristicofcognitiveactivity

duringthisperiodiscentration.Thechildtendstofocusonalimitedamountoftheinformationavailable.

In the conservationofnumber, he judges two sets equalwhen they are the same length and ignores

anotherrelevantvariable,thedensity.Intheconservationofcontinuousquantity,thechildjudgestwo

amountsequalwhen theheightsof thecolumnsof liquidare thesameand ignores thewidth. In the

constructionofordinalrelations(theproblemoforderingtensticksintermsofheight),hesucceedsonly

byconsideringthetopsof thesticksand ignoringthebottoms,orviceversa. Inall theseproblems, the

preoperational child deploys his attention in overly limitedways. He focuses on one dimension of a

situation,failstomakeuseofanother,equallyrelevantdimension,andthereforecannotappreciatethe

relationsbetweenthetwo.(Thenotionofcentration issomewhatsimilar toPiaget’searlierconceptof

juxtapositionwhichisthetendencytothinkintermsofthepartsofasituationandnotintegratethem

intoawhole.)

Bycontrast, theconcreteoperational child is characterizedbydecentration. He tends to focus on

severeddimensionsofaproblemsimultaneouslyandtorelatethesedimensions.Intheconservationof

number,hecoordinateslengthanddensity:twosetshavethesamenumberwhenthefirstislongerthen

the second but the second is denser than the first. In the conservation of continuous quantity, he

recognizes thatamountsareequalwhenonecolumnof liquid isat thesametimetallerbutnarrower

than a second. In the construction of ordinal relations, he determines whether a given object is

simultaneously bigger than some objects and smaller than others. In all these problems, the concrete

operational child attends to severed aspects of the situation at once. Centration anddecentration are

generalpatternsofthought,underlyingstructures.

Thetwomajorperiodsofdevelopmentcanbecharacterizedinotherwaysaswell.Thethoughtof

thepreoperationalchildisstaticinthesensethatitcentersonstates.Intheconservationofsubstancehe

focuses on the shape of Plasticine (sometimes a ball and sometimes a sausage) and ignores the

transformation,thatis,thechangefromonestatetotheother.Intheconservationofcontinuousquantity

he focuses on the heights of the columns of liquid and not on the act of pouring. He lacks adequate

representationsofanobject’sshiftfromonepositiontoanother.Ingeneral,heconcentratesonthestatic


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statesofasituationandnotonitsdynamictransformations.

Theconcreteoperationalchild,ontheotherhand,isattunedtochanges.Intheconservationshe

concentratesonthetransformation:theactofpouringtheliquid,orspreadingapartasetofobjects,or

deformingaballintoasausage.Heformsmoreorlessaccurateimagesofthechangeswhichhavetaken

place,and,therefore,canreason,forexample,thatasasetexpandsinlengthitsimultaneouslydecreases

indensity.

The preoperational child’s thought lacks reversibility. He may be able to predict an empirical

reversibility as, for instance, in the case of the liquidswhere hewould agree that if thewaterwere

pouredbackintoB,therewouldbethesamequantityasbefore.Butthisempiricalreversibilitydoesnot

changethefactthatnowhebelievesthereismore(orless)waterinthenewglassC.Itisasifpouring

fromBtoC,andfromCtoBweretotallyunrelatedactions.Theolderchild,ontheotherhand,realizes

thatpouringfromCtoBreversesornegatestheactionofpouringfromBtoCandisawarethatitisthe

sameactionperformedinanotherdirection.Bycarryingouttheactionmentally,thatis,byreversingthe

pouringinhismind,heisabletoascertainthatthequantityofwaterinC(thelowerwiderglass)isthe

sameasinB.Hecanperformamentaloperationwhichleadshimtoacertainconclusion,andthendothe

reverseofthisoperationwhichenableshimtoreturntohisoriginalstartingpoint.

Theconcreteoperationalchildcanalsoperformanothertypeofreversibilitywhenoperatingon

relations.Thisisreciprocity.Forinstance,intheexampleofliquidquantity,whenthechildsaysthatone

glassislongerandthinner,whereastheotherisshorterandwider,heiscancelingoutthedifferences

betweenthetwoglassesbyanactionofreciprocity.Onedifferencebalancesouttheother,withtheresult

thattheyhaveareciprocalrelationship.

Tosummarize,thepreoperationalchild’sthoughtisirreversibleandattentivetolimitedamountsof

information, particularly the static states of reality. The concrete operational child focuses on several

aspects of a situation simultaneously, is sensitive to transformations, and can reverse the direction of

thought. Piaget conceives of these three aspects of thought— centration-decentration, static-dynamic,

irreversibility-reversibility—asinterdependent.Ifthechildcentersonthestaticaspectsofasituation,he

isunlikelytoappreciatetransformations.Ifhedoesnotrepresenttransformations,thechildisunlikelyto


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reversehis thought.Bydecentering,he comes tobeawareof the transformations,which thus lead to

reversibilityinhisthought.Inconclusion,wecanseethatoneaspectofthoughtisnotisolatedfromthe

rest.Eventhoughthenatureofthesystemmayvarywiththedevelopmentofthechild,thoughtprocesses

formanintegratedsystem.

Invariant Sequence

Another striking regularity in cognitive development involves invariant order: the sequence of

activities (for example in classification, partial alignments, collections, class inclusion) assumes an

invariantorderdespitewidevariationsinculture.Cross-culturalresearchprovidesrelevantevidenceon

thisissue.WithinWesterncultureschildrenprogressthroughthevariousstagesintheorderdescribed

byPiaget.Inthecaseofconservationofcontinuousquantities, forexample,researchshowsthatSwiss,

British,American,andCanadianchildrenfirstfailtoconserve,thenvacillateintheirresponse,andlater

conservewithstability.Whilechildrenintheseculturesdonotnecessarilyachievethevariousstagesat

thesameaverageages, thesequenceofdevelopment—theorderof thestages—seems identical inall

cases.Eveninotherandverydifferentcultures,liketheThaiorMalaysian,thesamesequenceofstages

andtypeofresponsesappear.ChildreninThailand,forexample,exhibitclassificationactivitieswhich

arevirtuallyidenticaltothoseusedbyWesternchildren,andproceedthroughthesequenceofstagesin

theorderdescribedbyPiaget(Opper,inDasen,1977).Thereisgreatcross-culturalgeneralityinPiaget’s

findings.Atthesametime,wemustmakeonequalification:apparently,membersofsomeculturesdonot

advanceasfarinthesequenceofstagesasdoWesterners.Thus,forwhateverreasons,insomecultures,

individualsmaynot complete the stageof formaloperations.Not everyoneachieves thehighest level

possible in terms of Piaget’s stages. Yet, until their progress terminates, these individuals proceed

throughthesequenceofstagesinthestandardorder.Whiletheultimatelevelofdevelopmentmaydiffer

amongcultures, thesequenceseemstobe invariant,asPiagetproposes.Thephenomenadescribedby

Piagetarethusnearlyuniversal,occurringacrossextremevariationsincultureandenvironment.Piaget

hassurelycapturedsomethingverybasicinhumancognition.6

Irregularities

Piaget has gone to great lengths to dispel some misinterpretations concerning his theory. In


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particular,heshowsthattherearecertainirregularitiesindevelopment.Hepointsout,first,thattheages

atwhichthestagesoccurvaryconsiderablybothwithinandamongcultures.NotallGenevanchildren

attainstage3ofnumberdevelopmentat6or7years,andchildreninMartiniquelagbehindGenevans

byapproximatelyfouryears.InThailand,urbanchildrenattainstage3atthesametimeaschildrenin

Geneva,but ruralThai children lagbehindbyapproximately threeyears. InMalaysia, rural children

attainthenumberconceptoneyearaheadofurbanchildren,whointurnlagbehindSwisschildrenby

twoyears.Thus therateofdevelopmentseems tovary fromgroup togroup.Second, thecourseofan

individual’sdevelopmentiscontinuous.

Thechildisnotcharacterizedbystage1onedayandbystage2thenextday.Rather,thetransition

is gradual, occurring over a long period of time, and the child exhibits many forms of behavior

intermediary between the two stages. Indeed, an individual child’s behavior takes many forms in

addition to those Piaget describes as being typical of the various stages. Piaget’s stages are idealized

abstractions;theydescribeselectedandsalientpointsonanirregularcontinuumofdevelopment.Third,

thechildisnotalwaysinthesamestageofdevelopmentwithregardtodifferentareasofthought.The

childmaybe characterizedby stage2 in the case of classes, and stage1 in the case of relations. It is

unlikely,however,thathewillbeinstage1forclassesandstage3forrelations.Onlyinfrequentlydoes

onefindextremediscrepanciesbetweenstagelevelsindifferentareas.Fourth,aswehavealreadyseen,

there exists the phenomenon of horizontal décalage, in which the child displays different levels of

achievementinregardtoproblemsinvolvingsimilarmentaloperations;forexample,hemaybeableto

conservesubstancebutnotnumber.

Preoperational Strengths

Piaget (On the Development of Memory and Identity, 1968) tries to correct a widespread

misconception concerning preoperational thought. Typically, we characterize the young child as

intellectuallyincompetentsincehecannotconserve,cannotusereversibility,andcannotdecenter.Piaget

feelsthatthisviewisexaggerated;asaresultofrecentresearch,Piagetproposesthatthepreoperational

childpossessesanumberofimportantintellectualstrengthswhichmustnotbeoverlooked.Inparticular,

theyoungchildiscapableofidentity,functions,andcorrespondences.


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While unable to conserve, the young child nevertheless appreciates certain basic identities. For

example, in the standard conservation problem, the young child recognizes that the same liquid is

transferredfromonebeakertoanothereventhoughonelooksquitedifferentfromtheother.Heseesthat

thebasicsubstancedoesnotchange,eventhoughitsappearanceisalteredandeventhoughhefalsely

believesthattheamountofliquidhaschanged.Heappreciatesidentitybutfailstoconservequantity.

Piagetproposesthatthenotionofidentitymayderivefromthechild’sperceptionofhisownbody’s

growth.WithGilbertVoyat,Piagetaskedchildrentodrawthemselveswhentheywerebabies,whenthey

were a little bigger, and so on; then the experimenters questioned the children concerning the

maintenanceof their identitydespiteobviousphysicalchanges.Theexperimentersalsoposedsimilar

questions concerning the identityofotherobjects, includingplants.The results showed that children

easily appreciated their own identity despite changes in size, and were less likely to accept the

continuing identity of a plant over its various changes in appearance. Perhaps, then, the notion of

identity derives from the child’s perception of his ownbody’s growth and later is generalized to the

worldofobjects.

Thepreoperationalchildcanalsoperceivefunctionalrelationsintheenvironment.Oneexample

ofsuchfunctions(givenbySinclair,1971)involvestheopeningofacurtain:“thechildunderstandsthat

whenonepulls thecordofacurtain, thecurtainopens; the fartheronepulls, the farther thecurtain

opens”(p.4).Inotherwords,thereisafunctionalrelation,aco-variationbetweenpullingandopening,

and the child perceives that the two factors are positively related. (Theremay evenbe precursors of

functionsin infancy:thisexampleisreminiscentoftheinfantLaurentwhoseemedtorealizethatthe

morevigorouslyheshookachain,thelouderwouldbethesoundproducedbytheattachedrattles.)Itis

veryimportant,ofcourse,forthechildtorecognizesuchfunctionalrelationsintheenvironment:they

pervadeit.Thetallertheperson,thestrongerheislikelytobe;theharderonehitsanotherchild,the

more likely is the child to protest and even cry; the bigger the glass, themoremilk it holds. Despite

limitations in other areas of thought (for example, centration), the preoperational child has some

appreciation for basic functional relations, and this is of great value to him in coping with the

environment.

At the same time, Piaget points out that these functions are incomplete: they constitute only a


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semilogic.Foronething,thechild’sappreciationoffunctionsisimprecise.Toreturntotheexampleofthe

curtain, thechilddoesnotrealizeexactlyhowthepullingof thecord isrelatedto theopeningof the

curtain and cannot quantify the results with any degree of precision. Another Piagetian experiment

makes this clear. Children were presented with three toy fish, 5, 10, and 15 centimeters long,

respectively,andweretoldtofeedeachfishitsproperdietofmeatballs.Themiddle-sizedfishshouldget

twiceasmanymeatballsasthesmallest,andthelargestfishthreetimesasmany.Preoperationalchildren

understoodthefunctionalrelationbetweensizeof fishandnumberofmeatballsonly inanimprecise

way.Theyrealizedthatthelargerthefish,themoreitneedstoeat.Buttheywerenotabletoworkoutthe

functioninaprecisemanner(forexample,bygiving2,4,and6or3,6,and9meatballstotherespective

fish).

Toward the end of his life, Piaget (1979) stressed the role of “correspondences.” He used this

notiontorefertothechild’stendencytocompareobjectsorevents,todeterminethewaysinwhichthey

“correspond,” or are similar and different. This tendency appears at all levels of development, from

infancyonward,althoughittakesdifferentformsatdifferentlevels.

Forexample,aninfantfirsthitsatoyparrottomakeitswingandthenappliesthehittingschemeto

otherhangingobjectsaswell.Inasensehehascomparedthenewobjectwiththefamiliarparrotand

notedthesimilaritybetweenthem(thecorrespondenceofoneobjecttoanother).

Note:Ablackmarbleandawhitemarblearegluedtoaplate,withthewhiteoneabovetheblack

one(asinFigure12A).Thentheplateisrotatedsothatblackoneisabovethewhiteone(asinFigure

12B).


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FIGURE12CorrespondenceofMarbles.

The preoperational child displays different forms of correspondence. For example, in one

experiment,Piaget(1979)showedchildrentwoobjectsonarotatingdisk.Imaginethattheobjectsarea

whitemarbleandablackmarble,gluedtoadish,as inFigure12A.Whenthemarblesareon the left

(Figure12A),thewhiteisabovetheblack.Whenthedishisrotatedsothatthemarblesareontheright

(Figure12B),thentheblackisabovethewhite.Thepreoperationalchildobservesthesituations—the

marblesontheleftandontheright—andgraduallynotesthecorrespondencesbetweenthem.Thechild

seesthatwhenthemarblesareontheleftside,thewhiteishigher,butwhentheyareontheright,the

whitebecomesthelower.Atfirst,thechild’sapproachissimply“empirical”:torecordthefactswithout

interpreting them. But “the child discovers suddenly that there is a general order” (p. 24). He

determines,inotherwords,thatthereisareversalofposition.It’snotjustthatthewhiteishigherinone

situationandlowerintheother,butthatthewhitehasswitchedpositions.This insight thengradually

leadsthechildtoanother:thepositionswereswitchedbecauseatransformationtookplace.Therotation

ofthedishcausedtheswitchinposition.

We see then that the child begins by comparing two states, noting some basic similarities and

differences(theswitchinposition).Thesecorrespondencesareimportantbecausetheypavethewayfor

thechild’sappreciationoftransformations.Andaswehaveseen,anappreciationoftransformationsisat

theheartofconcreteoperationalthinking.

In brief, preoperational thought is not characterized solely by incompetence. Young children

appreciatecertainbasicaspectsofidentity,perhapsasaresultofexperiencewiththeirownbodies.They


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alsounderstand,albeitinanimprecisemanner,varioussimplefunctionalrelationsintheenvironment.

Theydetectcorrespondences,andthisleadsthemtoanappreciationoftransformations.Indealingwith

youngchildrenonemustbeawareof these strengthsaswell asof the commonly cited limitations, as

GelmanandGallistel(1978)andothercontemporarywritersconcurinmaintaining.

The Concept of Stage

Piaget’s theory describes a sequence of stages. For example, in the case of the conservation of

numberwehavereviewedthetransitionfromcentrationtodecentration.Nowitisimportanttoconsider

thenatureofsuchstages.WhatdoesPiagetmeanbystageandhowusefulaconceptisit?

AccordingtoPiaget(BiologyandKnowledge, 1971a,p. 17) thenotionof stage isusedwhen the

followingthreeconditionsarefulfilled.First,theremustbeaninvariantsequenceofactivities.Thus,in

thecaseofconservation,thereis,first,afailuretorecognizeequivalence;thenthereisvacillation;and,

finally,thereissuccess.Theorderofappearanceoftheactivitiesisthesameforallchildren.Second,each

stageinthesequenceischaracterizedbyanunderlyingstructure,acoresystemdeterminingthechild’s

overt behavior. Thus, underlying the child’s failure to conserve is the strategy of centration—the

tendencytofocusonlimitedamountsofinformation.Third,eachofthestructurespreparesthewayfora

succeedingone.Thus,inthecaseofconservation,theinitialcentrationpreparesthewayforavacillation

amongtheavailabledimensions,andthisinturnleadstothesubsequentdecentration.Inbrief,Piaget

proposes that stages are characterized by invariant sequence, underlying structures, and successive

integrations.

Piagetalsoemphasizedthatdespitetheexistenceofstages,developmentiscontinuous.Thechild

doesnotenteranewstageovernight;instead,thechangesaregradual,andindeedbarelyperceptible

fromclose-up.Piagetexplainedthisintermsofthescaleofmeasurement.Ifwelookcloselyatachild’s

development,observingeverydayandthususinga finescaleofmeasurement, it ishardforustosee

dramaticchanges;fromonedaytothenextwewillnotnoticedifferencesinstages.Butifwestandback,

observing the child infrequentlyand thususinga crude scaleofmeasurement,wewillbe impressed

withchanges;fromoneyeartothenextwewillseeprogressfromonestagetothenext.


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Wehavealreadyreviewedresearchconcerningthenotionsofinvariantsequenceandunderlying

structure. Cross-cultural study demonstrates that the sequence described by Piaget is extremely

widespread,ifnotuniversal.Also,thereseemtobedistinctunderlyingpatternsorstructuresineachof

the major periods under consideration—preoperational and concrete operational. Consider next

Piaget’sthirdconditionfortheexistenceofastage—therequirementthateachstagepreparethewayfor

thenext.Whileitishardtoadduceevidencesupportingthisnotion,itseemstohaveacertainamountof

facevalidity;forexample,afocusontwodimensionsseemsnaturallytofollowfromafocusonone.In

brief, the evidence concerning invariant sequence, underlying structures, and successive integrations

seemstosupportPiaget’spropositionconcerningtheexistenceofmajorstagesofdevelopment.

Atthesametime,thestagenotionsuffersfromanumberofdifficulties.One,alreadyalludedto,is

theexistenceof irregularities indevelopment.Wehaveseen that thechild isnotalways in thesame

stagewithregardtodifferentareasofthought.Thus,hemaybeinstage1withrespecttoclassesand

stage2inthecaseofrelations.Also,thephenomenonofhorizontaldécalageisverystriking:thechildmay

displaydifferentlevelsofachievementinregardtoverysimilarareasofthought.Thus,hemayconserve

substance but not number. The existence of these irregularities seems dissonant with the notion of

distinctunderlyingpatternsorstructuresofthoughtcharacterizingthemajorstagesofdevelopment.If

thepatternsaresostrongandpervasive,whyarethedécalagessostriking?

Anotherdifficultywiththestagenotionisthatthestructurespresumablyunderlyingastagemay

alsobeimplicatedinstagesoccurringearlierinthesequence.ThuswehaverecentevidencebyTrabasso

(1975), for example, to the effect thatunder certain conditions, preoperational children canperform

concreteoperationaltasks.Ifthesamestructuresunderliebehavioratdifferentstages,dowenotthen

have toalterournotionof stages?The issueof stages isextremely complexand isnow the subjectof

considerablerethinking(foranexcellentdiscussionseeFlavell,1985).

Indeed,towardtheendofhislife,Piagetseemstohaverethoughtthestagenotionhimself.Thelast

tenyearsofPiaget’sresearchrevolvedlargelyaroundissuesofcognitivechangeanddevelopmentand

did not employ stage notions to any significant degree. In this sense, Piaget became less of a

“structuralist”(onewhodealswiththeanalysisofmentalstructuresunderlyingthestages)andmoreof

a“functionalist”(onewhodealswiththefactorsdeterminingdevelopment).AsweshallseeinChapter


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6,Piaget’stheoryofequilibrationplacedtheemphasisongradualchangesorineffectonmanyfleeting

substages.WhatwasimportantforthelaterPiagetwasnotaconceptofbroad,stablestages,butatheory

ofthecontinuouschangeanddevelopmentofthechild’sintellectualstructures.

MENTAL IMAGERY

Afterhisbriefexaminationduringthe1920softhecontentofthought,Piaget’smainconcernhas

beenwiththeoperativeaspectofcognition.Thisreferstoactionsusedtodealwithorevenchangethe

world. These actions may be either overt or internal. Examples of overt actions abound in the

sensorimotorperiod.Theinfantkickstoshakearattle,orusesasticktodrawanobjectclose.Thepresent

chapterhascoveredtwomajorsubdivisionsofinternalizedactions:theisolatedandunrelatedactionsof

preoperationalthoughtandthestructuredandcoordinatedonesofconcreteoperationalthought.

Piaget has also shown an interest, albeit a lesser one, in the figurative aspect of cognition. This

referstothreewaysinwhichthechildproducesanaccountofreality.Oneisperception,asystemwhich

functionsbymeansofthesensesandoperatesonanimmediatelypresentobjectorevent.Itisthrough

perceptionthatthechildachievesarecordofthethingsinthesurroundingworld.Thisrecordisoften

inexact, as in the case of the visual illusions. A second subdivision is imitation, by which the child

reproducestheactionsofpersonsorthings. It is truethat imitation involvesactionsonthepartof the

child,buttheseactionsneverthelessfallunderthefigurativeaspectsincetheyproduceacopyofreality

butdonotmodifyit.Athirdportionofthefigurativeaspectismentalimagery.AswesawinChapter3,

mentalimageryreferstopersonalandidiosyncraticinternaleventswhichstandfororrepresentabsent

objectsorevents.Whenwe“picture”toourselvesourfirstbicycle,orthestrollwetooklastweek,thenwe

areusingmentalimagery.Asweseefromthislastexample,thetopicofmemoryiscloselyboundupwith

thefigurativeaspectofthought.Memory(recall)typicallyinvolvesretainingknowledgegainedthrough

thefigurativemode.

In recent years, Piaget has conducted important investigations into two important aspects of

figurative cognition, specifically imagery and memory. His theory stands in stark contrast to the

traditionalempiricistviewofthesematters.Thelatterassumesthatperceptionstampsontheindividual

a literal copy of reality. Given sufficiently frequent repetition of the initial event, a mental image


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mirroring the reality is formed and is stored in memory. If there is no further experience with the

originalevent,thememoryimagegraduallyfades,losingitsfidelitytothereality;itisforgotten.Piaget

criticizesthistraditionalviewonseveralgrounds.Mostimportant,hebelievethatrealitydoesnotsimply

imposeitselfonapassiveorganism.Rathertheindividualassistsintheconstructionofhisownreality.

Hisintellectualactivities—theoperativemodeofthought—servetoshapetheresultsofencounterswith

theenvironment.The resulting figurativeknowledge isnot simplya copyof reality.This theme—the

influence of operative structures on figurative knowledge—dominates Piaget’s discussion of mental

imageryandmemory.Wewillnowconsiderthesetwotopicsinsuccession.

History

Mentalimagerywasoneofthefirsttopicsstudiedbyexperimentalpsychologists.Attheendofthe

nineteenthcentury,theschoolofWundtusedtheintrospectivemethodtoanalyzethenatureofmental

imagery.TheWundtiansbelievedthatimageswerecomposedofabundleofsensationstiedtogetherby

meansofassociation.Atthebeginningofthetwentiethcentury,thestudyofimageryfellintodisrepute

fortworeasons.First,theWurzburgpsychologistsfoundthatmuchofthoughtdidnotseemtoinvolve

imageryatall,andsecond,thebehavioristrevolutionwhichoccurredintheUnitedStatesmaintained

thattheintrospectivemethodwasapoorone.Thebehavioristsfeltthatthedataofintrospection—one’s

impressions of one’s own consciousness—were not public enough. How could another psychologist

determine if an introspectionwere reliable and accurate?As a result of the behaviorist attack on the

methodofintrospection,thestudyofimagerywasconsidered“unscientific”andwaslargelyabandoned.

Recently,however,psychologistshaveshownarenewedinterestintheancientproblemofimagery,and

thetopicisonceagainbecomingcentraltoexperimentalpsychology(Neisser,1976).

Incontrasttomoderninvestigators,Piagethasbeenstudyingimagerysinceatleastthe1930s.In

Chapter3wediscussedPiaget’sworkonimageryintheyoungchilduptotheageof4years.Ifyouwill

recall,thistheoryproposedthatmentalimagesdonotoccuruntilaboutthemiddleofthesecondyear.

Before this timethechilddidnotpossessmentalrepresentationsof theenvironmentand,asaresult,

reactedmainly to events occurring in the present. After imagerymakes its appearance the child can

represent tohimselfbothevents thatoccurred in thepastandobjects thatareno longerperceptually

present. Also, according to Piaget’s theory, imagery results from imitation. At first, the child overtly


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imitatestheactionsofthingsorpeople; later,hisimitationbecomesinternalizedandabbreviated.It is

through this internalactivity that imagesarise.Clearly,Piaget’sviewscontrast stronglywithWundt’s.

Imagesarenotmerelybundlesofsensations,imposedbytheenvironmentandconnectedbyassociation;

rather,theconstructionofimagesinvolvestheactivityofinternalizedimitation.

Later,with Inhelder, Piaget returned to the studyof imagery (1971).His laterworkdealswith

childrenabovetheageof4,andposesanumberofinterestingquestions.Forexample,aretheredifferent

typesof imagesatdifferentstagesof intellectualdevelopment? If so,what is therelationbetweenthe

imagesandthementaloperationsofagivenstage?

Method

Whilethesequestionsareinteresting,thestudyofmentalimagesisverydifficult,especiallyinthe

caseofchildren.Imagesarepersonal,idiosyncraticeventswhichcannotbevieweddirectly.Onecannot

“see”anotherperson’simagery;theinvestigatormust,therefore, infertheirexistenceandnaturefrom

otherphenomena,suchasaverbalreport.Piagethasusedavarietyofmethodstostudyimagery.Oneof

thesemethodsistoaskapersontodescribehisownimages.Butlanguageisnotfullyadequateforthis

task,orevenfordescribingsomethingasconcreteastheimmediateperceptionofanobject.Wearenever

able to convey bywords the precise nature of whatwe see. In our attempt to describe percepts, we

inevitably emphasize certain features and neglect others.We have difficulty in describing shades of

colors,orgradationsof textures.Wecannotgivean impressionof theentireperceptatonce,butmust

describeitsdetails insequence,andtherebyoftenlosetheessenceofthewhole.If languagesopoorly

conveysperceptualeventswhichcontinuetoremainbeforeoureyesforfurtherinspection,howmuch

moredifficultisittodescribementalimageswhichoftenarefleetingandunstable?

Anothermethodof studyingmental images isbydrawing.Here theperson is asked todrawan

objectpreviouslypresented.Sincetheobjectisnolongerpresent,hemustproduceanimageofittoyield

the drawing. The drawing, therefore, gives some insight into the nature of the image, which is the

internal “picture” of the object. The method of drawing, however, presents several shortcomings.

Drawingisnotasimpleanddirectreflectionofimages; italsoinvolvesotherprocesses.Somepersons

havepoormemory.Iftheyhaveforgottentheirimageofanobject,theycannotverywelldrawit.Other


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personssimplycannotdrawwell.Itisnottheirimagethatisatfault,buttheirartisticskill.

A thirdmethodattempts tobypass theshortcomingsoforiginaldrawings.Thesubject isgivena

collection of drawings made by the experimenter, and must select from them the one most closely

correspondingtohisimageofwhathehadpreviouslyobserved.Thismethod,ofcourse,isnotaffectedby

variationsinsubjects’artisticabilitiesandreducesthedifficultiescreatedbyapoorevocativememory.

Buteventhemethodofselectionfromacollectionofdrawingsisnotaltogethersatisfactory.Oneproblem

is that the drawings presented are not likely to be exact copies of the person’s mental image. The

drawingsmayomitdetailsoftheoriginalimageoraddnewfeatures.Ineitherevent,thesubject’schoice

doesnotgiveafullyaccurateindicationofhisimage.

To study imagery, Piaget has used all thesemethods—verbal report, drawing, and selection of

drawings—either alone or in combination. As is customary with the explorations carried out by the

Genevaschool,themethodsweresupplementedbyverbalquestioningcarriedoutintheclinicalmanner.

Major Findings

One experiment was concerned with kinetic images, or the imagery of an object’s movement.

Childrenfromabout4to8yearsofagewerepresentedwithtwoidenticalblocks,oneontopoftheother

(seeFigure13A).Eachsubjectwasaskedtodrawthesituation,andgenerallydidthisquitewell.Then

thetopblockwasmovedsothatitslightlyoverlappedthebottomone,asinFigure13B.Afterthechild

hadhadachancetolookatthisforawhile,thetopblockwasreturnedtoitsoriginalposition(Figure

13A).Thechildwasthenaskedtodrawtheblockinitsdisplacedposition(Figure13B),whichwas,of

course, no longer visible. After this, a collection of drawingswas presented. This contained a correct

rendering of Figure 13B as well as an assortment of incorrect drawings which represented errors

typicallymadebychildrenofthisage.(Thistechniqueissimilartotheuseofcountersuggestionsinthe

interview.)Thechildwasaskedtoselectthedrawingwhichhefeltcorrespondedmostcloselytowhathe

hadseen.Inthefinalstepanothercontrolwasadded.Thetopblockwasonceagaindisplaced,andthe

childwasaskedtodrawthesituationwhileitwaspresent.Ifthechildcouldaccuratelydrawtheblocks

whenpresent,thenanyofhispreviouserrorsofdrawing(whentheblockswereabsent)mustbedueto

faultyimageryormemoryandnottofaultydrawingability.


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FIGURE13Movementofblocks.

Tosummarize,thechildFirstdrewthedisplacedblocksaftertheywerenolongervisible;thenhe

selectedfromagroupofdrawingsoneresemblingthedisplacedblocks;andfinally,whenthedisplaced

blockswereonceagainbeforehim,hedrewthem.

The findings show that before the age of 7 years, children candraw the displacedblocks quite

correctlywhentheyarepresent,butnotwhentheyareabsent;norcanthechildrenchooseadrawing

whichcorrespondstothesituation.Ingeneral,childrenofabout4and5yearsproducedandselected

drawingsofthetypesAthroughE(seeFigure14),whereaschildrenof6yearsmadeerrorslikethoseof

typesFandG.Itwasonlyat7yearsthatover75percentofthesubjectsbothdrewandchosethecorrect

drawings.

FIGURE14Drawingofblocks.

Across-culturalstudyofthisprobleminThailand(Opper,1971)showsthatThaichildrenmake

thesametypesoferrorsasdoSwisschildren,althoughitisnotuntil10yearsofagethat75percentof

theThaisubjectsmakecorrectdrawingsofthetwoblocks.

The responses of the younger child would seem to indicate that he forms only a very general

pictureofthesituation,thatis,thatoneblockhasbeenmoved.Whenaskedtodrawtheexactdetails,heis

unabletodoso.Thechildthereforereproducesthisgeneralimpressionofmovementbydetachingthe

topblockfromthebottom(cf.C),byasymmetricalmovementofshrinkingorenlargementofoneofthe


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twoblocks(cf.DandE),or,finally,bytheretentionofonecommonboundaryoridenticallineforthetwo

blocks, inadditiontomakingchangesontheothersideof theblocks(cf.FandG).His imagedoesnot

appeartocorrespondtotheactualsituation.Thechildseemstocenterononedimension,thatis,onone

particularaspectofthesituation—forexample,theoverlappingofthetopblockindrawingsEandF,or

theoverlappingof thebottomblock indrawingsDandG.However, thechilddoesnotcoordinate the

movementofoneblockwiththefinalstateofthetwoblocks.Apparentlythechilddoesnotanalyzethe

situationinsufficientdetailbutmerelyformsaglobalimpressionofwhathashappened.Heisawarethat

theblockhasmoved,but the intimatedetailsof themovementandtheensuingdisplacementseemto

haveescapedhisattention.Asaresult,hismentalimageisinadequate.

A second typeof imagery is static imagery. In this instance the image reproduces a collectionof

objects,ascene,orapicture—inbrief,anysituationinwhichtheelementsremainunchangedineither

shape or position. Piaget finds that the child is able to produce adequate static imagery earlier than

kinetic.

We have reviewed only a small sampling of Piaget’s experiments on imagery. Their results,

together with those of a great many more studies, have led Piaget to draw the following general

conclusionsconcerningimageryanditsrelationtointelligenceasawhole.First,imagerydevelopsina

gradualmanner.Theevolutionofimageryisnotasdramaticasthatofthecognitiveoperationswhich

display a clear-cut sequence of stages. There appears to be only one major turning point in the

developmentof images.Thisseemstooccurataroundtheageof7or8yearsandcorresponds to the

onsetoftheperiodofconcreteoperations.Beforethebreak,thatis,fromtheageof11/2toabout7years,

thechildseemscapableofproducingwithanydegreeofaccuracyonlystaticimages,andeventheseare

farfromperfect.Thechildcannotrepresentcorrectlythemovementsofanobjectorevensimplephysical

transformations;theimagesproducedforsuchsituationsaregrosslydeformed.

Piagetbelieves that thereason for thisdeficiency isoneaspectofoperativecognition,namely,a

tendencytoconcentrateontheinitialandfinalstatesofagivensituationandtoneglecttheintervening

events which are responsible for the changes. We have already seen this tendency, which is called

centration, operating in the case of conservation. If youwill, recall the situationwhere the childwas

presentedwitha lineofvases,eachofwhichcontainedaflower.Theflowerswereremovedfromthe


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vasesandspreadapart.Whenthisoccurs,theyoungchildusuallybelievesthattherearemoreflowers

thanvases,sincethelineofflowersisnowlongerthanthelineofvases.Hehascenteredonthelengths

andignoredanumberofotherfactors.Hehasfailedtodecenterandtoconsiderthedensityofthelines,

aswellastheirlength,andhehasignoredtheintermediarytransformation(theremovalandspacingof

theflowers).Thus,thechildfocusesmainlyontheinitialandfinalstates(theflowersinthevasesand

the flowersspacedout)and fails to integrate these impressionswithallelse thathasoccurred.Thus,

beforetheageof7or8imageryisextremelystatic.Asaresult,thechildproducesadistortedpictureof

realitycharacterizedbyanemphasisonsuperficialfeatureswhichareeachisolatedfromothersandnot

coordinatedintoacoherentwhole.

Fromabout theageof7yearsonward,however, thechildbecomescapableofproducing images

whichcanreproducekineticsituations.Thisimprovementisduetothefactthathecannowimaginenot

onlytheinitialandfinalstates,butalsotheintermediarytransformations.Hisimageryhasbecomeless

static.Ofcourse,itisneverpossibletoreproducealltheinterveningevents,sinceinsomecases(likethe

pouringofliquid),theyoccurrapidly.Butthechildrecognizesthatasequenceisinvolvedandthatthere

hasbeenaseriesofinterveningstepsbetweentheinitialandfinalstates.

Afinalquestionconcernstherelationbetweendynamicimagesandtheconcreteoperations.Kinetic

imagesoccuratapproximatelythesametimethatthechildbecomescapableoftheconcreteoperations;

whatthenistherelationbetweentheoperativeandfigurativeaspectsofthoughtatthisstage?Onthe

onehand,wehavealreadyseenthatoperativecognitioninfluencesthenatureofthechild’s imagery.

Thus,theconcreteoperationalchild’sdecentrationcontributestothedynamicnatureofhisimagery.In

Piaget’s theory, figurative cognition (here, imagery) is dominated by operative cognition (here, the

concrete operations).On the other hand, images canplay an auxiliary role in thinking. For example,

considerthenumberconservationtaskinvolvingflowersandvases.Theconcreteoperationalchildcan

formaccuratetransformational imagesofthedisplacementoftheflowers.Afterthetransformationhas

beendone,hecorrectlypicturesthewayinwhichtheflowershavebeenremovedfromthevases.The

ability to form imagesof this sortdoesnotguarantee that the child can conservenumber; aswehave

alreadyseen,theprocessesunderlyingconservationarenotsolelyperceptualorimaginal.Nevertheless,

thechildwhohasacorrectimageofthetransformationiscertainlyaheadofthechildwhodoesnot.In

otherwords, images are a useful andnecessary auxiliary to thought during the concrete operational


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stage. By providing relatively accurate representations of the world, images assist the process of

reasoningalthoughtheydonotcauseit.


Images represent absent objects or events. They are “symbols,” in the sense of bearing some

resemblance to the object represented, and are personal and idiosyncratic. Images do not give as

completeanddetailedareproductionoftheobjectasisprovidedbydirectperception.Imagesfirstmake

theirappearancearoundthemiddleofthesecondyearoflife,andtheyarisefromaprocessofimitation

whichgraduallybecomesinternalized.Untiltheageofapproximately7years,thechildisonlyableto

produceapproximatelycorrectmentalimagesofstaticsituations.Heconcentratesonstatesratherthan

ontransformations.Thelimitedimageryofthechildispartlytheresultofimmatureoperativestructures.

Asthesestructuresdevelop,sodoeshisimagery.Aftertheageofabout7years,thechildbecomescapable

ofcorrectkineticimagery.Thisnewabilitypermitsafurtherunderstandingofreality:thechildnowhas

availableamoreaccurateanddetailedrenderingoftheeventsonwhichtofocushisreasoning.

MEMORY

Memory,too,isinfluencedbyoperativecognition.Beforeexploringthis,itisnecessarytobeginby

clarifyingsometerminology.

Definitions

Inordinarylanguage,weusethewords“memory”or“remember”inseveraldifferentsenses.Here

isananecdotetoillustratethepoint.Anadulthasnotriddenabicyclesincechildhood,someyearsago.

Nowhis own child gets a bicycle and askswhether the adult “remembers” how to ride. “Of course, I

rememberhow to rideabicycle,” says theadult.Asked (skeptically) toprove it, theadult geton, and

pedals around a bit. Despite the lack of practice over a long period of time, he is able to ride very

smoothly,muchtothesurpriseofthechildwhoownsthebicycleandwhonowwonderswhetherhewill

gettorideit.Astheadultispedalingdownthestreet,he“remembers”ridingthebicyclewhichheowned

asachild.Hehasafairlyclearmentalpictureofitsoverallshapeandform,aswellastheplacesinwhich


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herode.

This example illustrates two very different kinds of “memory.” In the first kind, the adult

remembers how to do something. Although there has beennopractice formany years, he hasnot lost

general bicycle-riding skills. He “remembers” how to ride not just a specific bicycle, but any bicycle.

Through experience, he has acquired a physical skill of a general nature, and remembers it. In this

instance,weusethetermmemorytoindicatethatthepaststillexertsaninfluenceonthepresent.The

adult’s ability to ride a bicycle, acquired through a set of earlier learning experiences,was somehow

preserved within him. Note that after childhood this ability existed as a potential, since until this

incident hedidnot actually engage in thebehavior.Note, too, that the element of earlier learning is

crucialtothedefinition.Itwouldnotmakesensetosay,“Irememberhowtosneeze,”sincesneezingwas

neverlearned.Yetitwouldmakesensetosay, ‘‘Irememberhowtokeepfromsneezing”sincethatwas

learned.Inbrief,thisisonevaliduseofmemory:apersoncanretain,overaperiodoftime,abehavioral

potentialwhichistheresultofpreviouslearning.

Theothersenseofmemory isquitedifferent.When theadult ‘‘remembers”ridinghischildhood

bicycle,heisreferringtoaspecificeventandthinginthepast.Hehasaholdonaparticularsliceofhis

own history. He ‘‘remembers” a bicycle with wide tires, and a heavy frame—a Schwinn, in fact. He

remembers riding it up Commonwealth Avenue to a park with a certain kind of path. This kind of

memoryismorespecificandconcretethanthefirst.Inthiskindofremembering,theadultretainsspecific

eventsorthingsfromthepast;intheotherkindofremembering,hepreservesthegeneralskillsacquired

in the past. Often the two types of memory occur together. A person remembers how to type (thus

preservingthegeneralability)andalsoremembersthespecifictypewriterusedinhisearlylessons(thus

retaininginformationconcerningaspecificthingfromthepast).Butthetwotypesofmemorydonothave

tocoexist.Apersonmayrememberhowtotypeandyetmayhavetotallyforgottenthespecifictypewriter

orhisearlylessons.Similarly,apersonmayrememberthetypewriterandlessons,butnotrememberhow

totype.Thus,wehaveusedsomeexamplesofphysicalskillstoillustrateadistinctionbetweentwotypes

ofmemory.

In the intellectual domain, Piaget’s theory (Piaget and Inhelder,Memory and Intelligence,MEM,

1973)proposesasimilardistinctionbetween“memoryinthewidersense”and“memoryinthespecific


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sense.”Theformerrefersto“theconservationoftheentirepast,oratleastofeverythinginthesubject’s

pastthatservestoinformhispresentactionorunderstanding”(MEM,p.1).Moreprecisely,memoryin

thewidersensereferstothe“conservationofschemes,”totheretentionofacquiredpatternsofbehavior

orthought,liketheconcreteoperations.Bycontrast,memoryinthespecificsense“refersexplicitlytothe

past,” to specific eventsor thingsorpersons in an individual’shistory.Anotherwayof lookingat the

distinctionistosaythatmemoryinthewidersenseinvolvestheoperativeaspectofthought:itistheway

inwhichgeneraloperationsorwaysofdoing thingsarepreservedover time.Memory in the specific

senseisgenerallyfigurative: itpreserves information concerning specific things—a face, anobject, an

activity. (These “things” include actions, but only specific actions that are thought to have actually

occurred,notthepotentialforactionsofageneraltype.)

Piagetgoesontoproposesomefurtherdistinctionsconcerningmemoryinthespecificsense.This

typeofmemory—andweshallnowsimplyusethewordmemorytorefertoit—maytakeoneofseveral

forms.Perhapsthemostprimitiveisrecognition.Thisoccurswhenapersonencountersthings(anevent,

person, thing, etc.)previously experiencedand “has the impressionofhavingperceived thembefore

(rightlyorwrongly,fortherearefalserecognitions)”{MEM,p.5).Thus,weseesomeoneknownbefore,

and“saytoourselves”thatthepersonisfamiliar,eventhoughhisnamemayeludeusandwecannot

recallwhereweknewhim.Similarly,thebabyinthesensorimotorperiodrecognizesfacesandplaces

whentheyareencountered.Orthebabyshowsthroughhisabbreviatedschemesthatherecognizesatoy

he has played with. Recognition, then, is one form of (specific) memory, involving an impression of

familiarityuponanencounterwithapreviouslyexperiencedobject.

Recall isamuchmoresophisticatedanddifficultformofmemory.Itinvolvesproducingamental

account of a previously experienced thing in the total absence of that thing. One examplewould be

remembering your childhood bicycle or your first grade teacher.Recall sometimes involves a mental

picture,sometimeswords,sometimesanodor.Thecrucialaspectofrecallisthattheindividualproduces

some kind ofmental representation of the previously experienced event.7 It is evident that recall is

closely linkedwith the semiotic function, alreadydiscussed, since the latter involves the formationof

mentalrepresentationsforabsentthingsorevents.

The General Hypothesis


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Piaget’smaininterestisinthefunctioningofmemoryinthespecificsense—recognitionandrecall.

Howdoesspecificmemoryoperate?

According to some empiricist views, memory works in the following manner. An individual

perceivesanobjectandstoreswithinhimitsreplicaortrace.Themorefrequentlyorrecentlytheobjectis

perceived,thestrongerthetrace,andhencethestrongerandmoreaccuratethememory.Inthisclassic

view,memoryissimplyacopyofsomethingreal,andtheaccuracyofthecopydependsonsuchfactorsas

frequency,recency,andthe like.Notethat intheclassicview,theindividual ismainlypassive:things

imposethemselvesonhim;theymakeanimpressiononhim;theyformatraceinhimasapieceofchalk

leavesarecordonaslate(hencetheexpressiontabularasa,orblankslate).8

Piaget’sview isdifferent.Heproposes that the childdoesnot simply record reality inapassive

manner,storingacopyinthewarehouseofmemory.Instead,asPiagetseesit,thechildassimilatesand

interpretsreality,sothatmemoryisinpartafunctionofthechild’sintellectualoperations.Memorystems

notonlyfromexperiencebutfromintelligence.This,then,isthegeneralhypothesiswithwhichPiaget

beginshisempirical investigations.Giventhis theoretical framework,Piagetgoesonto investigate the

specificwaysinwhichmentaloperationsaffectmemory,especiallyrecall.

Experiments on Memory of a Series

Tostudytheinfluenceofknowingonremembering,Piagetconductedseveralexperiments,oneof

whichinvolvedmemoryforaseries,atopicalreadyreviewedinthischapter.Childrenofvariousages

wereshowntenwoodensticks,alreadyarrangedinacompleteseries,fromsmallesttolargest.Eachchild

was“toldtotakeagoodlookatitandrememberwhathehasseen.’’Thenaboutaweeklater,eachchild

wasaskedtorecalltheseriesbydrawingitorbytracingitoutwithhisfingersonthetable.Afterthis,the

experimenterdeterminedthechild’sstageofdevelopmentwithrespecttoseriationbygivinghimthe

usualtests.Theexperimenteralsoobtainedacheckonthechild’sdrawingabilitybyhavinghimcopya

seriesofsticksavailabletodirectperception.Thiscopycouldthenbecomparedwiththechild’sdrawing

frommemorytodetermineifdistortionsinthelatterstemfrommeredrawingdeficiencies.Inbrief,the

experiment involved (1) determining children’s intellectual level with respect to seriation, (2)

presentingthemwithacompletedseriestoremember,and(3)measuringrecallbyfingertracingand


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drawing.Furthermore,(4)ameasureofdrawingabilitywastakensothatthisfactorcouldbecontrolled.

Whatshouldhappen insuchanexperiment?According to theclassicview, theseries impresses

itselfonthepassivesubject,andtheaccuracyofrecalldependsontheextentofthesubject’sexperience

with it and on similar factors. The child’s drawings should to some degreemirror the realitywhich

impinges on him. Piaget’s view is much different: the child actively assimilates the reality into his

intellectualsystemandthisprocessofinterpretationdeterminesthenatureandqualityofrecall.Inthe

presentinstance,astage1childmaydistorthismemoryoftheseriesinaccordancewithhisimmature

intellectualoperations,andthiswillbereflectedinhisdrawingandtracing.Notethattheresultofthisis

notadrawingwhichissimplyapalecopyofthereality.Rather,itisadrawingwhichissystematically

distortedinlinewiththechild’sintellectualoperations.


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FIGURE15Drawingsofcompletedseries.

Consider a few examples of this. One childmade a drawing like that in Figure 15A, involving

several identical long lines and several identical short ones. This drawingwas similar to the child’s

actual arrangement of the sticks during the test of seriation: hemade one bunch of large sticks and


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anotherbunchofsmallsticks,butdidnotaccuratelyseriatewithineachbunch.Anotherchildproduceda

drawinglikethatinFigure15B.This,too,wassimilartohisactualarrangementofthesticks.Hemadethe

topsofthesticksincreaseinorderofsize,buttotallyignoredthebottoms.(Whenaskedtocopyawell-

formedseriesimmediatelyinfrontofthem,thesesamechildrenproducedfarmoreaccuratedrawings.

Thisallowsustoconcludethatdrawingskillinitselfisnotatissue.)Bycontrast,childreninstage3who

couldaccuratelyseriatewereaccurateinrecall,asindicatedbyveridicaldrawingsandtracings.

ThesefindingscanbetakentosupportPiaget’stheory.Theindividual’smemoryisinfluencedand

organizedtosomedegreebyhisintellectualoperations.Thechildrecallsnotwhathehasseenbutwhathe

knows.Inthepresentinstance,stage1children’srecallisdistortedbytheirimmatureseriationschemes.

(Weshallseecaseslaterwheretheeffectisofadifferentsort.)Atthesametime,Piagetpointsoutthatthe

resultsarenotentirelyclear-cut.Somestage1childrenmakeperfectlyaccuratedrawings.Theirmental

operationsdonotseemtointervenesoforcefullyintheactofrecall. Insteadtheyseemtofocusonthe

appearanceoftheseries—onits“figurativeaspects”—andmanagetorecall itverywell,muchasthey

wouldrecall(anddraw)acircleoratreeorastaircase.Itishardtoexplainwhysomestage1children

showthedistortingeffectsofintellectualoperationswhileothersdonot.

In brief, while there is some variability, the results show that intelligence—the intellectual

operations—structures the child’s recall. Knowledge interacts with perception to produce what is

remembered.

The Development of Memory

According toPiaget, there is a generaldevelopmentalprogression from theearly appearanceof

accurate recognition to the later use of accurate recall.Memory begins in a crude fashion during the

sensorimotorperiod.Atthistime,theinfantshowsevidenceofrecognition.Throughovertorabbreviated

behavior,hedemonstratesthatatoyorapersonisfamiliar.Theinfantdoesnotseemcapableofmore

demandingformsofmemory,especiallyrecall(thisofcourseinvolvesevokingamentalrepresentationof

absentobjectsorevents).Itisonlywiththeonsetofthesemioticfunction,atabout18months,thatthe

childbecomescapableofmentalrepresentationandhencerecall.Earlier,inanothercontext,wecitedthe

exampleofJacqueline,at1;11(11),whouponreturningfromatrip,wasabletoreportoneventswhich


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hadoccurredearlier:“Robertcry,duckswiminlake,goneaway”(Play,Dreams,andImitation,p.222).

Thisisanexampleofrecallinachildwhoisjustbeginningtogiveevidenceoftheuseofthesemiotic

function.Inbrief,infantsshowsignsofrecognitionmemory,whereasrecall,asoneaspectofthesemiotic

function,beginstoappearonlyatabout18months.

Aswehaveseen,oncerecallappears,itsfunctioningisinfluencedbytheintellectualoperations.

Nowweshallseethatthisinfluencecanhavedevelopmentalaspects.Piaget’sexperimentsonmemory

foraseriesshedlightonthisissue.Wealreadyknowthatthechild’srecallafteroneweekisdistortedin

linewithhiscurrentstageofseriation.Butwhathappenstorecalloveralongerperiodoftime,say,sixto

eightmonths?Accordingtotheclassicview,thememorytracesimplyfades,andthisfadingbecomesmore

completeastimegoeson.InPiaget’sview,mattersaremorecomplexthanthat.Inmanycases,theremay

wellbesomedeteriorationofmemoryoveralongperiodoftime.Andyetthereareotherpossibilitiesas

well. Memory, which depends on intelligence, therefore exhibits developmental changes which

correspondtothedevelopmentofintelligence.Indeed,Piaget’stheoryleadstothepredictionthatunder

certaincircumstances,recallmayactuallyimproveovertime.

Inthecaseofseriation,thematterworksasfollows:thestage1childseesawell-orderedseriesand

assimilates it into his intellectual operations. Since these are immature, one week later the child

inaccuratelyrecallsthesticksasacollectionofsmallonesandacollectionoflargeones.Hisintelligence

hasorganizedrecallpoorly.Thenoveraperiodoftime,thechild’smentaloperationsdevelopandhe

enters stage 3. Now, asked to recall the sticks, he remembers a well-formed series. His memory has

improvedovertimebecausehisintellectualstructureshavedevelopedmorefully.

This is indeed precisely the result which Piaget discovered. Of twenty-four stage 1 children,

twenty-twoshowed improvedrecall (asmeasuredbydrawings)when theyadvanced toa later stage

sevenoreightmonthsaftertheinitialtesting.

Severalcommentsshouldbemadeatthispoint.First,independentinvestigatorshavehadahard

timereplicatingthisresult(forexample,Samuels,1976).Agooddealofcarefulresearch,withadequate

controls,needstobedonetopindowntheeffect.Itisparticularlyimportanttoobtaindirectmeasuresof

thechild’sassumed intellectualdevelopment.Second, it is important torecognize thatPiaget’s theory


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doesnotalwayspredictimprovementinlong-termrecall.Improvementcanbeexpectedtooccuronlyif

theinitialrecallwasdistortedbyimmatureintellectualoperationsandiftheseoperationssubsequently

improve.This isaveryspecialcase,however,andoftendoesnotoccur.Forexample, supposeachild

learns someone’snameand tries to recall it ayear later.Memory for thename is likely todeteriorate

regardlessof the child’s stageofdevelopment.The child’s advancement fromstage1 to3of concrete

operationswillhavenoparticularbearingontherecallofnames,sincetherecall ismerely figurative

withnologicaloperationsinvolved.Hereisanotherexample,whichmayseemparadoxical.Supposea

stage1childisshownabadlyformedseries.Afteroneweekheaccuratelyremembersthebadlyformed

seriesbecausehehasassimilateditintohisimmaturementaloperations.Then,overthenextyear,the

child’smentaloperationsadvanceandhehasreachedstage3.Nowwhenaskedtorecallthesticks,he

producesawell-formedserieswhichistheproductofhiscurrentintellectualstructure.Unfortunately,

this is inaccurate recall, since the initial series was badly formed. This example is a case of an

improvement in intellectualstatus leadingtoadeterioration inrecall. (SeveralstudiescitedbyLiben,

1977,actuallyobtainthiskindofresult.)ThemainpointofPiaget’stheoryisnotthatmemorynecessarily

improves over time—it seldom does— but that memory is influenced by developing intellectual

operations,andnotjustbyrealevents.

Summary

Piaget distinguishes between two types of memory. Memory in the wider sense refers to the

individual’sabilitytoretainovertimethepotentialtoexhibitlearnedschemesoroperations.Memoryin

thespecificsensereferstotheindividual’sabilitytoretainovertimeinformationconcerningparticular

events,things,orpersons.Specificmemorymaytakeoneofseveralforms,themostimportantofwhich

arerecognition(animpressionoffamiliarityonanencounterwithapreviouslyexperiencedobject)and

recall(evocationofthepastthroughmentalrepresentations).Piaget’sgeneralhypothesisisthatspecific

memory is influencedby intelligence—the intellectualoperations. Intelligenceserves toorganizeand

shape memory. Piaget rejects the classic view in which events are seen to impress themselves on a

passiveobserver,leavingatraceorasimplecopyofthereality.

Piaget’sexperimentsonmemoryforaseriesdemonstratethatafteroneweek,recallisinfluenced

bytheindividual’sstageofintellectualdevelopment.Presentedwithawell-formedseries,somechildren


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recallnotwhattheyhaveseen,butwhattheyknowabouttheseries.Itisimportanttonote,however,that

there is some variability in these results. According to Piaget, there is a general developmental

progressionfromrecognitionmemorytorecall.Infantsshowsignsofrecognition;recalldoesnotseemto

appearuntiltheonsetofthesemioticfunctionatabout18months.

After it appears, recall is influenced by the development of intellectual structures. The general

hypothesisstatesthatasintellectualstructuresdevelop,theyexertcorrespondingdevelopmentaleffects

onrecall.Indeed,undercertaincircumstances,recallmayactuallyimproveovertime.Piagethasshown

thatinthecaseofseriation,recallbecomesmoreaccurateaschildrenadvancefromoneintellectualstage

to the next. It is important to note, however, that this result is not easily replicated and that Piaget’s

theorydoesnotalwayspredictimprovementinrecallovertime.Instead,themainpointofPiaget’stheory

is thatmemory is influencedandorganized(butnotnecessarily improved)bydeveloping intellectual

operations, and not simply by real events. Memory is the result of an interaction been knower and

known.

CONSCIOUSNESS

Wehaveseenhowthechilddevelopsoperativeandfigurativeaspectsofthought.Bytheageof7or

8years,heachievessomesuccessatclassifyingandorderingobjects,atproducingmentalimages,andat

remembering.Thesecognitiveprocesses,bothfigurativeandoperative,workmainlyonanunconscious

level.NowwewillassumeadifferentlevelofanalysistoconsideranewtopicwhichPiagethasrecently

studied,namely,thechild’sawarenessandverbalizationofhisownthoughtprocesses.

In studying the issueof consciousness,Piaget’s general strategy is first tohave the child solvea

problemandsecondtodeterminehisawarenessofthemethodsofsolution(TheGraspofConsciousness,

GC,1976b).Inoneinvestigation,Piagetusedstandardseriationtasks,involvingsuchmaterialsasasetof

cardsvaryinginheightandwidth,orasetofbarrelsvaryinginbothheightanddiameter.Eachchild’s

taskwastoarrangetheobjectsinorderofincreasing(ordecreasing)size.Hewastold,forexample,to

“makeanicelineofbarrels.”Assoonasthechildbegantodothis,theinvestigatoraskedhimtodescribe

whathewasdoingorwasabouttodo.Sometimesthechildwasasked“howhewouldexplaintoafriend

whatshouldbedone”(GC,p.3OI).Afterthechildcompletedthefirstseries(successfulornot),hewas


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askedtorepeatitandtodescribeandexplainhisactionsashewentalong.Thepurposeofthisrepetition

wastoensurethatthechildknewwhatwasexpectedofhim.

Suppose that a child succeeds at the seriation tasks just described: he produces an accurate

orderingintermsoflengthoftherodsorsizeofthebarrels.Giventhis,wemayinquireintothechild’s

consciousnessorcognizanceofseriation. It is important tobeginbyclarifyingwhat ismeantbyPiaget’s

usageofconsciousnessorcognizance.Piagetuses these termstorefer to thechild’sability toproducea

coherentverbalaccountofthementalprocessesunderlyinghisbehavior.Bythisdefinition,thechildis

consciousorcognizantofhisthoughtprocessesifhesays,forexample,“Ialwayslookforthebiggestone,

then I put it aside and look for the biggest one out of all the ones that are left.” In Piaget’s usage,

consciousnessreferstoanawarenessandverbalizationofone’sownthoughtprocesses.Notonlyisthe

consciouschildabletodosomething;heisalsoexplicitlyawareofhowhedoesit.9NotethatPiagetdoes

notuseconsciousnesstorefertotheelementaryandfleetingperceptionoftheimmediatesituation.Thus

thetermisnotusedtorefertothechild’sawarenessthattherearetoybarrelsonthetableorthathis

handismovingtowardthem,andsoon.Whilesuchelementaryawarenessappearsveryearlyinlifeand

isnodoubthighlyprevalent,itisnotthesubjectofPiaget’sinvestigation.Inbrief,Piagetisinterestedin

the child’s explicit knowledge of his thought processes, and not merely in the crude awareness of

ongoingactivities.

Severalquestionsthenarisewithrespecttoconsciousness.Itisespeciallyinterestingtoinquireinto

the temporal relations between action and cognizance. There are of course several possibilities. One

alternativeisthatactionandcognizanceemergesimultaneously.Asonedevelopssodoestheother,and

it is impossible to determine the direction, or even existence, of causality. A secondpossibility is that

consciousnesscomesfirst,andthusdirectsthesubsequentaction.Perhapsthechildfirstconceptualizes

his action and this helps him to perform it. A third possibility is just the reverse. Perhaps successful

behaviorprecedescognizanceofit.Thechildmaybeablefirsttoperformcertainactions,andonlylater,

uponreflection,doeshebecomeawareofhisbehavior.

ThebehaviorofoneofPiagets’subjects,STO,at6-1,workingatseriation,shedssomelightonthese

issues.Onhisfirstattempt,STOfailedtocompleteasuccessfulseries.Hecouldnotarrangecardsinorder

ofsizeandputthesmallestonesinthecenteroftheline.Hesaid,“I’vemadeastaircasethatgoesupor


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down.”Theexaminerrespondedthatthestaircaseshouldgodownallthetime,“butfirsttellmehoware

yougoingtomakeit?”STOresponded:“I’mgoingtoputthebigone,anotherbigone,anotherbigone,the

middle-sizeone,thesmallermiddle-sizeone,thesmallermiddle-sizeone,andthesmallermiddle-size

one”(GC, p. 312). STO proceeded to produce a good series, with only onemistake, which he easily

corrected.Onsubsequent trials, thesamesortof thinghappened:STOproducedgoodseriesbutpoor

verbaldescriptions.

AccordingtoPiaget,thisexampleshowsthatSTO’sseriationwasfarinadvanceofhisconsciousness

ofit.STOcouldorderthecardsinafairlysystematicwayandyetcouldreferonlyinanimprecisemanner

to“anotherbigone,anotherbigone,”or to “thesmallermiddle-sizeone,andthesmallermiddle-size

one.”Otherchildrenexhibitsimilarbehavior.Forexample,theyuseanextremelysystematicprocedure

forseriation(likeselectingthesmallestandthenthesmallestofallthoseleft)andyetcansayonlythat

theyfirsttookasmallone,thenanothersmallone,andsoon.Piagetconcludesfromdatalikethesethat,

in general, the child’s successful activities—including operative activities like seriation—precede

cognizanceofthem.Thechildcanactandthinkeffectivelybeforehecanverbalizeorbeconsciousofhis

actionsorthoughts.

Howdoesconsciousnessofproblemsolvingdevelop?Piagetproposesthatatfirstthechildisonly

dimlyawareofgoals.Forexample,hewantstomakea“staircase.”Thechildthengraduallydevelops

variousstrategies forachievinghisgoal, forexample,randomplacementorsystematicselectionof the

largest.Atfirst,heisquiteunawareofthesestrategies,justasthe3-month-oldbabyisnotconsciousofthe

procedureswhichheusesforgettinghisthumbintohismouth.Heacts,successfullyorunsuccessfully,

but does not explicitly analyze his actions. With development, however, the child observes his own

activitiesandreflectsonthem.Heinterpretshisactions;hetriesto“reconstruct”themontheplaneof

thought.Atfirst,thisprocessofinterpretationmayleadtodistortionandmisunderstanding.Piagethas

observedmanycasesinwhichtheinitialconsciousnesswasinerror—wherethechilddidnotaccurately

seewhatinfacthehaddone.Butgradually,thereconstructionbecomesmoreandmoreaccurate.The

child’sreflectiononhisownactivitiesallowsthedevelopmentofexplicitknowledgeconcerningbothhis

problem-solving processes and the objects under consideration. In this way, the child learns about

himselfandabouttheobjectssurroundinghim.Hedevelopsabstractconceptsthatcanbeverbalized.


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Piaget’spositionhasmuchtorecommendit.Itseemsusefultomakeadistinctionbetweenatleast

twolevelsofknowledge.Theredoesseemtobeakindof“actionknowledge”or“how-toknowledge”in

whichwesolveproblemsusingmeansofwhichweareunaware.ThusSTOcouldseriate,butwithout

consciousnessofhismethod.Atthesametime,thereisalsoanotherlevelofabstractknowledge,inwhich

wecanexplicitly formulateourmethodsofsolutionandeventheprinciplesunderlyingthem.Thusa

child cannot only seriate but explicitly understands the principles which he uses. The process of

transformingactionknowledgeintoabstractknowledgemaybecrucialforhumanlearning.Thereisa

gooddealofwisdombuiltintoourbehavior,andamajortaskforlearningmayconsistinmakingexplicit

whatinasensewealreadyknowunconsciously.

While these are useful points, Piaget’s investigations in this area seem to suffer from a major

weakness, namely, an overreliance on verbalizations as a source of evidence. In these studies,

verbalizationistakenasthemain,orevenonly,sourceofevidenceforconsciousnessorcognizance.Thus

STOissaidtolackconsciousnessofhisactions,sincehislanguageisinadequate.ButSTO’srepetitiveuse

of vague terms like “the smaller middle-size one” may not accurately reflect the true level of his

consciousness.Seriation ishardtoexpress inwords,andperhapsSTOcouldconceptualize itbutwas

unabletoofferadequatedescriptionsoftheprocess.Piaget’sinterpretationseemsweakinthisregard.At

thesametime,despitethedifficulties,Piaget’sresearchraisesextremelyprovocativeissuesrequiringa

gooddealoffurtherstudy.

GENERAL CONCLUSIONS

Whilecriticismsmayandshouldbemade,andwhilerevisionsarenecessary,Piaget’stheoryisan

enormouslysignificantaccomplishment.Indeed,onreviewingPiaget’slaterworkonthechildfrom2to

11,oneisstruckaboveallbytheincrediblecreativityanddiversityofhiscontribution.Between1940

and1980,Piagetrevolutionizedthestudyof thechild.He introducedascoreof fascinatingproblems

andexperimentaltasks—conservationisonlyoneexample—whichforalongtimedominatedresearch

inchildpsychology.Moreimportant,heofferedanextraordinarilydeepandsubtletheoryofcognitive

development,whichcontinuestoinformourunderstandingofthemind’sgrowth.

Notes


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1SeeH.P.Ginsburg, “TheClinical InterviewinPsychologicalResearch:Aims,Rationales,Techniques,”For theLearningofMathematics,Vol.3(1981),pp.4-11,andS.Opper, “Piaget’sClinicalMethod,” JournalofChildren’sMathematicalBehavior, Vol. 1 (1977),pp.90-107.

2See,forexample,R.GelmanandC.R.Gallistel,TheYoungChild’sUnderstandingofNumber(Cambridge,Mass.:HarvardUniversity,Press,1978),Chap.3.

3 Our exposition of Grouping I is simplified and incomplete: for example, we have defined only one binary operator.We have kept themathematical development at a very informal level. The reader interested inpursuing thematter should see JeanPiaget,TraitedeLogique (Paris:Colin,1949),andalsoj.B.Grize’s formalizationofPiaget’s systemasdescribed inE.W.BethandJeanPiaget,MathematicalEpistemologyandPsychology(Dordrecht,Holland:D.ReidelPublishingCompany,1966).

4 Although it does not seem to help with conservation, counting is far from useless in children’s arithmetic. Hebbeler has shown, forexample,thatyoungchildrenmakeverygooduseofcountingindoingaddition.SeeK.Hebbeler,“YoungChildren’sAddition,”JournalofChildren’sMathematicalBehavior,Vol.1(1977),pp.108-21.

5Strictly speaking, in the caseofnumberPiagetusesa somewhatdifferent logico-mathematicalmodel, called theGroup. The essentialdifferencebetweentheGroupingsandtheGroupisthatthefifthGroupingoperation,tautology(e.g.,A+A=A),isnotusedintheGroup.TautologydoesnotapplytonumbersincethereA+A=2A,notA.Therefore,theGroupmustbeusedfornumber.

6Recently,GelmanandBaillargeon (1983,p.171)haveargued that thephenomenonof invariant sequence isnotas clear-cutasPiagetsuggests.Theydescriberesearchshowingthat insomeareassomechildrendonotexhibitthestagesintheorderpredictedbyPiaget.Thisseemstopresentseriousdifficultiesforthetheory.

7Therecanbeinstancesoffalserecall.Piagethimselffalselyrememberedbeingtheobjectofanabortivekidnapattemptwhenhewasachild.

8 Piaget’s exposition of the classic view probably refers to theorists like Ebbinghaus, who in the nineteenth century invented nonsensesyllablesandspentmanyyearsofhislifememorizingthemhimself.Hewashisonlysubjectanddeservessomesortofprizefor an immense capacity for boredom. In recent years, however, theorists ofmemory have given up both the inclinationthemselves tomemorize nonsense syllables (althoughmay require their subjects to do it) and theoretical accountswhichtreat thesubjectaspassive.Manymoderntheoriesare insubstantialagreementwithPiageton the issueofactivity.ForacomparisonofPiaget’s theorywithothers, aswell asanexcellent critiqueofPiaget’swork, seeL.Liben, “Memory fromaCognitive-DevelopmentalPerspective:ATheoreticalandEmpiricalReview,”inKnowledgeandDevelopment,W.F.OvertonandJ.M.Gallagher,eds.(NewYork:PlenumPress,1977),Vol.I,pp.14-9-203.

9Recently, Flavell andothershavebeen investigating a similar topic,which they term “meta cognition,” andwhich involves the child’sknowledgeabouthisownknowledge.(Forareview,seeJ.H.Flavell,CognitiveDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1985.)Anexampleiswhetherthechildisawareofusingsystematicstrategiestoaidinmemory.


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The Years 2 through 11: Piaget’s Later Work

ThischapterdealswithaspectsofPiaget’slaterwork(fromapproximately1940onward)onthe

childfromabout2to11years.AswasshowninChapter1,thisportionofPiaget’sresearchandtheoryis

voluminous and covers suchmatters as the child’s conception of chance, space, geometry,movement,

number,andother topics.Sincewecannotreviewall the laterworkhere,weshall focusonwhatwe

consider tobebasic issues and conceptswhich reappear in andapply to almost all ofPiaget’s recent

writings.We will consider (1) the revised clinical method, (2) the child’s classification of objects or

events, (3) the ability to place them in ordinal relations, (4) the concept of number (particularly its

conservationovertransformations),(5)thenatureofmental imagery,(6)thedevelopmentofmemory

andconsciousness,and(7)somegeneralcharacteristicsofthought.

THE REVISED CLINICAL METHOD

WesawinChapter3thatPiaget’soriginalclinicalmethodwashighlydependentonverbalizations.

Theexaminerposedthequestionsinwords,andthechildwasrequiredtogivetheanswersinthesame

way.Theexaminer’squestionsusuallydidnotrefertothingsoreventsthatwereimmediatelypresent,

andtheproblemsdidnotalwaysinvolveconcreteobjects

whichthechildcouldmanipulateorevensee.Forexample,theexaminermightdepictachildwho

had unwittingly broken some cups andmight then ask the subject being questioned for a judgment

concerningthechild’snaughtinessandthepunishmenttobemetedout.Insuchasituationasthis,the

subjectisrequiredtodoseveralthings.Hemustinterprettheexaminer’sdescriptionsoastopicturethe

scenetohimself;hemustmakeaspecialefforttocomprehendcertaincrucialaspectsofthequestion,like

theword“naughty”;andhemustexpresshisjudgmentinwords.

Aftersomeexperiencewiththismethod,Piagetcametofeelthatitwasinadequatebecauseitrelied

too heavily on language. The childmight not understand everything said to him, particularly if the

wordsdidnotalwaysrefertoconcreteobjects.Evenifthechilddidunderstand,perhapshecouldnot


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adequately express in words the full extent of his knowledge. Consequently, Piaget modified his

procedures, and the result iswhatwe shall call “the revised clinicalmethod” (sometimes called the

“method of critical exploration”). The new method involves several features. First, the examiner’s

questionsrefer toconcreteobjectsoreventswhichthechildhasbeforehim.No longermust thechild

imaginethesethingsmerelyonthebasisofaverbaldescription.Second,aneffortismadetoletthechild

expresshisanswerbymanipulatingtheobjects,andnotsolelyexpresshimselfthroughlanguage.

For example, let us suppose that the examinerwishes to knowwhether the child can form two

distinctclasses.Toinvestigatethematterhemightpresentthechildwithanarrayofcirclesandsquares

allmixedtogetherinnoorder,andaskhimtoputtogethertheonesthatbelongtogether,orsortouttwo

distinctpiles.Whatthechilddoeswiththeobjects—whatsortofpileshemakes—andnotwhathesays

aboutthem,constitutestheprimarydataofthestudy.Ifafterencouragementachildstillcannotforma

pileofcirclesseparatefromapileofsquares,thentheexaminermightconcludethathedoesnothavethe

classificationskillsunderinvestigation.Whilecompletelynonverbaltestsaredesirable,itisoftenhardto

inventthem.ThisisespeciallytrueforPiaget,sinceheusuallyinvestigatesthechild’sunderstandingof

abstractconceptsthatarenoteasilymanifestedinthebehavioralmanipulationofconcretematerials.The

revisedclinicalmethod, therefore,mustoftendepend for itsdataon thechild’sverbal responses.But

evenwhenthisisnecessary,thechild’sanswersrefertoaproblemstatedintermsofconcretematerials

whicharepresent.

Third, Piaget introduced the use of counterarguments or countersuggestions. These involve

presentingthechildwithapointofviewthatcontradictshisown,andaskinghimwhathethinksofthe

opposingview.Thepurposeofthesecounterargumentsistodeterminethestabilityandauthenticityof

thechild’sthinking.Childrenwhohavemasteredaconceptwillresistthecountersuggestion;thosewho

havenottendtobeswayedbythecontradictoryargument.

Afourthfeatureoftherevisedclinicalmethodisnotnew:theexaminer’squestioningisflexible.

Ratherthanemployastandardizedlistofquestions,hemodifiesthemoraddsnewonesasthesituation

demands.Asbefore,Piagetstillfeelsthatthereisnopointeitherinaskingachildaquestionthathedoes

notunderstandorinfailingtoclarifyananswer.


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To summarize, the revised clinical method involves posing questions concerning concrete

materials; allowing the child to “answer” by manipulating the materials, if this is at all possible;

introducing counterarguments; and, as in the earlier clinicalmethod, statingquestions andpursuing

answersinaflexibleandunstandardizedway.Whetherornottherevisedclinicalproceduregivesan

accurateassessmentofthechild’sabilitiesisamatterfordebate.Ingeneral,mostpsychologists(outsideof

Geneva) do not use this method in research, mainly on the grounds that it is not sufficiently

standardized.Wethink that thisattitude ismistaken,especiallysince thereareverygoodreasons for

avoiding standardization.1 In any event, the revised clinical method is less exclusively verbal than

Piaget’searlierprocedureandattemptstogiveanaccurateassessmentofthechild’sthoughtprocesses

whichinlargemeasuremaybenonverbal.

CLASSIFICATION

Piaget has used the revised clinical method to study classification in the child. The preceding

chaptershavealreadytouchedonthisandrelatedmatters,anditmaybeusefultoreviewsomeofthe

materialhere.Wesawthatthereisaprimitivesortofmotorclassificationinthesensorimotorperiod(0to

about2years)whentheinfantappliestoobjectsintheenvironmentabbreviationsoffamiliarschemes.

Forexample,Luciennesawatoyparrothangingabovehercribandkickedherfeetveryslightly.Thiswas

anabbreviationofaschemewhichshecouldquiteeasilyhaveappliedtothepresentsituation.Itseemed

asifheractionclassifiedtheparrotasa“thingtobeswung.”Moreover,theabbreviationshowsthatthe

behaviorwasbecominginternalized.Eventuallyitcouldbereplacedbythethought:“That’stheparrot;

that’s something I can swing.” But the abbreviated schemes are not yet instances of legitimate

classification.Onereasonisthattheschemesapplytoindividualobjectsoveraperiodoftimeandnottoa

collectionofobjects.Forexample,Luciennekickedfromtimetotimewhenevershesawparrotsandthus

indicatedrecognition.Butthis

recognitiondoesnotimplythatsheconsideredtheparrotstobelongtoaclass.Matureclassification,

on the other hand, involves the conception of a collection of things, whether they are immediately

presentorimagined.AsecondreasonwhyitisnotpossibletocreditLuciennewithclassificationhasto

do with inclusion relations, which will be expanded on shortly. Briefly, this refers to the ability to

constructahierarchicalclassification,suchthattoyparrotsareasubclassofalarger,moreinclusiveclass


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liketoysingeneral.

From about 2 to 4 years the child begins to classify collections of objects in away that is quite

primitive. He uses the preconcept. Sometimes he fails to see that one individual member of a class

remains the same individual despite slight perceptual changes, and sometimes he thinks that two

different members of the same class are the same individual. Between 5 and 10 years, the child’s

classificationisstillfaultyinseveralways.Thereisthephenomenonofjuxtaposition,theinabilitytosee

thatseveralobjectsareindeedmembersofthesameclass.Thereisalsosyncretism,thetendencytogroup

togetheranumberofdisparateeventsintoanill-definedandillogicalwhole.

As was pointed out, Piaget’s investigations of the preconcept, syncretism, and juxtaposition,

conductedinthe1920sand1930swerepreliminaryandtentative.First,thereexistedmethodological

defects:thedatawerealmostexclusivelyverbalsothatPiaget’sinterpretationwasbasedlargelyonwhat

the child said. Second, Piaget’s concepts—syncretism, juxtaposition, the preconcept—were somewhat

vagueandneededelaboration. Inthe1950sPiagetreturnedtothestudyofclassificationinthechild

fromabout2to12years.Theseinvestigationsmakeuseoftherevisedclinicalmethod;theyalsomodify

thenotionsofpreconcept,syncretism,and juxtapositionandsuggestnewwaysofconceptualizingthe

child’sclassificatoryactivities.

Some Properties of a Class

BeforeexaminingPiaget’sresearchintoclassification,wemustclearlyunderstandwhathemeans

byaclass.Supposewehavebeforeusanumberofobjectsallmixedtogether.Thearraycontainsalarge

red triangle, a small blue circle, a large pink circle, and a small black triangle. All the objects are

discriminablydifferentonefromtheother.Thatis,thereisnodifficultyinperceivingthatanyoneobject

isdifferentfromanyoftheothers.Forexample,thelargeredtriangleisveryobviouslylargerandredder

thanthesmallblacktriangle.Suppose,too,thatwewishtoplacetheseobjectsintotwodifferentclasses.

Onewayofdoingthisistoputinoneseparatepilethelargeredtriangleandthesmallblacktriangle.In

thesecondpilewouldgothesmallbluecircleandthelargepinkcircle.Iftheoriginalarraycontained

additionaltriangularobjects,regardlessoftheir


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sizeorcolor,theywouldofcoursegointhefirstpile.Similarlyallothercircularobjectswouldgoin

thesecondpile.Thetwopileseachrepresentaclass.Ofcourse,wemightclassifytheobjectsinanother

way.Wecouldputinonepilethetwosmallobjects(regardlessoftheircolororshape)andinthesecond

pilethetwolargeobjects.Thereareusuallymanydifferentclassesthatonemayformfromagivenarray

ofobjects.

Piagetmakesanumberofpointsabouttheclassesformedfromtheoriginalarray(forpurposesof

illustrationconsiderjustourfirstexample,theclassoftrianglesandtheclassofcircles):

1.Noobjectisamemberofbothclassessimultaneously.Forexample,thelargeredtriangleisintheclassoftrianglesandnotalsointheclassofcircles.Thus,theclassesaremutuallyexclusiveordisjoint.Thisholdseven if therearemore than twoclasses formed. (Forexample, wemight divide some animal pictures into the classes of lions, tigers, andelephants,allofwhicharedisjoint.)

2.Allmembersofaclasssharesomesimilarity.Forexample,thesmallbluecircleandthelargepinkcirclebothsharethepropertyofcircularity.Circularityisthedefiningproperty,thecrucialattribute,oftheclass;thatis,weincludeintheclassofcirclesanyobjectwhichiscircular.Anotherwayofputtingitistosaythatcircularityistheintensionoftheclass.Thedefiningpropertyorintensionoftheotherclassistriangularity.

3.Eachclassmaybedescribedintermsofalistofitsmembers.Insteadofdescribingaclassintermsofitsdefiningpropertyorintension(forexample,theclassoftriangularobjects),wemay simply list theobjects in the class (forexample, large red triangleandsmallblack triangle). Sucha list is theextensionof the class.Note that the listmay involveconcreteobjects(likelarge,bluecircles)orabstractideas,events,actions,andsoon(likethelistofthepartsofspeech).

4. The defining property of a class determineswhat objects are placed in it. Anotherway ofstatingthisisthatintensiondefinesextension,orthe“fieldofapplication”ofaconcept.Forexample,ifweknowthatoneclassistobeformedonthebasisoftriangularityandanotheronthebasisofcircularity,wecanpredictthecontentofthelistofobjectsineachclass.

Thesearesomefundamentalpropertiesofclasses,asPiagetdefinesthem.(Thereareothercrucial

attributestoo,likeinclusionrelations,whichwewilldiscusslater.)Piagetthenaskswhetherthechild

classifiesobjectsinaccordancewiththeseproperties.Whenaskedtogroupobjects,doesthechildform


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mutuallyexclusiveclasses?Dohisclasseshavedefiningpropertieswhichdeterminethelistofobjectsin

eachclass?

Piaget discovers three stages of development. The first two—both of which we may call

preoperational—occur roughlyduring theyears2 to7.The third stage—thatofconcrete operations—

occursroughlyfromtheyears7to11.

Stage 1

To investigate classification,Piagetperformedanumberof experimentswhichused the revised

clinicalmethod.Inonestudy,hetestedanumberofchildrenfromabout2to5yearsofage.Theywere

presentedwith flat geometric shapes ofwood and of plastic. The shapes included squares, triangles,

rings,andhalf-rings,allofwhichwereinseveralcolors.Theshapesweremixedtogetherandthechild

wastold:“Puttogetherthingsthatarealike.”Sometimesadditionalinstructionsweregiven:“Putthemso

thatthey’reallthesame”or“Putthemhereifthey’rethesame,andthenoverthereifthey’redifferent

fromthisonebutthesameaseachother”(EarlyGrowthofLogic,EGL,p.21).

Thechildrendisplayedseveralmethodsofgroupingtheobjects.Onemethod iscalledthesmall

partialalignment.Withthismethodthechildusesonlysomeoftheobjectsintheoriginalarrayandputs

them together in severalways apparentlywithout any overall guiding plan. For example, one child

beganbyputtingsixhalf-rings(semicircles)ofvariouscolors inastraight line; thensheputayellow

triangle on top of a blue square; later she put a red square in between two blue triangles; then put

squaresandtrianglesinnoparticularorder,inastraightline.Thereareseveralpointstonoteaboutthis

performance. Sometimes similarities among objects determine the collection. For example, the subject

whoseperformancewas just describedbeganwith a line of half-rings. At other times the same child

groupedthingsonthebasisofnodetectablesimilarity;thatis,sheputayellowtriangleonabluesquare,

oraredsquarebetweentwobluetriangles.Inbothofthesecases,thereisnosimilarityofeithercoloror

form.

Itisclearthatsmallpartiedalignmentsarenottrueclassesforseveralreasons.Oneofthemisthat

intension does not define extension; that is, no consistent defining property determined which


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geometric formswereput invariouscollections.Thechilddoesnotoperateunderanoverallguiding

plan like a system of rules (defining properties) which organize theway in which he arranges the

objects.

Otherchildrenofthisageusethegeometricfigurestoconstructaninterestingformorpicture.One

childarrangedanumberofcirclesandsquarestorepresentalongverticalobjectandthenproclaimedit

tobetheEiffelTower;anotherchildplacedanumberofhalf-ringsinbetweenseveredsquares,allina

horizontalline,anddescribedtheresultasabridge.Piagetcallstheseproductionscomplexobjects.Itis

obviousthatlikethesmallpartialalignments,andlikesomeothertypesofcollectionsnotdescribedhere,

thecomplexobject isnotatrueclass.Figuresarenotplaced inthecomplexobjectbecausetheyshare

somedefiningproperty;rather,extensionisdeterminedsolelybytherequirementsofthepictureunder

construction.

Inanotherinvestigation,Piagetpresentedchildrenofthesameagewithnongeometricfiguresfor

classification—little toyswhich included people, houses, animals, and so on. Once again, the results

showedaninabilitytoformclasses.Onechildputtwodollsinacradle,thentwowheelbarrowstogether,

thenahorse.Whentheexamineraskedthechild forall theobjects likeahorse,shegavehimall the

animalsandthenababyandtwotrees.Thisexampleillustratesthefactthatalthoughtheyoungchild

may perceive similarities among the objects, these do not fully determine what objects go into the

collection. That is, the child saw that all animalswere in some respect similar and gave them to the

examinerwhenaskedforobjectslikethehorse.Ifthechildhadstoppedthere,shemighthaveformeda

classwhichwasbasedonthedefiningpropertyof“animalness.”However,shewentontothrowinthe

babyand two trees.The similarity (intension) that she firstperceiveddidnot fullydeterminewhich

objectswere to be grouped together (extension). It is as if the child forgot about the initial defining

property(animalness)andthenswitchedtosomeother.

Wemaymakeseveral commentson these investigations.First, theymakeclear thenatureof the

revisedclinicalmethod.Theexaminergivesthechildconcreteobjectstoworkwith.Thetaskinstructions

andquestionsarestillverbal,ofcourse,buttheyrefertorealthingsthatthechildcanmanipulate.The

childisrequiredtosayverylittle.Mostofhisresponsesarenotverbalbutbehavioral.Hedoesnothaveto

saythatalloftheanimalsdoordonotgotogether;rather,hecanputthemtogetherorfailtodoso.


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Second,althoughtherevisedclinicalmethod isan improvementoverwhatwasusedbefore,we

wonderwhetherthetaskwasentirelycleartothechild.Theinstructions(e.g.,“Puttogetherthingsthat

arealike”)seemrathervagueandsusceptibletomanyinterpretations.Wesuspectthatdifferentmethods

of presenting the task to the child might produce entirely different results. Piaget considered this

objectionandtriedanessentiallynonverbalmethod.Hebegantoclassifytheobjectshimselfandasked

thechildtodothesamething.Theresultagainwasnottrueclassification,but“complexobjects,”andso

on.Whilethismethodwasnotsuccessful,itdoesnotexhaustthepossibilities.Otherinvestigatorshave

exploreddifferentprocedures,withsomesuccess.2

Stage 2

Childrenfromabout5to7yearsproducecollectionsthatseemtoberealclasses.Whenpresented

withthesituationdescribedearlier,onechildproducedtwolargecollections,onewhichcontainedall

thepolygonsand theother the curvilinear forms.Moreover, eachof these collectionswas subdivided

further. Thepolygons, for instance, contained separatepiles of squares, triangles, and so on, and the

curvilinearformsinvolvedseparatecollectionsofcircles,half-rings,andsoon.Thus,thechildnotonly

seemstoformclasses,butarrangesthemhierarchically,asinFigure2.Therearetwogeneralcollections

(polygons and curvilinear forms) at the top of the hierarchy, and these both branch out into several

subcollections below (squares, triangles, etc.). The child’s activities may be characterized in several

additionalways.(1)Heplacesintheappropriatecollectionalloftheobjectswhichwereintheinitial

array.Theyoungerchilddidnotdo this;he leftsomeobjectsunclassified. (2) Intension fullydefines

extension.Thatis,ifthechilddefinesacollectiononthebasisofthedefiningpropertyofcircularity,all

circlesgointothatpile,andnoneisplacedinanyotherpile.(3)Atagivenlevelofthehierarchy,similar

definingpropertiesareusedtodeterminecollections.Forexample,atthelowerlevelofthehierarchyin

Figure2,allthecollectionsaredefinedintermsofgeometricform—squares,triangles,andsoon.Itisnot

thecasethatsomecollectionsaredefinedbyformandsomebycolor.Tosummarize,itwouldseemthat

thechildfromabout5to7yearsproducesratherelaboratehierarchicalcollectionswhichdeservetobe

calledtrueclasses.


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FIGURE2Classificationofgeometricobjects.

Piaget feels, however, that the child of this stage fails to comprehend one crucial aspect of the

hierarchyhehasconstructed.Thechilddoesnotunderstandkeyrelationsamongthedifferentlevelsof

thehierarchy.Thisistheproblemofclassinclusionwhichwewillnowillustrate.Supposewearegivena

randomly organized array of blue and red squares and black and white circles. We construct an

arrangement(seeFigure3)suchthattherearetwomajorcollections(squaresversuscircles)andwithin

eachofthesetherearetwofurthersubdivisions(blueversusredsquaresandblackversuswhitecircles).

Thus,thereisahierarchywhosehigherlevelisdefinedbyshapeandwhoselowerlevelisdefinedby

color.Consider for themomentonlyone-halfof thehierarchy,namely, thesquareswhicharedivided

intoblueandred.Ifweunderstandinclusionrelations,thenwecanmakestatementsofthissort:(1)All

ofthesquaresareeitherblueorred.(2)Therearemoresquaresthantherearebluesquares.(3)There

aremoresquaresthanthereareredsquares.(4)Iftheredsquaresaretakenawayfromthesquares,then

theblueonesareleft.(5)Ifthebluesquaresaretakenawayfromthesquares,thentheredonesareleft.

(6)Allthebluesaresquares,butonlysomeofthesquaresareblue.These,then,aresomeofthepossible

statementsaboutinclusionrelations—therelationsofthepartstothewhole,ofthewholetotheparts,

andthepartstotheparts.Theymayseemveryobvious,butsodomanyotherprincipleswhichchildren

failtounderstand.


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FIGURE3Classificationofsquaresandcircles.

Piaget investigated the understanding of inclusion relations in children of various ages. Let us

considernowthechildfromabout5to7years.Piagetpresentedeachofhissubjectswithanumberof

picturesof flowersandotherthings.Thechildwasfirstrequiredtogroupthepicturesinanywayhe

wished, and then he was asked a number of questions concerning inclusion relations. The results

concerning spontaneous classification replicatedwhatwas found earlier: the child from5 to 7 years

constructscollectionswhichseemtoinvolveahierarchy.Onechildformedtwolargecollections:flowers

versusotherthings;thenhefurthersubdividedtheflowersintoprimulasversusotherkindsofflowers.

IntermsofFigure4,thechildseemedtohaveconstructedthetoptwolevelsofthehierarchy.(Hedidnot

makeafurthersubdivisionintermsofyellowversusotherprimulas.)Itwouldseemthattheconstruction

ofsuchahierarchyimpliestheunderstandingofinclusionrelations.Ifthesubjectdividedtheflowers

intoprimulasversusotherkinds,musthenotunderstand that therearemore flowers than thereare

primulas? The results of Piaget’s questioning, however, point to different conclusions. Consider this

protocolofachildaged6years2months:

A little girl takes all the yellow primulas andmakes a bunch of them, or else shemakes a bunch of all theprimulas.Whichwaydoesshehavethebiggerbunch?—Theonewith theyellowprimulaswillbebigger. [Hethencountedtheyellowprimulasandtheotherprimulasandfoundthattherewerefourofeachkind]Oh no,it’sthesamething....—Andwhichwillbebigger:abunchmadeupoftheprimulasoroneofalltheflowers?—They’reboththesame.(EGL,p.102)


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FIGURE4Classificationofflowersandotherthings.

Although this child had earlier constructed a hierarchical arrangement of the materials, he

maintainedthattheyellowprimulasdidnotformasmallercollectionthantheprimulasasawholeand

thattheprimulasdidnotformasmallercollectionthantheflowersasawhole.Bothoftheseanswers,of

course,arequitewrong.Inbothcases,thepartissmallerthanthewholefromwhichitderives.

What is the explanation for the child’s inability to comprehend inclusion relations? Piaget

postulates that once the child has divided a whole into two subgroupings, he cannot then think

simultaneouslyintermsofthelargercollectionandthesubdivisionswhichhehasconstructedfromit.

For example, suppose a child divides a collection of flowers (thewhole) into primulas versus other

flowers(subdivisionsofthewhole).Whenheisasked“Aretheremoreprimulasormoreflowers?”he

mustconsiderboththeoriginalcollection(flowers)andoneofhissubdivisions(primulas)atthesame

time.Hemustcomparethe“size”ofoneagainstthatoftheother.Undertheseconditions,hefocusesor

centersonthecollectionhecansee(theprimulas)andignorestheoriginalcollection(alloftheflowers),

whichisnolongerpresent in its initialstate(acollectionoftheprimulasandotherflowersallmixed

together).Andsincehecentersonthepart,ignoringthewhole,hisanswerstoinclusionquestionsare

oftenwrong.

Stage 3

Childrenfromabout7to11yearsofagearebothcapableofconstructinghierarchicalclassifications


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andofcomprehendinginclusion.Forexample,afterconstructingahierarchy,onechildof9yearsand2

monthswasasked:

Whichwouldmakeabiggerbunch:oneofalltheprimulasoroneofalltheyellowprimulas?—Alltheprimulas,ofcourse,You’dbetakingtheyellowonesaswell.—Andalltheprimulasoralltheflowers?—Ifyoutakealltheflowers,youtaketheprimulastoo.(EGL,p.109)

Thisprotocolmakesquiteclearthechild’sabilitytothinksimultaneouslyintermsofthewholeand

itsparts(e.g.,“Ifyoutakealltheflowers,youtaketheprimulastoo”).Whilehephysicallyseparatesthe

flowersintoprimulasandotherkinds,thechildisabletoreasonbothabouttheoriginalwholeandits

part at the same time.His thought hasdecentered from exclusive preoccupationwith the part or the

whole.

Piagetalsofoundthatwhenthechildofthisagewasaskedthesamequestionsabouthypothetical

objects,thesubjectoftenfailedtogivecorrectanswers.Apparently,thechild’sclassificationisconcrete:

he understands the inclusion relations of a group of real objects, but fails to comprehend the same

relationswhenimaginaryclassesareinvolved.Thegapbetweenhypotheticalandconcretereasoningis

anotherexampleofverticaldécalage.

Wemaysummarizebystatingthatthechildfrom7to11hasreachedthemostadvancedstageas

farastheclassificationofconcreteobjectsisconcerned:hecanconstructahierarchicalarrangementand

understand the relations among the levels of the hierarchy. Piaget then proposes that this

accomplishmentcanbedescribedintermsofalogicomathematicalmodel.Letusexplorethisidea.

Rationale for the Use of a Logicomathematical Model

WehaveseenthatPiagetattemptstodescribethebasicprocessesunderlyingtheclassificationof

objectsor events.Heproposes that the stage1 child (2 to4or5years) fails to constructhierarchical

arrangementspartlybecauseafterashortwhileheforgetsthedefiningproperty(intension)whichhe

hasusedtoformacollection.Thestage2child(5to7years)canconstructahierarchybecauseofthe

ability to use a defining property to determinewhich objects go in a collection, but at the same time

cannot understand inclusion relations because of the inability to simultaneously consider several

immediatelypresentcollectionsandthelargeronefromwhichtheywerederived.Thestage3child(7to


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11years)cancorrectlyanswerquestionsconcerninginclusionbecauseofhisabilitytothinkoforiginal

classesandtheirderivativesatthesametime.

Thusfar,wehavedescribedthesebasicprocesses(theabilitytothinksimultaneouslyofsubclasses

andlargerclasses)intermsoftheordinarylanguage.Manypsychologistsbelievethatthisistheproper

procedure;butothers,includingPiaget,feelthatdescriptionsofstructureshouldbephrased,asmuchas

possible,inaformallanguagelikemathematics.

Letusconsiderfirst,however,someaspectsoftheuseofthecommonlanguage.Mostpsychological

theorieshavebeenstatedinthisway.Freud,forexample,wroteexclusivelyinGermanandnotinlogic

nor mathematics, and no doubt there is not a single formula in the entire corpus of psychoanalytic

doctrine.AnotherexamplefromanotherpointonthepsychologicalspectrumisTolman,anexperimental

psychologist,whoproducedhistheoriesoflearninginordinaryEnglishandmadeuseofonlyafew(and

nonessential) symbols.TolmanandFreudarehardly isolatedexamples.Today, too, themajorpartof

psychological theorizing is done in English, or Russian, and so forth. Several advantages are usually

claimedforthisprocedure.Theordinarylanguagemaybericherandsubtlerthanformallanguages,and

alsoitisgenerallyeasiertoreadthanmathematicsorlogic.

However,anotherapproachtothisproblemispossible.Piagetfeelsthatforscientificpurposesthe

ordinary language is fundamentally ambiguous and must be supplemented by formal approaches.

Anyoneevenslightly familiarwith thehistoryofpsychologyknows thatmost, ifnotall,psychological

theories stated in the common languagehavebeenvagueandeasily susceptible tomisinterpretation.

Even today there aremany fruitless arguments over themeaningofwords like “concept” or “ego” or

“learning.”Asanexample,letusconsidertheword“thought,”whichwehaveusedwithoutdefinition

quitefrequently.Nodoubt“thought”meansquitedifferentthingstodifferentreaders.Tosomeitmay

mean “ideas,” and to some “consciousness”; to others it may mean “mental effort,” “meditation,”

“concentration,”“opinion,”andsoforth.Isitanywonderthatagivenpsychologicaltheorywhichuses

words like this will elicit a variety of interpretations and, hence, considerable argument and

misunderstanding?PerhapsaprimeexampleofthedifficultyisPiaget’sownuseofverbaltheoriesinhis

earlywork.Considerableconfusionstillsurroundstheterms“egocentrism,”“moralrealism,”andsoforth.


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Piaget feels, then, that the ordinary language produces obscure and ambiguous psychological

theorizing, andmust therefore be supplemented, if not replaced, by othermodes of description. The

physical sciences have convincingly shown that mathematics is an extremely powerful tool for

communicating certain precise ideas. Piaget—along with increasingly large numbers of other

psychologists—feelsthatitwouldbefruitfulforpsychologytoadoptasimilarapproach,andhehimself

has attempted to do so in the case of classification and othermatters. Let us now explore his formal

descriptionofthestructureofclassification.

FIGURE5Classificationhierarchy.

Grouping I

The formal description called a Grouping3 begins with this situation: we have a classification

hierarchyofthesortconstructedbythe7-to11-year-oldchildreninPiaget’sexperiments(seeFigure5).

Thisiswhatwestartwith(thatis,itisagiven)andtheGroupingdescribeswhatthechildcandowith

thehierarchy.Atthetopofthehierarchythatthechildhasconstructedarethetwoclasses,flowerswhich

weshallsymbolizeas(C)andotherthings(C').Onthemiddlelevelofthehierarchywefindprimulas

(B)andotherflowers(B').Onthelowestlevelthereareyellowprimulas(A)andprimulasofothercolors

(A').Eachoftheclasses(A,A',B,B',C,C')isanelementofthesystem.Thereisonebinaryoperatorthatmay

beappliedtotheelements,namely,combining.Wewillsymbolizecombiningby+,althoughthereader

shouldbeawarethatcombiningclassesisnotpreciselyequivalenttoaddingnumbers.Theoperator+is

binarysinceitcanbeappliedtoonlytwoelementsatatime.Justaswecanaddonlytwonumbersatany


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onetime,sowecanonlycombinetwoclassesatatime.

Given theelements and thebinaryoperator, the fiveproperties describe theways inwhich the

operatormaybeappliedtotheelements.

Thefirstpropertyiscomposition(usuallyreferredtoinmathematicsasclosure)whichstatesthat

whenwecombineanytwoelementsofthesystemtheresultwillbeanotherelementofthesystem.For

example,ifwecombinetheyellowprimulaswiththeprimulasofothercolors,wegetthegeneralclassof

primulas.ThismaybewrittenasA+A'=B.Orifwecombinetheyellowprimulaswithalltheprimulas,

wegetall theprimulas.WemaywritethisasA+B=B.Thispropertydescribesaspectsofthechild’s

abilitytounderstandahierarchy.Forexample,hecanmentallyconstructalargerclassbycombiningits

subclasses.

Thesecondpropertyisassociativity,whichmaybestbeillustratedinaconcretemanner.Suppose

we want to combine three classes such as yellow primulas, primulas, and flowers (A, B, and C,

respectively). Remember thatwe cannot just add all three of them together simultaneously since the

operator (combining) is binary; that is, it can be applied to only two elements at a time. Given this

limitation,thereareatleasttwowaysofaddingA,B,andC.Wemightfirstcombinetheyellowprimulas

andtheprimulasandgetprimulas.Thatis,wedoA+B=B.Thenwemightcombinethisresult(B)with

flowers-in-general(C)andgetflowers-in-general.Thus,wedoB+C=C.Tosummarize,wefirstperform

A+B=BandthenB+C=CsothatourfinalresultisC.Anotherwayofstatingthisis(A+B)+C=C.

There is yet a second way of combining the classes. We could start by combining the yellow

primulas(A)withthecombinationofprimulasandflowersingeneral(B+C)andfinishwiththesame

result:flowers-in-general,(C).ThuswecanwriteA+(B+C)=C.Notethatthefinedresultofperforming

theoperationbyeithermethodisC,sothatthetwomethodsmaybeconsideredequivalent.Wemaywrite

thisequivalenceas(A+B)+C=A+(B+C).Thisequationexpressesthefactthatthechildcancombine

classesindifferentordersandcanrealizethattheresultsareequivalent.

The third property is identity, which states that there is a special element in the system (the

“nothing” element), that produces no changewhen combinedwith any of the other elements. If we

combine the nothing elementwith the yellowprimulas the resultwill be the yellowprimulas. Ifwe


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symbolize nothing by 0, thenwe have A + 0 = A.More concretely, if we do not combine the yellow

primulaswithanyoftheotherclasses,then,ofcourse,westillhavetheyellowprimulas.

Thefourthpropertyisnegationorinverse,whichstatesthatforanyelement(class)inthesystem,

thereisanotherelement(theinverse)thatproducesthenothingelementwhencombinedwiththefirst

element.Thatis,ifweaddtotheclassofyellowprimulasitsinverse,thenweareleftwithnothing.The

inverseisequivalenttotheoperationoftakingawaythesameclass.Ifwestartwithyellowprimulasand

combinewiththisclassitsinverse,weareineffecttakingawaytheyellowprimulaswiththeresultthat

weareleftwithnothing.WecanwritethisasA+(-A)=0orA-A=0.Theinverserulemightapplytoa

trainofthoughtlikethis:“SupposeIcombinetheyellowprimulaswithalloftheotherprimulas.ThenI

havealloftheprimulas.ButifItakeaway[inverseornegation]alloftheotherprimulas,thenIamleft

again just with the yellow primulas. ’ ’ Note how this train of thought is reversible. First, the other

primulasareadded,butlatertheyaretakenaway,sothatthethinkerisonceagainatthepointwherehe

started.Negation,then,isonekindofreversibility.

Theinversealsomaybeusedtoexpressaspectsofclassinclusion.Supposewestartwiththeclassof

primulas (B) and take away (or add the inverse of) the primulas which are not yellow (A'). This

operationleavesuswiththeyellowprimulas(A).WemaywritethisasA=B+(-A')orA=B-A'.Thistype

ofreasoningunderliesthechild’sabilitytosaythattherearemoreprimulasthanyellowones,thatthe

yellowprimulasareincluded intheclassofprimulas,orthattheyellowprimulasareonlysomeofthe

primulas.

Thefifthpropertyactuallyencompassesseveralaspects.Oneofthemisrelatedtospecialidentity

elements.Supposewecombinetheclassofyellowprimulaswithitself.Theresultisyellowprimulas.We

maywritethisasA+A=A.Inthisequation,Afunctionsasanidentityelementlike0.AddingAtoAislike

adding0toA:theresult,A,isunchanged.Piagetcallsthistautology.Anotheraspectisresorption.Ifwe

combinetheclassofyellowprimulaswiththeclassofprimulas,theresultisprimulas.Wemaywritethis

asA+B=B.Here,too,Afunctionsasanidentityelement.AddingAtoBislikeadding0toB;theresult,B,

isunchanged.Inasense,thisisanotherwayoflookingatinclusionrelations.Theyellowprimulasmust

be includedintheclassofprimulas(ormustbesomeoftheprimulas)sinceaddingtheformertothe

latterdoesnotchangethelatter.


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These,then,aresomeoftheaspectsofGroupingIandareintendedasaformaldescriptionofthe

processes underlying the child’s classification. The model involves elements (classes), the binary

operatorofcombining,andfivepropertiesgoverningtheapplicationoftheoperatortotheelements.

Discussion of Grouping I

AfewgeneralremarksshouldbemadeconcerningGroupingI.First,Piaget’suseofmathematicsis

notatallmeanttoimplythatthechildunderstandsthelogicomathematicalmodelinanyexplicitsense.It

is obvious thatmost children have never heard of the special identity element, let aloneGrouping I.

Clearly,thechildisnotamathematicianatthislevel.Infact,heoftencannotdescribeinanyclearway,

mathematicalorotherwise,hisprocedureforsolvingaparticularproblem.Hisreportisoftenincoherent.

Piagetusesthelogicomathematicalmodel,therefore,nottocharacterizethechild’sconsciousness,butto

describetheprocessesunderlyinghisclassification.

Second,GroupingIisnotmetricallyquantitativeinthesensethatitdoesnotinvolvenumbers.The

operations involve classes whichmay be of any size. It does notmatter whether there are 5 yellow

primulasand6whiteones,or5,000yellowprimulasand300whiteones.Inbothcasestherearemore

primulasthantherearewhiteprimulas,andsoforth.

Third,wemayexpandonourearlierpointthattheGroupingisintendedtodescribethestructure

ofthechild’sclassification.Piagetisnotinterestedintheminordetailsofthechild’sperformance;thatis,

whetherheisclassifyingflowersorfishorwhetherhefirstputtheflowersinanarrangementandthen

theanimals.Piaget insteadattempts tocapture theessenceof thechild’sactivitiesand to identify the

processesunderlyingthem.TheGroupingisPiaget’swayofdescribingtheseprocessesinaclearway.

Therefore,theGroupingisnotsimplyaprotocol listingeverythingthatthechilddoes. It is insteadan

abstractionwhichdescribesbasicprocessesliketheabilitytocombinementallytwosmallerclassesintoa

largerone,ortotakeawayoneclassfromanother.

The grouping also is a comprehensive and integrated structure. It is comprehensive since it

describes the processes underlying basic classification activities. The Grouping describes the

potentialities of the child, and not necessarilywhat he does in any one task at any one time. Let us


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suppose that a child constructs a hierarchy of classes. In doing so hemay notmake use of inclusion

relations.Inthiscase,theGroupingdoesnotsomuchdescribewhatthechildactuallydoes,butwhathe

iscapableofdoingundertheproperconditions.

Also,theGroupingisanintegratedsysteminthesensethateachofthepropertiesdoesnotstand

alonebut isrelated toallof theothers.Onthemathematical level, this iseasy tosee.Thepropertyof

associativitydescribestheorderinwhichelementsmaybecombined,butthepropertyofcompositionor

closure is needed to interpret the result of the associative combination. In other words, associativity

showsthattwodifferentordersofcombiningelementsareequivalent,andcompositionrevealsthatboth

oftheseordersofcombinationresultinanotherelementwhichmustbeinthesystem.Thus,theproperty

ofassociativitywouldbemeaninglesswithoutthepropertyofcomposition.Wecannothaveoneproperty

withouttheother.ThisfeatureoftheGroupingis,ofcourse,intendedtoreflectanimportantaspectofthe

child’s activities: the child’s successful classification (including the understanding of inclusion)

presupposes an interrelatedwhole, a structure of mental operations. For example, suppose the child

recognizesthattherearemoreprimulasthanyellowprimulas.Thisachievement impliesanumberof

interrelatedmentalacts.

Thechildmustbeawarethattheprimulas(whicharenolongerpresentinasinglecollection)are

thecombinationofyellowprimulasandprimulasofother colors (A+A'=B).Thechildmustalsobe

aware thatwhenyellowprimulasare takenaway from theprimulas, there remainprimulasofother

colors(B-A=A').These, then,aresomeoftheoperationsunderlyingthechild’sanswertoaquestion

concerninginclusion.Whenthechildcorrectlyanswersthequestion,hemaynotfirstactuallyperformall

theseoperations.However,theyareimplicitinhisanswer;hecouldnotanswercorrectlyifitwerenot

possibleforhimtoperformalltheoperationsinvolvedintheclassificationsystem.Tosummarize,any

particularresponsethatthechildmakestoaclassificationproblemcannotbeconsideredinisolation.His

responsepresupposesacomplexstructure,and it is thiswhichPiagetdescribesas theGrouping.The

Grouping,inotherwords,describesthementaloperationswhichmakeitpossibleforthechildto“really”

understandclassification.

Fourth, the Grouping explains and predicts behavior. Insofar as the Grouping describes the

processes underlying the child’s classification, it may be said to explain performance. The Grouping


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statesthatthechildcancombinetwoclassestogetalargerone.Thisoperation,amongothers,underlies

thechild’sabilitytounderstandinclusionrelationsandinthissenseexplainsit.InsofarastheGrouping

isgeneral itmaybesaidtopredictbehavior.TheGrouping isnot limitedtotheobjectsPiagetusedto

studyclassification.BecausetheGroupingprovidesadescriptionofstructure,itgoesbeyondthedetails

ofanyparticularproblemandallowsustopredictwhatthechild’sperformanceislikeonothersimilar

tasks.

Fifth,PiagethasdescribedseveralotherGroupingsallofwhichareintendedtorefertothechild’s

ability(from7to11)todealwithconcreteobjectsorthoughtaboutthem.Therefore,stage3istermed

concreteoperational.

Sixth,towardtheendofhislife,PiagetbegantofeelthattheGroupingmodelisnotfullyadequate

as an account of the concrete operations. While the facts concerning children’s performance on the

classificationtasks(andothersaswell)remainaswellestablishedasever,theGroupingmodelsuffers

fromseveraldeficiencies.“[TheGrouping]model...hasgeneratedlittleenthusiasmfromlogiciansand

mathematiciansbecauseof itsunavoidable limitations . . . and consequent ‘lackof elegance’ ” (Piaget,

1977b).(Indeed,onemightevengofurtherandclaimthatthelogicofthemodelisnotonlyinelegant,

butnotentirelycoherent.)“[TheGroupingmodel]...wastoocloselylinkedtothetraditionalmodelof

extensional logic and truth tables” (Piaget, 1980, p. 5, quoted in Beilin, 1985). In view of these

limitations, Piaget felt it is necessary to develop new formal models to characterize the essence of

concrete operational thought. “Abetterway, I nowbelieve, of capturing thenatural growthof logical

thinkinginthechildistopursueakindoflogicofmeanings”(Piaget,quotedinBeilin,1985b).While

Piagetdidnothave the time todevelopsuchmodels indetail,hebegan theeffortby introducing the

notion of “correspondences,” which we describe in our discussion of pre-operational strengths. It is

importanttorealize,asBeilinpointsout,“thatPiagetwasnotirrevocablycommittedtoaparticularlogic

or abstract model; consequently, following Piaget’s example, others are free to [select] the logical or

mathematicalmodelsthatbestexplainthedataofcognitivedevelopment”(Beilin,1985,p.112).

Inbrief,Piagetbelievedthatwhilethinkingisbestdescribedintermsof logicalmodels,hisown

effortsinthisareawerenotentirelysuccessful.Henceitisnecessarytoexpandthetheorybydeveloping

newmodels.AsPiagetclaimed,hehimselfwasthechief“revisionist”ofPiagetiantheory.


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Piaget’searlywork(inthe1920sand1930s)dealtwithclassificationinapreliminaryway.Inthe

1950shereturned to theproblem,using therevisedclinicalmethod.Hepresented2- to11-year-old

childrenwithanarrayofobjectstobeclassified.Thefindingswerethatinstage1(2to5years)thechild

fails to use consistently a clear rule or defining property to sort the objects into different classes. He

insteadconstructsgraphiccollectionswhicharesmallpartialalignmentsorinterestingforms.Instage2

(5 to 7 years), the child sorts the objects by a reasonable defining property and even constructs a

hierarchical classification, but fails to comprehend inclusion relations. Stages 1 and 2 are termed

preoperational.Instage3,whichisconcreteoperational(7to11years),thechildhasamaturenotionof

class, particularly when real objects are involved. The child sorts them by defining properties,

understands the relations between class and subclass, and so forth. To describe clearly the processes

underlyingthechild’sactivities,PiagetproposesalogicomathematicalmodelwhichhecallsGroupingI.

ThisGroupinginvolvessomeelements,abinaryoperator,andfivepropertiesrelatingtheoperatortothe

elements.Also,theGroupingisnotmetricallyquantitativeinthesensethatitdoesnotmatterhowbigor

small(innumericalterms)arethevariousclassesinvolved.Thechild,ofcourseisnotconsciousofthe

Grouping; rather theGrouping is intended todescribe thebasic structuresofhis activities. Inhis last

years,Piagetrecognizedtheshortcomingsof theGroupingmodelandproposedthedevelopmentofa

new“logicofmeanings.”

Piagetstressesthattheagenormsdescribingclassificationareonlyapproximate.Aparticularchild

maypassfromstage1tostage2at6yearsandnotnecessarilyat4or5years.Onechildmayspendthree

years in stage 1while another childmay spend four years in the same stage. Piaget doesmaintain,

however,thatthesequenceofdevelopmentisinvariant.Thechildmustfirstbecharacterizedbystage1

before he can advance to stage 2 and then to stage 3. Piaget also points out that a child may not

necessarilybe inthesamestageofdevelopmentwithrespecttodifferentareasofcognition.That is,a

childmaybeinstage1withrespecttoclassification,andinstage2ofnumberdevelopment.Thus,achild

maybeslightlymoreadvancedinsomecategoriesofthoughtthaninothers.

Oneimportantissueregardingclassification,andindeedalltheconceptsstudiedbyPiaget,isthe

generalityofthefindingsforchildrenindifferentcultures.Recently,muchcross-culturalworkhasbeen


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carriedouttodeterminewhetherchildrenindifferentculturesemploythetypesofreasoningdescribed

byPiaget, andwhether the sequenceof stages is invariant across cultures, asPiagetproposes.Opper

(1971;andinDasen,1977)hasexaminedanumberofPiagetianconcepts,includingclassification,in

rural and urban children in two Southeast Asian countries, Thailand andMalaysia. Likemany other

investigators(forareview,seeDasen,1977),Opperfindsthatalthoughtheagesmayvary,thesequence

ofdevelopmentisthesameindifferentcultures:first,Thaichildrenarecharacterizedbystage1,then

stage2,andsoon.

Moreover, Opper finds that Thai andMalaysian children present responses similar to those of

Swisschildren.Forexample,whenaMalaysiangirlinstage2ofclassificationwasaskedwhetherthere

aremorerosesorflowersinabunchofsevenrosesandtwoorchids,sheresponded,“Therearemore

roses than flowers.” The examiner said, “Show me the flowers.” The child then pointed to the two

orchids.

AThaiboy,inthesamestage,waspresentedwithsevenrosesandtwolotus.He,too,maintained

thattherearemorerosesthanflowers.Moreroses.—Morethanwhat?—Morethanflowers.—Whatarethe

flowers?—Roses.—Are there any others?—There are.—What?—Lotus.—So in this bunch, which is

more,rosesorflowers?—Moreroses.—Thanwhat?—Thanlotus.

Turningtothestage3child,wealsofindthesameresponsesastheSwisschildren.Forexample,a

Malaysiangirlsaid:Therearemoreflowersbecauseifit’sroses,it’sonlythese[pointingtoroses],butthe

flowersareplus thesealso [pointing to orchids].We see then that inmany casesThai andMalaysian

children’sargumentsarevirtuallyidenticaltothoseofSwisschildren.

How can we evaluate Piaget’s work on classification? On the one hand, Piaget has been very

successfulatwhathehasattemptedtodo.Anumberofindependentinvestigatorshaveconfirmedthat

stage1classificationtakesunusualforms(e.g.,Vigotsky,1962),thatyoungchildrenexperiencegenuine

difficulty with class inclusion (Klahr andWallace, 1972), and that the course of development with

respecttoclassificationisgenerallyasPiagethasdescribed(Kofsky,1966).Ontheotherhand,itshould

bepointedoutthatPiaget’sapproachtoclassificationisofaveryspecificsort.Hefocusesmainlyonthe

hierarchicalstructureofclasses,forexample,classinclusion.Heisnotparticularlyconcernedwithother


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aspectsof conceptswhichnowseemtobequite important.ThusNeisser (1967)haspointedout that

everyday concepts are often vague and difficult to define, and Rosch (1973) has developed a new

approachfocusingonnonlogicalaspectsofchildren’sconcepts.Thedefiningpropertyorintensionofa

classisoftenquitevague,aparticularobjectmayfitintoseveralclassessimultaneously,theboundaries

betweenclassesmaybe fuzzy,and itmaynotbepossible to formasimplehierarchy. Inbrief,Piaget’s

approachfocusesononlyoneofmanyimportantaspectsofclasses.

RELATIONS

In Chapters 2 and 3 we have already reviewed several aspects of relations, a problem (like

classification)withwhichPiagethasbeenconcernedsincehisearliestworkinpsychology.Wesawthat

in the sensorimotor period the infant displays precursors of relations. He can broadly discriminate

withinthedimensionsofnumerosity,intensityofmusculareffort,andloudnessofsounds(amongother

dimensions).Inthecaseofnumerosity,youwillrecallthatLaurentsaid“papa”whenPiagetsaid“papa,”

thatLaurentsaid“bababa”whenPiagetsaid“papa-papa,”andthatLaurentsaid“papapapa”inresponse

to “papapapapapapa.” Laurent’s imitation, although not exact, nevertheless implies an ability to

discriminateorhearthedifferenceamongseveralsoundswhichdifferedinnumberofrepetitionsofone

syllable.Similarly,inthecaseofmusculareffort,Laurentappearedabletodetectthedifferenceamong

thevariationsinvigorwithwhichheswungachain,andalsohewasabletodiscriminateamongsounds

ofdifferentdegreesofloudness.Thus,theinfantcandifferentiategradationswithindifferentkindsof

stimuli:somethingsarelouderthanothers,ormorenumerous,orbigger,andsoforth.Hecanperceive

differencesinvariousaspectsofhisworld.Theabilitytomakesuchdiscriminationsisaprerequisitefor

reasoningaboutdifferences.

Piaget’s early research on the child from about 5 to 10 years investigated reasoning about

differences, but not the perception of differences. He presented children with this verbal problem

(amongothers):“Edithisfairer(orhasfairerhair)thanSuzanne;EdithisdarkerthanLili.Whichisthe

darkest,Edith,Suzanne,orLili?”{JudgmentandReasoning,p.87).Theresultsshowedthatchildrenfrom

5to10yearsareunabletodealwithproblemsofthissort,calledtransitivity,ataverballevel.

Asinthecaseofclassification,Piagetreturnedtotheproblemofrelationsinhislaterwork.Using


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therevisedclinicalmethod,heperformedseveralinterestingstudiesonordinalrelations,whichwewill

nowcharacterizebriefly.

Some Properties of Ordinal Relations

Piaget’sdefinitionofordinalrelationsinvolvesseveralfeatures.Supposewehaveseveralnumbers,

suchas17,65,25,3,and1,0OI.Itispossibletoarrangetheminorderofincreasingsize.Wemayusethe

symbol<tostandfor“isasmallernumberthan”andwrite3<17<25<65<1,0OI.Thesequenceisan

orderingofthenumberswiththesmallestbeingfirst,thenextsmallestsecond,andsoforth.Notethatthe

absolutesizeofthenumbersmakesnodifference.Thesecondnumberdoesnothavetobeexactlyone

morethanthefirstorexactlytwiceasbigasthefirst.Thelastnumber,solongasitislargerthan65,may

beofanysizewhatsoever.Also,wedonotneedtohavezeroas thebeginningof theseries.Theonly

requirements forordering thenumbersare that theyaredifferent fromoneanother, thatat leastone

numberissmallerthantherest,thatanotherislargerthanalltherest,andthatanynumberinbetween

thesmallestandthelargestisbothlargerthantheoneimmediatelyprecedingitintheseriesandsmaller

than the one immediately following it. Of course, orderings are not limited to numbers.Wemay also

ordersoundsonthedimensionofloudness.Supposesoundaisverysoft,bismuchlouderthana,andc

isslightlymoreloudthanb.Thenwehavea<b<c,where<means“issofterthan.”Againtheprecise

degreeofloudnessdoesnotaffecttheordering.

Piaget’s work deals with such matters as the child’s ability to construct orderings or ordinal

relationsandtomanipulatetheminvariousways.Thesestudies,involvingchildrenfromabout4to8

yearsofage,usuallydetectthreedistinctstagesofdevelopment:stage1lastingfromabout4to5,stage2

fromabout5to6,andstage3fromabout7andabove.Thefirsttwostagesarepreoperational,andthelast

isconcreteoperational.Whiletheagenormsareapproximate,thesequenceiscrucial.

Stage 1

Onestudywasconcernedwiththeabilitytoconstructanorderingofacollectionoftenstickswhich

differedonly insize.Wewillcall theshortestof thesticks(about9centimeters in length)A, thenext

largerB,andsoonthroughJ,thelargest(about16centimetersinlength).AdifferedfromBbyabout.8


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centimeters,andthisalsowastrueofBandC,andsoon.Piagetpresentedthechildwiththesticksina

randomlyorganizedarrayandaskedhimtoselectthesmallestofthelot.Afterthiswasdone,Piagetgave

aninstructionlikethis:“Nowtrytoputfirstthesmallest,thenonealittlebitbigger,thenanotheralittle

bitbigger,andsoon”(Child’sConceptionofNumber,CCN,pp.124-25). Inanotherstudythechildwas

askedtomakeastaircasefromthesticks.

Whenconfrontedwiththisproblem,childreninstage1showedseveredreactions,noneofwhich

wassuccessful. Somechildrenproducedrandomarrangementsof the sticks, likeH,E,B, J, and so on.

Otherchildrenmanagedtoorderafewofthesticks,butnotallofthem.AnexampleofthisreactionisA,B,

C,D,H,F,E,andsoon.

Anotherstrategywastoplacethelargersticksinonecollectionandthesmallersticksinasecond

collection.Withineachofthesecollections,however,thestickswereinarandomorder.Amoreadvanced

reactionalsoappearedwhichmaybeconsideredatransitiontothenextstage.Thechildstartedwith

somestick,likeB,apparentlyselectedatrandom;thenhetookanotherstick,likeH,andmadethetopofit

extendslightlyabovethetopofB;athirdstick,forexample,A,wasmadetoextendslightlybeyondthe

topofB;andsoforth.Theresultwasthatthetopsofthesticksformanordering;Hisslightlyhigherthan

B,andAslightlyhigherthanH,andsoforth,asinFigure6.Butthebottomsofthesticksalsodifferedina

randomway,andfailedtolieonastraightlineastheyshould.Thus,thechildconstructsanordering,but

onlybyignoringthelengthofeachstick.Thisprocedurefreeshimfromthenecessityofcomparingeach

stickwiththeoneimmediatelyprecedingitandwiththeonetofollow.Onewayofcharacterizingthese

activitiesistosaythatthechildfocuses(centers)ononeaspectoftheproblem(puttingthetopsinorder)

butignoresanother,equallyimportantaspect(arrangingthebottomsinastraightline).Tosummarize,

thechildatthisstagefrequentlycannotformasystematicorderingofanynumberofobjectsalthoughhe

issometimesabletoorderafewofthem.


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FIGURE6Orderingofsticks.

Stage 2

Presentedwiththesameproblem,childreninthesecondstagegenerallysucceedinconstructing

theordinalarrangementofsticks,sothatA<B<C<D<E<F<G<H<I<J.Butthechilddoesnotbuildthe

orderingswithout difficulty. Sometimes he begins by ignoring the bottomsof the sticks, as in stage 1.

Sometimeshemakesmanyerrors,likeA<D<B,andsoon,andtakesalongtimetorecognizeandcorrect

them.Thechildcontinuallyrearrangeshisordering,andshiftsthesticksfromonepositiontoanother.

Essentiallythechild’sprocedureisoneoftrialanderror,lackinganoverallplanorguidingprinciple.

Forexample,ifhehaschosenAasthesmallest,hemightthenchooseanothersmallone,like

D,andlineitupnexttoA.Thenhemightchooseanothersmallone,likeC,andplaceitnexttoDand

seethatitissmallerthanD.Sincethisisso,hemightrearrangethesticksplacingCafterAbutbeforeD.

AfterbeginningwithA,thechildfailstolookforastickthatislongerthanAbutsmallerthanalltheones

remaining. If this rule is followed, then each step of the ordering can be constructed without any

difficulty.However, thechildat this stagedoesnotemploysucha logicalprocedure.He fails tomake

systematic comparisons between a given stick and the one immediately preceding it and all those


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following.

This tendencywas furtherrevealedby theadditionofonemoreproblem.Afterconstructing the

orderingAthroughJ,thechildrenweregivenanewcollectionoftensticks,a,b,c,d,e,f,g,h,i,j.Eachof

thesenewstickscouldfitinbetweenapairofsticksofthefirstseries.Thatis,ifthenewsetofstickswere

orderedcorrectlyalongwiththefirstset,thearrangementwouldbeA<a<B<b<C<c<D<d<E<e<F<

f<G<g<H<h<I<i<J<j.Thechild’staskwastodopreciselythis;tofitthenewsticksintotheordering

alreadyconstructed(AthroughJ),soastomakeanewordinalarrangementinvolvingalltwentysticks.

Childrenofthisstagehadgreatdifficultywiththeproblem.Infact,manyfailedtosolveit.Partof

one child’s orderingwasC e d D, and another producedH g G I h j c, and so forth. Other children

succeededinproducingthecorrectordering,butonlyafterconsiderabletrialanderror.

Thesedifficultiesseemduetoseveralfactors.Onefactorappearstobethatthechildperceivesthe

originalseriesasawholeandfindsithardtobreakuptheseriesintosmallerunits.Also,childrenofthis

stagedonotapproachtheproblemwithaguidingprinciple.Theyfailtousearulelike,“Startwiththe

smallestofa-j)insertitinbetweenthepairofthesmalleststicksinA-J)thentakethesmallestofb-jand

insertitbetweenthesmallestpairofsticksinB-J)andsoforth.”Notonlydidthechildrenfailtousearule

likethis,buttheyalsohaddifficultyindecidingthatagivenelementofa-jwasatthesametimebigger

thanonestickinA-JandsmallerthanthenextlargerstickinA-J.Toplacedproperly,thechildmustsee

thatd<EandthatD<d.Hemustcoordinate thesetworelationsbutfailstodosoconsistently.That is,

somechildrenwouldtakeeand,seeingthatitwaslargerthanB,wouldplaceitrightafterB.Theyfailed

toconsiderwhetherewasatthesametimesmallerthanC,andthereforemadeanerror.

Afterinvestigatingthechild’sabilitytoconstructanorderingandplacenewelementsinit,Piaget

wenton to study the child’s ability to construct equivalencesbetween two separateorderings (which

involveequalnumbersofelements).Toillustratethis,letustakeaclasswithfifteenboysandfifteengirls

andordereachofthesegroupsintermsofheight.Wefindtheshortestboy,thenext-to-shortestboy,and

soon,andwedothesameforgirls.Wecanseethatthetwoorderingsareequivalentinsomewaysand

differentinothers.Somedifferencesarethattheheightoftheshortestboymaybe48inches,whereasthe

height of the shortest girl is 44 inches. Also, the second shortest boymay be 4 inches taller than the


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shortestone,whereasthesecondshortestgirlisonly1inchtallerthantheshortestgirl.Despitethese

realdifferences,thereareimportantsimilaritiesbetweenthetwoorderings.Theboywhois48inches

tallandthegirlwhois44inchestall,despitetheirdifferenceinheight,areequivalentintermsoftheir

positionintheordering.Theyareboththeshortest.Thesameholdstrue,ofcourse,forthetallestboyand

girl,thenexttotallest,andsoforth.

Piagetthenraisesthe issueofwhethertheyoungchildcanrecognizetheequivalencesbetween

twodistinctorderings.Doesheunderstandthattwoobjects,whiledifferinginheight,forexample,canat

thesametimebeequivalentintermsoftheirrelativepositioninanordering?Tostudythematterhefirst

presentedchildrenwithtendolls,A-J,whichwerepresentedinarandomdisplayandwhichcouldbe

arrangedinorderofheight;andwithtensticks,A'-J',alsorandomlyarranged,whichcouldbeorderedin

size.Thesticksweresmallerthanthedolls,andthedifferencesbetweenadjacentpairsofstickswere

smallerthanbetweenpairsofdolls.Thechildwastoldthatthedollsaregoingforawalkandthateachof

themmust have the proper stick. The intention of the instructions, of course,was to get the child to

produceanorderingofthedollsandofthesticksandtomakeeachmemberofoneorderingcorrespond

totheappropriatememberoftheotherordering.Thus,dollAshouldhavestickA',dollBshouldhave

stickB',andsoon.Piagetcallsthisprocesstheplacingoforderingsintoone-to-onecorrespondence.

Theresultsshowedthatchildrenofthisstagecanproduceaone-to-onecorrespondenceofdolls

andsticks,butonlyinatrial-and-errorfashion.Themostcommonprocedureistoorderthedolls(bytrial

anderror)andthentoorderthesticks(bytrialanderror).Onlyaftertwoseparateorderingshavebeen

constructedaretheelementsofeachputintoone-to-onecorrespondence.Thatis,thechildfirstidentifies

thelargestdoll,thenexttolargestdoll,andcompletestheorderingofdolls;thenhegoesontoorderthe

sticks.Itisonlyafterthisisdonethatthechildplacesthelargeststickwiththelargestdoll,thenextto

largest stick with the next to largest doll, and so forth. While this procedure works, it is somewhat

cumbersome.Aneasiermethodistobeginbyidentifyingthelargest(orsmallest)dollandthelargest(or

smallest)stickandimmediatelyplacingthetwotogether.Thesecondstepistochoosethe largestdoll

andstickofallthoseremainingandtoplacethemtogether,andsoforth.Inanyevent,thechildinthis

stage does succeed in setting the two orders into one-to-one correspondence. He seems to have

establishedthattheorderingsareequivalent.


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FIGURE7Theequivalenceofrelativeposition(dollsandsticks).

The next problem concerns the stability of the equivalence established by one-to-one

correspondence.Letussupposethatthesticksareplacedveryclosetogetherwiththeirorderpreserved

(asinFigure7).Theshorteststickisclosesttothethirdtallestdoll,thesecondstickisclosesttothefourth

tallestdoll,andso forth.Doesthechildrecognizethat thesecondtalleststick isstill equivalent to the

secondtallestdoll,eventhoughtheformerisnowclosesttothefourthtallestdoll?Thatis,doesthechild

conservetheequivalenceofrelativepositionwhentheovertone-to-onecorrespondenceisdestroyed?

Piaget presented this and similar problems to a number of children. He placed the sticks close

togetherandaskedwhichstick“goeswith”whichdoll.Piagetdiscoveredseveredmethodsofattacking

theproblem.Themostprimitivereactionistoassertthatadollisequivalenttothestickclosesttoit.Thus,

thesecondlargeststickandfourthlargestdollareconsideredtobelongtogethersimplybecauseoneis

belowtheother.Thechild’sjudgmentisdominatedbyspatialrelations.Otherchildrentrytosolvethe

problembycounting,buttheyfailtodosoproperly.Forexample,onechildsaidthatthefourthlargest

stickwasequivalenttothethirdlargestdoll.Thereasonforhismistakewasthathenoticedthatthere


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werethreesticksprecedingthefourthlargeststick;hethencountedoutthreedolls,stoppedthere,and

identifiedthethirddollwiththefourthstick.Thismethodisquitefrequentamongchildrenofthisstage;

thatis,theyfindadollcorrespondingtothenthstick,countingtheprecedingn-1sticks,thencountthe

dolls,stoppingatthen-1thelement.Thechildconfusesthepositiontobefound(say,stick4)withthe

numberofprecedingelements(3).

Stage 3

Afterabouttheageof6-7years,thechildissuccessfulinallofthetaskswehavedescribed.When

askedtoconstructasingleorderingofsticksdifferinginsize,thechilddoessoquiteeasily.Theordering

isguidedbyanoverallplan.Thechildusuallybeginswiththesmallest(orsometimes,withthelargest),

then thenext smallest, and so forth, in sequenceuntil theordering is complete.This strategymaybe

characterizedasstartingwiththesmallestandcontinuingtotakethesmallestofeverythingthatisleft,

untilthestickshavebeenexhausted.Whenaskedtoplaceadditionalsticks(a-j)intheirproperpositions

within the ordering (A-J) already constructed, the child does so with almost no errors. The process

underlyingthisachievementisthecomparisonofoneofthenewsticks(say,d)withtwointheoriginal

orderingsimultaneously.That is, toascertaind'sproperposition, thechilddeterminesthat it isat the

sametimebiggerthanDbutsmallerthanE.Tophrasethematterdifferently,hecoordinatestwoinverse

relations—biggerandsmallerthan.

Inasimilarwaytheconcreteoperationalchildeasilyplacestwoseparateorderingsintoone-to-one

correspondence.Onechildimmediatelyputthebiggestdollwiththebiggestball(ballsweresometimes

usedinplaceofsticks),thenexttobiggestdollwiththenexttobiggestball,andsoforth.Hisstrategywas

to identify thebiggestdollandballofall thoseremainingand toplace the twotogetheratonce.This

procedureismoreeconomicalthanthatoftheyoungerchildwhofirstordersthedolls,thentheballs,

and finallybegins toput them together.When thisone-to-onecorrespondence isdestroyed, thechild

conservestheequivalenceofrelativeposition.Herealizesthatthesmallestdollisstillequivalenttothe

smallestballandnottotheballtowhichithappenstobeclosestinspace.

Insummarizingthematerialontheconcreteoperationalchild,then,wecanstatethatheisadeptat

understanding and manipulating ordinal relations. However, as in the case of classification, one


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limitation applies: he can deal with relations on a concrete level only; that is, when real objects or

thoughtsaboutthemareinvolved.Nevertheless,histhoughtisfarmoreadvancedthanthatofthechild

in stages 1 and 2. The child can construct orderings, put two such orderings into one-to-one

correspondence,andconservetheresultingequivalences.Asinthecaseofclassification,theprocesses

underlying the child’s ability tomanipulate relations form integrated and comprehensive structures.

Each of his mental operations cannot be understood without reference to the others of which he is

capable. These processesmust be interpreted in terms of complex systemsof operations. To describe

thesesystems,Piagethasdevelopedseverallogicomathematicalmodels,similartoGroupingI(although

they,of course,deadwithrelations,notclasses).Also,Piagethas investigatedseveralotheraspectsof

ordinalrelations,suchastransitivity(ifa>bandb>c,thena>c),whichwewillnotcoverhere.

NUMBER

Theabilitytounderstandclassesandrelations,accordingtoPiaget,isbasictomatureconceptsin

many areas. The several groupings which describe the processes underlying the older child’s

performance in problems of classes and relationsmay also be used to characterize concepts of space,

chance,geometry,andsoforth.Sincewecannotreviewall theseconcepts,wewillconcentrateonone

thatisparticularlyinterestingandthathasreceivedconsiderableattentionintheAmericanandBritish

researchliterature,namely,theconceptof(whole)number.

First,wemustunderstandwhatPiagetdoesanddoesnotmeanbytheconceptofnumber.Hedoes

notmean and isnot interested in computational abilities as taught in the first few grades of school.

Whetherthechildcanadd2and2,orsubtract3from5,isnottheissue.ThereasonforPiaget’slackof

interest in thesematters is that simple addition and subtraction of whole numbers, aswell as other

manipulationsof them,canbecarriedoutentirelybyroteandwithoutunderstanding.Thechildcan

simply memorize the addition and subtraction tables and fail to comprehend the basic concepts

underlyingthem.Piagetdoesnotdenythatitisusefultomemorizethefactsofadditionandsubtraction;

for purposes of computation, we all find it helpful to do so. He asserts, however, that for mature

understanding of number, such rotememorization is not sufficient andmust be accompanied by the

masteryofcertainbasicideas.


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Amongthese ideasareone-to-onecorrespondenceandconservation.Letus firstconsiderone-to-

onecorrespondence.SupposewearepresentedwithacollectionorsetofdiscreteobjectsasinFigure8.

Thesizeoftheobjects,theircolor,andsofortharecompletelyirrelevant.Allthatisrequiredisthattheset

contain a finite number of discrete objects. We are then given a box of objects and are required to

construct from it another setwhich has the same number property as the first set. It does notmatter

whethertheobjectsinthesecondset(whichwewillcallsetB)arethesamecolor,size,andsoonasthose

inthefirstset(setA).WhethersetAcontainselephantsandsetBcontainsgeraniumsisirrelevant.The

onlyrequirementisthattheyhavethesamenumber.OnewayofconstructingasetBsothatitwillhave

thesamenumberpropertyasAisbycountingtheobjectsinA(say,therearefive)andthentakeoutofthe

boxthesamenumberofobjects.Thisprocedure,whichofcourseisquiteadequate,probablyoccursfirstto

adults.Butsupposewecannotcount.SupposewedonotknowthenumberofobjectsinsetA.Evenwith

theselimitationsthereisasimplewayofconstructinganewset,B,whichwillhavethesamenumber

propertyasA.ThismethodmerelyinvolvesputtingnexttoeachmemberofsetAone,andonlyone,new

object.Thesenewobjects,aftertheone-to-onecorrespondencehasbeenestablished,formaset,B,with

thesamenumberasA.Ofcoursewedonotreallyhavetophysicallyplaceeachnewobjectnexttoonein

A;wecannotetheone-to-onecorrespondencementally.That is,wecan“saytoourselves,”“Thisnew

object corresponds to the first in the lineof setA,” and soon.The important idea is not thephysical

placingtogetherofthesets,butthepairingofonememberinsetAwithoneinsetB,howeverthisisdone.

FIGURE8Collectionofobjects.

Althoughverysimple, the ideaofone-to-onecorrespondence isbasicandpowerful,andmaybe

usedinavarietyofsituations.Ifwewanttodeterminewhethertherearethesamenumberofseatsas

peopleinanauditorium,allwehavetodoisaskeveryonetositdown(withnooneallowedtositon


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anyoneelse’s lap!). Ifall thepeopleare inseats(inone-to-onecorrespondencewith theseats)and if

noneoftheseatsisempty,thenthenumbers(whatevertheymaybe)ofpeopleandseatsareequal.If

therearepeoplestanding,thenthisdefinestherelationofmorepeoplethanseats.Ifthereareempty

seats, then this defines the relation of more seats than people. In brief, one-to-one correspondence

establishesthatanytwosets—regardlessofthenatureoftheobjectscomprisingthem—areequivalentin

number.Countingorotherproceduresarenotneeded.Lackofone-to-onecorrespondenceestablishes

thatonesetislargerthantheother(andonesmallerthantheother).

FIGURE9Conservationofnumber.

ThesecondbasicideawhichPiagetinvestigatesisconservation.Supposethatwehaveestablished

thatsetsAandBareequalinnumber,asinFigure9A.Thatis,wehaveputsetAinaline,andbeloweach

memberofsetAwehaveputanewobject.The lineofthenewobjects issetB.Supposethatwethen

compress themembers of set B, as in Figure 9B, so that the perceptual one-to-one correspondence is

destroyed.NoweachmemberofsetBisnotdirectlybelowadifferentmemberofsetA.Theproblemis

whetherthetwosetswhichnowdifferinphysicalarrangementstillareequalinnumber.Inotherwords,

istheequivalenceestablishedinFigure9AconservedwhentherearrangementshowninFigure9Bis

performed?Toadults,thismayseemlikeafoolishquestion.Ofcourse,theequalityofnumbershasnot

changed!Buttheproblemiswhetherchildrenacceptthissimpleandbasicidea,too.Iftheydonot,then

theirworldofnumbermustbeverychaoticindeed.Ifquantityisseentochangewhenevermerephysical

arrangement isaltered, thenthechild fails toappreciatecertainbasicconstanciesor invariants in the

environment.

Piagethasconductedanumberof investigationsonthechild’sunderstandingofthesetwobasic

ideas: one-to-one correspondence and conservation of the equivalence of twonumbers.He finds that


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youngchildrenfailtounderstandthesetwonotionsandthataperiodofdevelopmentisrequiredbefore

thechildachievesthementaloperationsnecessaryforthoroughcomprehensionofnumber.Letusnow

reviewtheexperiments.

Stage 1

Tostudytheabilitytoconstructsetsofequivalentnumber,Piagetpresentedchildrenwithavariety

ofproblems.The simplestof these involvedplacingbefore the childa rowof sixor sevenpenniesor

buttonsorsweets,andsoon.Theexaminerthenaskedthechildtopickoutthe“samenumber”or“as

many” from a large collection of similar objects. Thus the childwas given set A andwas required to

constructasecondset,B,whichwasequivalentinnumber.Thechildrenwere,ofcourse,nottoldhowto

constructsetB.Hereisaprotocoldescribinghowastage1child,4yearsand7monthsofage,dealtwith

theproblem.Piagethadplacedsixsweetsinarowandtoldthechildthattheybelongedtohisfriend

Roger:

“Putasmanysweetshereastherearethere.Those...areforRoger.Youaretotakeasmanyashehas.”(Hemade a compact row of about ten,whichwas shorter than themodel.)—“Are they the same?”—“Not yet”(addingsome).—“Andnow?”—"Yes.”—“Why?”—“Becausethey’relikethat”(indicatingthelength).(CCN,p.75)

FIGURE10Failuretoconstructequalsets.

The example makes clear the predominant tendency of this stage. The child does not use the

methodofone-to-onecorrespondence.Instead,hethinksthatthetwosetsareequivalentinnumberif

theyhavethesamelengths.InPiaget’sterms,thechildcentersononedimension—thelength—ofsetA

(Roger’ssweetsorthemodel)andbaseshisconstructionofsetBsolelyintermsofthatonedimension.

TheresultispicturedinFigure10.Thelengthsofthetworowsareequal,buttheirnumbersarenot.The

newrowisdenser;thatis,therearesmallerspacesbetweenthesweets,thanRoger’srow,butthechild

ignoresthisfactandconcentratesonlyonthelengths.Sincehefailstocoordinatethetwodimensionsof

lengthanddensityatthesametime,hecannotconstructsetsequivalent innumberexceptwhenvery


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smallnumbersareinvolved,orexceptbyaccident.

In another investigation, Piaget tried tomake the child understand the principle of one-to-one

correspondence,andthenperformedtheconservationexperiment.Inthisstudy,setAwasarowoften

vasesandsetBconsistedofflowers.Onechild,4yearsand4monthsofage,

put13flowersclosetogetherinarowopposite10vasesrathermorespacedout,althoughhehadcountedthevases from 1 to 10. Since the rowswere the same length, he thought that the flowers and vaseswere “thesame.”—“Thenyoucanputtheflowersintothevases?”—“Yes.”—Hedidso,andfoundhehad3flowers[left]over.(CCN,p.50)

Thechild,then,initiallyconstructedsetBsoastomakeitthesamelengthassetAandthoughtthat

thetwosetswerethereforeequalinnumber.Theexaminerthenmadethechildconstructaone-to-one

correspondencebetweentheflowersandvases;thatis,thechildputeachflowerinavase.Theresult

was ten flowers in ten vases (or two sets equivalent in number), and the three extra flowers were

discarded. The question now iswhether the child realizes that the two sets are really equivalent in

number.Doesthechildconservetheequivalencedespiteamerephysicalrearrangementoftheobjects?

Tofindout,Piagetcontinuedtheexperimentwiththesamechild.

The flowerswere taken out andbunched together in front of the vases. [That is, they formed a shorter rowthan did the vases.] “Is there the same number of vases and flowers?”—“No.”—“Where are there more?”—“There are more vases.”—“If we put the flowers back into the vases, will there be one flower in eachvase?”—“Yes.”—“Why?”—“Becausethereareenough.”(Thevaseswereclosedupandtheflowersspacedout.)—“Andnow?”—“Therearemoreflowers.”(CCN,p.50)

Notethatafterthechildhadhimselfestablishedaone-to-onecorrespondencebetweentheflowers

andvases,hefailedtoconservethenumericalequivalenceofthetwosets.Whentheflowerswereput

intoashorterrowthanthevases,thechildbelievedthatthenumberswerenolongerequalandthatnow

thereweremorevases.Hemaintainedthiseventhoughherealizedthattheone-to-onecorrespondence

couldbereestablished;that is, that theflowerscouldbereturnedtothevases.Thenwhentherowof

vaseswasmadeshorterthanthatoftheflowers,hechangedhismindonceagain.Heassertedthatnow

thereweremore flowers. Clearly, this child centered on the lengths of the rows and used only this

informationtomakejudgmentsofequivalenceorlackofequivalenceofnumber.Whentherowswerethe

samelength(aswhentheflowerswereinthevases),hesaidthattheywereequalinnumber.Whenthe

rowsdifferedinlength,hebelievedthatthelongerlinehadthegreaternumber.


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Piagetalsoinvestigatedtheroleofcounting,questioningthewayinwhichcountingthetwosets

affectsthechild’sjudgment.Onechild,5yearsand3monthsofage,failedtheconservationproblem.He

saidthatsetA(sixglasses)wasgreaterthansetB(sixbottles)becauseonewaslongerthantheother.

Thentheexaminersaid:

“Can you count?”—“Yes.”—“Howmany glasses are there?”— “Six.”—“And how many bottles?”—“Six.”—“Sothere’sthesamenumberofglassesandbottles?”—“Therearemorewhereit’sbigger[thatis,longer].”(CCN, p.45)

This examination shows thatwhile the child can count, the act ismeaningless in deedingwith

conservation.Althoughhecanreciteastringofnumbers,hedoesnotcomprehendwhattheysignify.The

fact that he counted six bottles and also six glasses does not imply to him that the sets are equal in

number. For him, equality of number is determined solely by equality of lengths, and counting is an

extraneousandirrelevantact,whichdoesnotassureeithertheequivalenceofsetsoritsconservation.4

Stage 2

The child of this stage easily constructs two sets equivalent innumber, but fails to conserve the

equivalencewhenthesetsarerearranged.Per,achildof5years,7months,

hadnodifficultyinmakingarowof6sweetscorrespondingtothemodel.[Piagetuses“model”torefertosetA, the row to be copied, and “copy” to refer to set B.] The model was then closed up: “I’ve got more.”—“Why?”—“Becauseit’salongerline.”(Theprocesswasreversed.)—Nowtherearemorethere,becauseit’sa big line.” But a moment later, Per said the opposite: “Are there more here [referring to the longerrow]?”—“No.”—“Why not?”—“Because it’s long.”—“And there [the shorter row]?”—“There are more there,becausethere’salittlebundle”[Thechildmeantthattheshorterrowwasdenser].—“Thenaretheremoreinalittlebundlethaninabigline?”—“Yes.”AfterthisPerwentbacktousinglengthasthecriterion,madethetworowsthesamelengthagainandsaid:“Nowthey’reboththesame.”(CCN,p.79)

Theprotocolshowsthatthechildofthisstageeasilyconstructsasetequalinnumbertoanother.He

also establishes the equivalence by the method of one-to-one correspondence. That is, in order to

constructsetB,heplacesanewsweetjustbeloweachinsetA.Buttheone-to-onecorrespondenceisnot

fullyunderstood;itisjust“perceptual.”WhensetBismadeshorterthansetA,thechildfailstoconserve

the equivalencewhich he so easily constructed. The protocol also shows that the child is ambivalent

about thecriteriaused toestablishequalityor inequalityofnumber.Sometimeshemaintains that the

longerrowhasmorebecauseitislonger;atothertimeshebelievesthattheshorterrowhasmorebecause


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it is denser. In Piaget’s terms the child sometimes centers on the lengths (ignoring densities) and

sometimes centers on the densities (ignoring lengths). This tendency is an improvement over what

occursinthepreviousstage,sincetheyoungerchild(instage1)consistentlycentersononlyoneofthe

twodimensions,usuallylength,anddoesnotconsidertheother,usuallydensity,atall.Bycontrast,the

childinstage2haswidenedthesphereofhiscentrations.Henotices,albeitatdifferenttimes,thatboth

dimensionsmayberelevantandusestheinformationfromeitherofthesedimensionsseparatelytomake

ajudgment.Thisuseofpartialinformationiscalledregulations.Wewillseenexthowthechildinthe

periodofconcreteoperationscoordinatesthetwodimensions.

Stage 3

The results of this stage are easy to describe. The child can now construct a set numerically

equivalenttoanothersetandcanconservetheirequivalencedespitechangesinphysicalarrangement.

Hereisaprotocolillustratingthisstage:

“Takethesamenumberofpenniesastherearethere[therewere6 insetA],Hemadearowof6underthemodel,butputhismuchclosertogethersothattherewasnospatialcorrespondencebetweentherows.Bothendsof themodel extendedbeyond thoseof the copy. “Haveyougot the samenumber?”—"Yes.”—“Are youandthatboy[referringtothehypotheticalownerofsetA]justasrichasoneanother?”—“Yes.”—(The penniesof the model were then closed up and his own were spaced out.)—“And now?”— “Thesame.”—“Exactly?”—“Yes.”—“Whyaretheythesame?”—“Becauseyou’veputthemclosertogether.”(CCN,p.82)

Thisprotocolcontainsseveralinterestingfeatures.OnefeatureisthatinmakingsetBequaltosetA,

theconcreteoperationalchilddoesnotbothertoplaceeachelementinBdirectlyundereachelementin

A.Hedoesnotneedtorelyontheperceptionofspatialproximitybetweentheelementsofeachset.How

thendoesheconstructnumericallyequivalentsets?Onemethod,ofcourse,issimplytocountthenumber

ofobjectsinsetA,andthenmerelycountoutthesamenumberforsetB.Probablysomechildrenusedthis

method,butPiagetconcludedfromhisclinicalexaminationsthatotherchildrendidnotusecounting.

Theyseemedtousethemethodofone-to-onecorrespondence,butinamoresophisticatedwaythanthe

youngerchild.Theconcreteoperationalchild’stechniquemaybedescribedasfollows:toconstructsetB

equaltosetA,heputsoutonepennyforthefirstpennyinsetA,andsoforth.Itdoesnotmatterwherehe

putsthemembersofsetB.TheonlycrucialrequirementisthathematcheachmemberinsetAwithone

andonlyonememberinsetB(anonspatialone-to-onecorrespondence).Thechildmustnotforgettoput


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outapennyforeachmemberofsetA(thatis,hecannotskipanymemberofsetA)andmustnotputout

morethanonepennyforeachmemberofsetA(thatis,hemustnotcountanymemberofsetAtwice).

Theprocessofestablishingsetsequalinnumbermaybedescribedintermsofclassesandrelations.

Asfarasrelationsareconcerned,thechildusesthemethodofvicariantordering.SupposethatsetA(the

model)isalineofpennies,andthechildmustconstructasetB(thecopy)fromalargesupplyofcandies.

Hebeginsbypointingatthepennyontheextremeleftandputsoutasweet.Thenhepointstothesecond

pennyfromtheleft,putsoutasweetforit,andcontinuesuntilthelineofpennieshasbeenexhausted.

Thisprocessofpointingtoonepennyatatime,beingcarefultocounteachpennyonceandonlyonce,is

anordering. It isequivalent tosaying: “Thispennycomes first, thisonesecond, thisone thirdandso

forth.Inaway,theorderingofpenniesislikearrangingaseriesofsticksordollsinorderofheight.There

is a first stick, a second stick, and so forth, just as there is a firstpennyanda secondone.Therefore,

something like the ability to construct ordinal relations underlies the child’s construction of sets

equivalentinnumber.

Despite theevident similarity, the twoprocesses—constructingordinal relations (as inordering

thesticks)andvicariantordering(thepennies)—arenotidentical.Inthecaseofthesticks,thereisone

andonlyoneshorteststickwhichmustcomefirst intheseries,oneandonlyonesecondshorteststick

whichmustcomesecondintheseries,andsoforth.Inthecaseofthepennies,itdoesnotmatterwhich

pennyisconsideredfirstintheseries,whichcomessecond,andsoon.Onecouldstartcountingatthe

extremeleft,attheextremeright,inthemiddleorwhereveronepleased,justsolongasoneiscarefulnot

toomitpointingtoeachofthepenniesandnottopointtoanyofthemmorethanonce.Theorderingof

penniesiscalled“vicariant”forthisveryreason:theorderinwhichthepenniesarecounteddoesnot

matter.

Other aspects of relations are involved too.When putting out one and only one sweet for each

penny,thechildiscoordinatingtwoorderings.Thisissimilartotheproblemofdollsandsticks.Justasthe

childcangivetotheshortestdolltheshorteststick,tothesecondshortestdollthesecondshorteststick,

andsoforth,socanheplacethefirstsweetwiththefirstpenny,thesecondsweetwiththesecondpenny,

andsoforth.Ofcourse,theone-to-onecorrespondenceofpenniesandsweetsisvicariant,whereasthe

one-to-onecorrespondenceofdollsandsticksisnot.Inthelatterinstance,thereisoneandonlyonestick


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(theshortest)whichgoeswiththeshortestdoll,andsoforth.Inthecaseofpenniesandsweets,itdoes

notmatterwhichsweetisplacedintocorrespondencewithanypenny,solongasoneandonlyonesweet

isusedforeachpenny.

Theconstructionofequivalentsetsalsoinvolvesclassification.Tothechild,thepenniesinsetA,for

instance,areinsomewaysallthesameandinsomewaysdifferentfromoneanother.Theyaredifferent

inthatacertainpennyiscountedfirst,anotheronesecond,andsoforth.Theyarethesameinthatitdoes

notmatterwhichiscountedfirst,whichsecond,andsoforth.Inotherwords,itisonlythechild’sactof

pointingtoeachinturnthatdifferentiatesthepennies;otherwise,theyareallequivalent.Insofaraseach

ofthepenniesisanelementequivalenttoalltherest,theyareallmembersofthesameclass.Thesameis

true,ofcourse,ofthesweetsinsetB.

Thus far we have seen how the child’s ability to construct sets equivalent in number may be

analyzedintoanumberofcomponentskills.Underlyingthechild’sovertperformance(e.g.,placingona

table seven sweets corresponding to seven pennies) are a number of concrete operations: vicariant

ordering, one-to-one correspondence of two vicariant orderings, and classification. Some of the

operations involveclassesandothers relations.Thus,number isaunionof classesandrelations.The

operationsareconcretesincethechildcanapplythemonlytoimmediatelypresentobjectsorthoughts

about them.Theyareoperations since theyare actionswhich the childperformsmentally andwhich

have the added property of being reversible. This means that for each particular mental action, for

instanceaddition, thechildcanperformitsoppositeaction, in thiscasesubtraction,which leaveshim

wherehestarted.Asoperations,theymayalsobedescribedintermsofoverallstructuresorsystems,that

is,intermsoftheGroupings,anexampleofwhichwehavegiveninthecaseofclassification.5

Inthestageofconcreteoperations,thechildcanalsoconservenumber.Afterconstructingtwosets

equivalent in number, the child recognizes that the sets remain equivalent despite mere physical

rearrangementofthesets.Ifthesevensweetsarecompressedtomakeashortlinewhilethelineofseven

penniesremainsthesame,thetwosetsareneverthelessstillequalinnumber.Theequivalencehasbeen

conserved.

Whatenablestheconcreteoperationalchildtoconservewhilethepreoperational(stages1and2)


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childfailstodoso?Recallthemechanismunderlyingthepreoperationalchild’sfailure:centration.The

youngerchildcentersononlyalimitedamountoftheinformationavailable.Whentherowofsweetsis

compressed,henoticesonlythatthelineofpenniesisnowlongerthanthelineofsweets.Heignoresthe

fact that the line of sweets is denser (has smaller spaces between adjacent elements), and bases his

judgmentonlyonthelengths.Thepreoperationalchildknowsthatempiricalreversibilityispossible:he

realizesthatifthesweetswerereturnedtotheiroriginalpositions,therewouldbeonesweetforeach

penny.Thisknowledgedoesnothelp,however;despite it, he feels that thenumberof a set changes

whenitsappearanceisaltered.Perceptualfactorshavetoostrongaholdonthechildatthisstage.They

arenotyetsufficientlycontrolledbymentalactionswhichcancompensateformisleadinginformation.

Bycontrast,theconcreteoperationalchilddecentershisattention.Heattendstoboththerelevant

dimensionsandusesthisinformationinseveralways.

1.Henoticesthatthelineofpennieshasbecomelongerthanthelineofsweetsandthatthelineofsweetshasbecomedenserthanthelineofpennies.Moreover,hecoordinatesthetwodimensions. He mentally manipulates the visual data available to him. This mentalactivity leads him to realize that while the length of the line of pennies increases(relativetothesweets)byacertainamount,thedensityofthelineofsweetsincreasesbyanequivalentamount.Inotherwords,thechildconceivesthatthepennies’increaseinlengthisbalancedby,orcompensatedfor,bythesweets’increaseindensity:thereisarelation of reciprocity or compensation between length and density. In effect, oneincreasecancelsouttheotherwiththeresultthatthesetsremainequivalentinnumber.Thisreciprocityisoneformofreversibility.Sincetheincreaseinlengthcounteractstheincreaseindensity,theresultisareturn,orareversal,totheoriginalsituation,whichisequalnumber.

2.Theconcreteoperationalchildalsocomestousetheoperationofnegation.Wehavealreadyseenthatwhentherowofsweetsiscompressed,theconcreteoperationalchildrealizesthatthesweets’ increaseindensityisreciprocatedbythepennies’ increaseinlength,and that, as a result of these reciprocal transformations, the number of the two setsremains equivalent. The concrete operational child is also able to imagine that thesechangescanbeannulledornegated.Hereasonsthattheactionofcontractingthesweetscanbenegatedbytheinverseactionofspreadingthemout.Theoneactionisannulledby theother. Suchannulmentornegation isanother formof reversibility; that is, thechild mentally reverses the action of contracting the row of sweets. As a result heattributesequalnumberstothetwosets.Notethatthestage3childbothreversestheactofcontractingandrecognizesthatthefinalresultistheoriginalarrangementofsweets


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andpennies.Thestage2child,whoiscapableofempiricalreversibility,recognizesthatthesweetscanbereturnedtotheiroriginalpositionbutdoesnotfocusonorappreciatetheactofrearrangement.Heattendstostates,nottransformations.

3. The concrete operational child sometimes uses an identity argument, reasoning that thenumbersmustbethesamesincethesameobjectsareinvolved:nothinghasbeenaddedortakenaway.

Thestage3child’s thought isconcrete inaspecialsensewhichSinclair(1971),oneof themost

importantGenevaninvestigators,expressesquiteclearly:“Concreteoperations...doesnotmeanthatthe

childcanthinklogicallyonlyifhecanatthesametimemanipulateobjects....Concrete,inthePiagetian

sense,meansthatthechildcanthinkinalogicallycoherentmanneraboutobjectsthatdoexistandhave

realproperties,andaboutactionsthatarepossible;hecanperformthementaloperationsinvolvedboth

whenaskedpurelyverbalquestionsandwhenmanipulatingobjects....Theactualpresenceofobjectsis

nointrinsiccondition”(pp.5-6).

Tosummarize, thestage3child,havingenteredtheperiodofconcreteoperations,canconstruct

two sets equivalent in number, and can conserve this equivalence despite changes in appearance.

Underlyingtheseachievementsareanumberof thoughtprocesses.Theability toconstructequivalent

setsrequiresvicariantorderingandclassification.Theabilitytoconserve,whichisacquiredasaresultof

thedecentrationofthechild’sattention,issupportedbythreetypesofoperationswhicharesometimes

explicitlyexpressedinthechild’sjustificationofhisresponse:reciprocity,negation,andidentity.These

areaspectsofconcreteoperations,whichmaybedescribedbythegroupings.Thechilddoesnotalways

performallofthethoughtprocesseswhenpresentedwithaproblemofconstructingequalsets,nordoes

herefertoallthreeargumentswhenaskedforajustificationofconservation.Hemightonlyrefertoone

or perhaps two of them. The child is, however, capable of performing all the concrete operations,

althoughhemaynot alwaysdo so. In fact, after a periodof time the concrete operational child takes

conservation for granted.He immediately recognizes that number is conserved anddoes not need to

proveconservationtohimselfbymeansofnegationorreciprocity.Whenaskedwhynumberisconserved,

hethinksthatthequestionissillyandthatthefactofconservationisself-evident.Forhim,conservation

has become amatter of logical necessity. This is evidence that the child has acquired an underlying

structureofmentaloperations inwhicheach isdependentupon theotherandnone isperformed in


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isolation.Thestage3child’sthoughtisconcreteinthespecialsensethathecanthinkcoherentlyabout

anddealwithrealobjectsbutnothypotheticalentities.

In conclusion, Piaget’s work on number has been extraordinarily productive. It has stimulated

volumes of research on children’s number, and many of Piaget’s findings have been successfully

replicated,eveninnon-Westernsocieties(seeDasen,1977).AsweshallfindinChapter6,theworkhas

alsohadimplicationsforeducationalcurricula.Likemanymajorcontributionstopsychology,thework

has aroused a good deal of controversy, and several alternative views have been proposed (see, for

example,GelmanandGallistel,1978;andGinsburg,1982).

CONSERVATION

Thus far, we have described only the conservation of number—that is, the child’s ability to

recognize that thenumericalequivalencebetween twosets remainsunchangeddespitealterationsof

physical arrangement. Piaget has also investigated severed other conservations which include

continuous quantity, substance, weight, and volume. The conservation of continuous quantity may be

definedbythissituation.Thechildispresentedwithtwoidenticalbeakers(AandB),eachfilledwith

equalamountsofliquid(seeFigure11),andisaskedwhetherthetwoglassescontainthesameamount

ornotthesameamounttodrink.Afterheagreestotheequivalenceofquantities,theliquidispouredby

either the experimenter or the child from one of the two identical beakers (say, B) into a third,

dissimilarlyshapedbeaker(C).Thecolumnoftheliquidinthethirdclass(andtheglassitself)isboth

shorterandwiderthanthatintheremainingoriginalglass(A).Thechildisnowaskedwhetherthetwo

beakers(nowAandC)containequalamounts.Ifheassertsthattheydo,heisaskedtoexplainwhy.The

liquid inC is then returned to theoriginalbeakerB, and the child is againasked ifA andB contain

identicalamounts.Themanipulationisrepeated,thistimewithaglass(D)whichistallerandthinner

thantheoriginalbeakers.Finally,theliquidofeitherAorBispouredintoaset(E)ofaboutthreeorfour

smallerglassesandthesamequestionsareaskedofthechild.Ifthechildcontinuouslyassertsineach

casethattheamountthathasbeenpouredfromBintothedifferentbeakersisalwaysthesameasthe

amountremaining in theoriginalbeaker(A), thenhehasconservedcontinuousquantity.That is, the

childrecognizesthatmerelypouringtheliquidfromBtoCorDorE,doesnotincreaseordecreasethe

quantity;the“amount”ofliquidremainsthesame(orisconserved)whetheritisinBorinC.Sincethe


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quantitiesAandBwereequal,andsincepouringtheliquidofBintoCdoesnotchangeitsquantity,then

thequantitiesinAandCmustalsobeequal.Ifthechilddoesnotconsistentlyassertthisequality,thenhe

hasfailedtoconserve.

FIGURE11Conservationofcontinuousquantities.

Inthecaseofconservationofsubstance,thechildispresentedwithtwoidenticalballsofPlasticine

(orclay,etc.).HeisfirstaskedwhetherthereisthesameamountofPlasticineinbothballs.Ifhedoesnot

think so, he is asked to take away or add some clay tomake them identical. Then, the experimenter

changesoneoftheballstoasausageshape,whilethechildwatches.Thechildmustnowdecidewhether

ornottheballandthesausagehaveequalamountsofsubstance.As inthe liquidsituation, theball is

changed into a varietyofdifferent shapes. If the child consistently asserts that thebelli and thenew

shapesdohaveequalamountsofsubstance,thenhehasconservedsubstanceandhasrecognizedthat

merelychangingtheshapedoesnotaltertheamountofmatterinvolved.

To test theconservation ofweight, the experimenter again presents the childwith two identical

ballsofPlasticineandplacesthemonabalance.Thechildseesthatthetwoballsweighthesame.Then

theyareremovedfromthebalanceandoneballistransformedintotheshapeofasausage.Thechildis

askedtoanticipatetheresultsofplacingtheballandthesausageonthetwosidesofthebalance.Will

theystillremainbalancedorwillonesidebeheavierthantheother?Thequestioniswhetherthechild

recognizesthatweightisconserveddespitechangesinshape.Hereagainaseriesofchangesaremadeto

oneoftheballsandthequestionastotheidentityofweightisrepeated.

Inthecaseofconservationofvolume,twoballsofPlasticineareplacedintwoidenticalbeakers,each

filledwithequalquantitiesofliquid.Thechildseesthattheballsdisplaceanequalvolumeofliquidin


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bothbeakers.Or,inthechild’sterms,theliquidgoesupanequaldistanceinbothcases.Thentheballs

areremovedfromthebeakers,andoneballischangedintotheshapeofasausage.Thequestionnowis

whetherthechildrecognizesthatbothballandsausagecontinuetodisplaceequalvolumes,orwhether

thewatergoesupanequalamountinbothcases.

All theseconservationsaresimilar.Theyinvolvea firstphase inwhichthechildmustrecognize

thattwoamounts—liquidquantity,substance,weight,orvolume—areequal.Mostchildrenabovetheage

of 4 years are quite successful in this task. All the conservations also involve a visible transformation

whichmaybedonebyeitherthechildortheexperimenter.Whilethechildwatches,orasaresultofhis

ownactions,theliquidispouredfromonebeakertoanother,ortheballischangedintoasausage.Itis

quiteapparentthatnoliquidorPlasticineisaddedortakenaway.It isalsoapparentthatthingsnow

lookdifferent.Thecolumnofliquidisshorterandwider,andtheballisnowasausage.And,finally,all

theconservationsinvolveasecondphaseinwhichthechildmustonceagainjudgewhethertheamounts

inquestion are still the same.Of course, they are equivalent, and the issue iswhether the childwill

recognizethisorbemisledbytheobservedchangesinappearance.

Piaget’sgeneral findingsare that there isasequenceofdevelopmentwithregard toeachof the

conservations.Childrenbeginbyfailingtoconserveandrequireaperiodofdevelopmentbeforetheyare

able to succeedat the task.Forexample, in the caseof continuousquantities, childrenarenotable to

conserveuntilabouttheageof6or7years.Inthefirstphaseoftheproblem(twoidenticalbeakers,each

filledwithequalamountsofliquid),theyoungestchildren,around4or5yearsofage,correctlyconclude

that theamountsof liquidareequal.Since thechildhaseitherpouredout the liquid into thesecond

beaker,orhastoldtheexperimenterwhentostoppouring,thisisnotsurprising.Ifaskedtojustifythe

identity,thechildwillsaythatthewatercomesuptothesamelevelineachglasssothattheamountsare

equal.Whentheliquidinonebeakerispouredintoathirdglasswhichisdifferentinshapefromthefirst

two,thechildnowmaintainsthattheamountsarenolongerequal.Oneglasshasmoretodrinkthanthe

other.Askedtoexplainhisanswer,hesaysthattheglasswiththetallercolumnofliquidhasthegreater

amount.Thisjudgmentofamountsistiedexclusivelytotheheightsofthecolumnsofliquid:whenthe

heightsare the same (as inphase1), the child thinks that theamountsare the same;when theyare

different(asinphase2),thentheamountsmustbedifferenttoo.


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Instage2,thechildof5or6yearsvacillatesinhisresponsestotheconservationproblem.Whilehe

usuallyfailstoconserve,hisapproachtotheproblemvariesfromtimetotime.Inthesecondphaseofthe

experiment(whenonebeaker isshorterandwiderthantheother), thechildsometimessaysthatthe

tallerbeakerhasmore todrink,andsometimesmaintains that thewideronehas thegreateramount.

Unlikethestage1child,hedoesnotconcentrateexclusivelyontheheightsofthecolumnsofliquid,but

sometimesbaseshisjudgmentsonthewidthsaswell.

Instage3,thechildiscapableofconservation.Whenaskedwhytheamountsdonotchangeafter

thepouring,hegivesatleastoneofseveralreasons.OneisthatiftheliquidinCwerereturnedtoits

originalcontainer,B, thenthetwoinitialbeakers,AandB,wouldcontain identicalcolumnsof liquid.

Thisisthenegationargument.Asecondreasonistheidentityargument:it’sthesamewater.Youhaven’t

addedanyortakenanyaway.Athirdargument,involvingcompensationorreciprocity, isthatthethird

glass,C,isshorterthantheoriginalbeaker,A,butwhatClostinheightwascompensatedbyC’sgainin

width;therefore,theamountinCmustbeequaltotheamountinA.

Towardtheendofhislife,Piagetreturnedtotheproblemofconservationandstressedtheroleof

commutability. Inoneexperiment,Piaget (1979)presentedchildrenwithaconservationofsubstance

problemofthefollowingtype.Aballofclayispresentedandthenapieceisremoved.Thechildisasked

iftheballhasthesameamount,andsaysno,sincesomethinghasbeentakenaway.Thepiecethathad

beenremovedfromonesideoftheballwasplacedontheothersideandthechildwasagainaskedifthe

ballhasthesameamountnow(withthepieceaddedtotheotherside)asdidtheoriginalball.Piaget

findsthatundertheseconditions,childrenassertconservationataveryyoungage.Theysayessentially

that“It’sthesamething,youtookitawayandthenputitbackandit’salwaysthesame”(p.21).Inother

words,thechildrenhaveunderstood“thatthereisdisplacement,andthatwhenonedisplaces,whatis

addedatoneplacehasbeentakenawayfromanotherplace”(p.21).ThisPiagetcalls“commutability”

andclaimsthatitisoneimportantfactorinconservation.Commutabilitybearsasimilaritytothenotionof

compensation.

In the case of conservation of substance, weight, and volume, a similar progression to that of

quantityappears.Inthefirststage,thechildfailstoconserveapparentlybecauseofaconcentrationon

onlyoneofthestimulusdimensionsinvolved.Thatis,inthecaseofweighthemaysaythatthesausageis


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heavier than the ball because the former is longer. In the second stage, he again fails to conserve,

although now he vacillates between the two dimensions involved. For instance, he may sometimes

believethattheballisheavierbecauseitiswiderandatothertimesassertthatthesausageisheavier

because it is longer. In the third stage, the child conserves, for reasons similar to those cited for

continuousquantities.

Whilealltheconservationsfollowasimilarcourseofdevelopment,thereisastrikingirregularityas

well—thephenomenonofhorizontaldécalage.Thisreferstothefact,whichhasbeenwellsubstantiated,

thatthechildmasterstheconservationofdiscontinuousquantityandsubstanceataboutage6or7;does

notachievestage3oftheconservationofweightuntilage9or10;doesnotunderstandtheconservation

ofvolumeuntilapproximately11or12.Ineachcasetheargumentsusedarethesame,sometimeseven

involvingthesamewords.Buthavingmasteredconservationinonesubstantivearea,likesubstance,the

child is not able to generalize immediately to another area like that of weight. First, he acquires

conservationofdiscontinuousquantityandsubstance,andthenweight,andthenvolume.Thedécalage,

orlackofimmediatetransfer,illustrateshowconcreteisthethoughtofthechildduringtheagesofabout

7to11years.Hisreasoningistiedtoparticularsituationsandobjects;hismentaloperationsinonearea

maynotbeappliedtoanother,nomatterhowusefulthismightbe.

GENERAL CHARACTERISTICS OF THOUGHT

Wehavereviewedthedevelopmentofvariousaspectsofthought:classes,relations,number,and

conservation.Itwouldseemusefulatthistimetotakeabroaderlookatsomegeneralcharacteristicsof

cognitivedevelopment.

Underlying Patterns of Thought

There are striking regularities in the child’s cognitive development. In each of the two major

periodsofdevelopmentdiscussedinthischapter(preoperationalandconcreteoperational),thechild

usesdistinctivepatternsofthoughttoapproachdifferentsubstantiveproblems.Thereappeartobesome

generalpatternswhichcharacterize the thoughtof thepreoperational childandsomeotherpatterns

manifestedintheconcreteoperationalchild’scognition.


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Consider,first,thechildfromabout4to7yearsinthepreoperationalperiod.(Rememberthatthis

age designation is only approximate, since a child as old as 9 or 10 years typically shows a

preoperationalapproachtotheconservationofvolume.)Onegeneralcharacteristicofcognitiveactivity

duringthisperiodiscentration.Thechildtendstofocusonalimitedamountoftheinformationavailable.

In the conservationofnumber, he judges two sets equalwhen they are the same length and ignores

anotherrelevantvariable,thedensity.Intheconservationofcontinuousquantity,thechildjudgestwo

amountsequalwhen theheightsof thecolumnsof liquidare thesameand ignores thewidth. In the

constructionofordinalrelations(theproblemoforderingtensticksintermsofheight),hesucceedsonly

byconsideringthetopsof thesticksand ignoringthebottoms,orviceversa. Inall theseproblems, the

preoperational child deploys his attention in overly limitedways. He focuses on one dimension of a

situation,failstomakeuseofanother,equallyrelevantdimension,andthereforecannotappreciatethe

relationsbetweenthetwo.(Thenotionofcentration issomewhatsimilar toPiaget’searlierconceptof

juxtapositionwhichisthetendencytothinkintermsofthepartsofasituationandnotintegratethem

intoawhole.)

Bycontrast, theconcreteoperational child is characterizedbydecentration. He tends to focus on

severeddimensionsofaproblemsimultaneouslyandtorelatethesedimensions.Intheconservationof

number,hecoordinateslengthanddensity:twosetshavethesamenumberwhenthefirstislongerthen

the second but the second is denser than the first. In the conservation of continuous quantity, he

recognizes thatamountsareequalwhenonecolumnof liquid isat thesametimetallerbutnarrower

than a second. In the construction of ordinal relations, he determines whether a given object is

simultaneously bigger than some objects and smaller than others. In all these problems, the concrete

operational child attends to severed aspects of the situation at once. Centration anddecentration are

generalpatternsofthought,underlyingstructures.

Thetwomajorperiodsofdevelopmentcanbecharacterizedinotherwaysaswell.Thethoughtof

thepreoperationalchildisstaticinthesensethatitcentersonstates.Intheconservationofsubstancehe

focuses on the shape of Plasticine (sometimes a ball and sometimes a sausage) and ignores the

transformation,thatis,thechangefromonestatetotheother.Intheconservationofcontinuousquantity

he focuses on the heights of the columns of liquid and not on the act of pouring. He lacks adequate

representationsofanobject’sshiftfromonepositiontoanother.Ingeneral,heconcentratesonthestatic


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statesofasituationandnotonitsdynamictransformations.

Theconcreteoperationalchild,ontheotherhand,isattunedtochanges.Intheconservationshe

concentratesonthetransformation:theactofpouringtheliquid,orspreadingapartasetofobjects,or

deformingaballintoasausage.Heformsmoreorlessaccurateimagesofthechangeswhichhavetaken

place,and,therefore,canreason,forexample,thatasasetexpandsinlengthitsimultaneouslydecreases

indensity.

The preoperational child’s thought lacks reversibility. He may be able to predict an empirical

reversibility as, for instance, in the case of the liquidswhere hewould agree that if thewaterwere

pouredbackintoB,therewouldbethesamequantityasbefore.Butthisempiricalreversibilitydoesnot

changethefactthatnowhebelievesthereismore(orless)waterinthenewglassC.Itisasifpouring

fromBtoC,andfromCtoBweretotallyunrelatedactions.Theolderchild,ontheotherhand,realizes

thatpouringfromCtoBreversesornegatestheactionofpouringfromBtoCandisawarethatitisthe

sameactionperformedinanotherdirection.Bycarryingouttheactionmentally,thatis,byreversingthe

pouringinhismind,heisabletoascertainthatthequantityofwaterinC(thelowerwiderglass)isthe

sameasinB.Hecanperformamentaloperationwhichleadshimtoacertainconclusion,andthendothe

reverseofthisoperationwhichenableshimtoreturntohisoriginalstartingpoint.

Theconcreteoperationalchildcanalsoperformanothertypeofreversibilitywhenoperatingon

relations.Thisisreciprocity.Forinstance,intheexampleofliquidquantity,whenthechildsaysthatone

glassislongerandthinner,whereastheotherisshorterandwider,heiscancelingoutthedifferences

betweenthetwoglassesbyanactionofreciprocity.Onedifferencebalancesouttheother,withtheresult

thattheyhaveareciprocalrelationship.

Tosummarize,thepreoperationalchild’sthoughtisirreversibleandattentivetolimitedamountsof

information, particularly the static states of reality. The concrete operational child focuses on several

aspects of a situation simultaneously, is sensitive to transformations, and can reverse the direction of

thought. Piaget conceives of these three aspects of thought— centration-decentration, static-dynamic,

irreversibility-reversibility—asinterdependent.Ifthechildcentersonthestaticaspectsofasituation,he

isunlikelytoappreciatetransformations.Ifhedoesnotrepresenttransformations,thechildisunlikelyto


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reversehis thought.Bydecentering,he comes tobeawareof the transformations,which thus lead to

reversibilityinhisthought.Inconclusion,wecanseethatoneaspectofthoughtisnotisolatedfromthe

rest.Eventhoughthenatureofthesystemmayvarywiththedevelopmentofthechild,thoughtprocesses

formanintegratedsystem.

Invariant Sequence

Another striking regularity in cognitive development involves invariant order: the sequence of

activities (for example in classification, partial alignments, collections, class inclusion) assumes an

invariantorderdespitewidevariationsinculture.Cross-culturalresearchprovidesrelevantevidenceon

thisissue.WithinWesterncultureschildrenprogressthroughthevariousstagesintheorderdescribed

byPiaget.Inthecaseofconservationofcontinuousquantities, forexample,researchshowsthatSwiss,

British,American,andCanadianchildrenfirstfailtoconserve,thenvacillateintheirresponse,andlater

conservewithstability.Whilechildrenintheseculturesdonotnecessarilyachievethevariousstagesat

thesameaverageages, thesequenceofdevelopment—theorderof thestages—seems identical inall

cases.Eveninotherandverydifferentcultures,liketheThaiorMalaysian,thesamesequenceofstages

andtypeofresponsesappear.ChildreninThailand,forexample,exhibitclassificationactivitieswhich

arevirtuallyidenticaltothoseusedbyWesternchildren,andproceedthroughthesequenceofstagesin

theorderdescribedbyPiaget(Opper,inDasen,1977).Thereisgreatcross-culturalgeneralityinPiaget’s

findings.Atthesametime,wemustmakeonequalification:apparently,membersofsomeculturesdonot

advanceasfarinthesequenceofstagesasdoWesterners.Thus,forwhateverreasons,insomecultures,

individualsmaynot complete the stageof formaloperations.Not everyoneachieves thehighest level

possible in terms of Piaget’s stages. Yet, until their progress terminates, these individuals proceed

throughthesequenceofstagesinthestandardorder.Whiletheultimatelevelofdevelopmentmaydiffer

amongcultures, thesequenceseemstobe invariant,asPiagetproposes.Thephenomenadescribedby

Piagetarethusnearlyuniversal,occurringacrossextremevariationsincultureandenvironment.Piaget

hassurelycapturedsomethingverybasicinhumancognition.6

Irregularities

Piaget has gone to great lengths to dispel some misinterpretations concerning his theory. In


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particular,heshowsthattherearecertainirregularitiesindevelopment.Hepointsout,first,thattheages

atwhichthestagesoccurvaryconsiderablybothwithinandamongcultures.NotallGenevanchildren

attainstage3ofnumberdevelopmentat6or7years,andchildreninMartiniquelagbehindGenevans

byapproximatelyfouryears.InThailand,urbanchildrenattainstage3atthesametimeaschildrenin

Geneva,but ruralThai children lagbehindbyapproximately threeyears. InMalaysia, rural children

attainthenumberconceptoneyearaheadofurbanchildren,whointurnlagbehindSwisschildrenby

twoyears.Thus therateofdevelopmentseems tovary fromgroup togroup.Second, thecourseofan

individual’sdevelopmentiscontinuous.

Thechildisnotcharacterizedbystage1onedayandbystage2thenextday.Rather,thetransition

is gradual, occurring over a long period of time, and the child exhibits many forms of behavior

intermediary between the two stages. Indeed, an individual child’s behavior takes many forms in

addition to those Piaget describes as being typical of the various stages. Piaget’s stages are idealized

abstractions;theydescribeselectedandsalientpointsonanirregularcontinuumofdevelopment.Third,

thechildisnotalwaysinthesamestageofdevelopmentwithregardtodifferentareasofthought.The

childmaybe characterizedby stage2 in the case of classes, and stage1 in the case of relations. It is

unlikely,however,thathewillbeinstage1forclassesandstage3forrelations.Onlyinfrequentlydoes

onefindextremediscrepanciesbetweenstagelevelsindifferentareas.Fourth,aswehavealreadyseen,

there exists the phenomenon of horizontal décalage, in which the child displays different levels of

achievementinregardtoproblemsinvolvingsimilarmentaloperations;forexample,hemaybeableto

conservesubstancebutnotnumber.

Preoperational Strengths

Piaget (On the Development of Memory and Identity, 1968) tries to correct a widespread

misconception concerning preoperational thought. Typically, we characterize the young child as

intellectuallyincompetentsincehecannotconserve,cannotusereversibility,andcannotdecenter.Piaget

feelsthatthisviewisexaggerated;asaresultofrecentresearch,Piagetproposesthatthepreoperational

childpossessesanumberofimportantintellectualstrengthswhichmustnotbeoverlooked.Inparticular,

theyoungchildiscapableofidentity,functions,andcorrespondences.


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While unable to conserve, the young child nevertheless appreciates certain basic identities. For

example, in the standard conservation problem, the young child recognizes that the same liquid is

transferredfromonebeakertoanothereventhoughonelooksquitedifferentfromtheother.Heseesthat

thebasicsubstancedoesnotchange,eventhoughitsappearanceisalteredandeventhoughhefalsely

believesthattheamountofliquidhaschanged.Heappreciatesidentitybutfailstoconservequantity.

Piagetproposesthatthenotionofidentitymayderivefromthechild’sperceptionofhisownbody’s

growth.WithGilbertVoyat,Piagetaskedchildrentodrawthemselveswhentheywerebabies,whenthey

were a little bigger, and so on; then the experimenters questioned the children concerning the

maintenanceof their identitydespiteobviousphysicalchanges.Theexperimentersalsoposedsimilar

questions concerning the identityofotherobjects, includingplants.The results showed that children

easily appreciated their own identity despite changes in size, and were less likely to accept the

continuing identity of a plant over its various changes in appearance. Perhaps, then, the notion of

identity derives from the child’s perception of his ownbody’s growth and later is generalized to the

worldofobjects.

Thepreoperationalchildcanalsoperceivefunctionalrelationsintheenvironment.Oneexample

ofsuchfunctions(givenbySinclair,1971)involvestheopeningofacurtain:“thechildunderstandsthat

whenonepulls thecordofacurtain, thecurtainopens; the fartheronepulls, the farther thecurtain

opens”(p.4).Inotherwords,thereisafunctionalrelation,aco-variationbetweenpullingandopening,

and the child perceives that the two factors are positively related. (Theremay evenbe precursors of

functionsin infancy:thisexampleisreminiscentoftheinfantLaurentwhoseemedtorealizethatthe

morevigorouslyheshookachain,thelouderwouldbethesoundproducedbytheattachedrattles.)Itis

veryimportant,ofcourse,forthechildtorecognizesuchfunctionalrelationsintheenvironment:they

pervadeit.Thetallertheperson,thestrongerheislikelytobe;theharderonehitsanotherchild,the

more likely is the child to protest and even cry; the bigger the glass, themoremilk it holds. Despite

limitations in other areas of thought (for example, centration), the preoperational child has some

appreciation for basic functional relations, and this is of great value to him in coping with the

environment.

At the same time, Piaget points out that these functions are incomplete: they constitute only a


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semilogic.Foronething,thechild’sappreciationoffunctionsisimprecise.Toreturntotheexampleofthe

curtain, thechilddoesnotrealizeexactlyhowthepullingof thecord isrelatedto theopeningof the

curtain and cannot quantify the results with any degree of precision. Another Piagetian experiment

makes this clear. Children were presented with three toy fish, 5, 10, and 15 centimeters long,

respectively,andweretoldtofeedeachfishitsproperdietofmeatballs.Themiddle-sizedfishshouldget

twiceasmanymeatballsasthesmallest,andthelargestfishthreetimesasmany.Preoperationalchildren

understoodthefunctionalrelationbetweensizeof fishandnumberofmeatballsonly inanimprecise

way.Theyrealizedthatthelargerthefish,themoreitneedstoeat.Buttheywerenotabletoworkoutthe

functioninaprecisemanner(forexample,bygiving2,4,and6or3,6,and9meatballstotherespective

fish).

Toward the end of his life, Piaget (1979) stressed the role of “correspondences.” He used this

notiontorefertothechild’stendencytocompareobjectsorevents,todeterminethewaysinwhichthey

“correspond,” or are similar and different. This tendency appears at all levels of development, from

infancyonward,althoughittakesdifferentformsatdifferentlevels.

Forexample,aninfantfirsthitsatoyparrottomakeitswingandthenappliesthehittingschemeto

otherhangingobjectsaswell.Inasensehehascomparedthenewobjectwiththefamiliarparrotand

notedthesimilaritybetweenthem(thecorrespondenceofoneobjecttoanother).

Note:Ablackmarbleandawhitemarblearegluedtoaplate,withthewhiteoneabovetheblack

one(asinFigure12A).Thentheplateisrotatedsothatblackoneisabovethewhiteone(asinFigure

12B).


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FIGURE12CorrespondenceofMarbles.

The preoperational child displays different forms of correspondence. For example, in one

experiment,Piaget(1979)showedchildrentwoobjectsonarotatingdisk.Imaginethattheobjectsarea

whitemarbleandablackmarble,gluedtoadish,as inFigure12A.Whenthemarblesareon the left

(Figure12A),thewhiteisabovetheblack.Whenthedishisrotatedsothatthemarblesareontheright

(Figure12B),thentheblackisabovethewhite.Thepreoperationalchildobservesthesituations—the

marblesontheleftandontheright—andgraduallynotesthecorrespondencesbetweenthem.Thechild

seesthatwhenthemarblesareontheleftside,thewhiteishigher,butwhentheyareontheright,the

whitebecomesthelower.Atfirst,thechild’sapproachissimply“empirical”:torecordthefactswithout

interpreting them. But “the child discovers suddenly that there is a general order” (p. 24). He

determines,inotherwords,thatthereisareversalofposition.It’snotjustthatthewhiteishigherinone

situationandlowerintheother,butthatthewhitehasswitchedpositions.This insight thengradually

leadsthechildtoanother:thepositionswereswitchedbecauseatransformationtookplace.Therotation

ofthedishcausedtheswitchinposition.

We see then that the child begins by comparing two states, noting some basic similarities and

differences(theswitchinposition).Thesecorrespondencesareimportantbecausetheypavethewayfor

thechild’sappreciationoftransformations.Andaswehaveseen,anappreciationoftransformationsisat

theheartofconcreteoperationalthinking.

In brief, preoperational thought is not characterized solely by incompetence. Young children

appreciatecertainbasicaspectsofidentity,perhapsasaresultofexperiencewiththeirownbodies.They


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alsounderstand,albeitinanimprecisemanner,varioussimplefunctionalrelationsintheenvironment.

Theydetectcorrespondences,andthisleadsthemtoanappreciationoftransformations.Indealingwith

youngchildrenonemustbeawareof these strengthsaswell asof the commonly cited limitations, as

GelmanandGallistel(1978)andothercontemporarywritersconcurinmaintaining.

The Concept of Stage

Piaget’s theory describes a sequence of stages. For example, in the case of the conservation of

numberwehavereviewedthetransitionfromcentrationtodecentration.Nowitisimportanttoconsider

thenatureofsuchstages.WhatdoesPiagetmeanbystageandhowusefulaconceptisit?

AccordingtoPiaget(BiologyandKnowledge, 1971a,p. 17) thenotionof stage isusedwhen the

followingthreeconditionsarefulfilled.First,theremustbeaninvariantsequenceofactivities.Thus,in

thecaseofconservation,thereis,first,afailuretorecognizeequivalence;thenthereisvacillation;and,

finally,thereissuccess.Theorderofappearanceoftheactivitiesisthesameforallchildren.Second,each

stageinthesequenceischaracterizedbyanunderlyingstructure,acoresystemdeterminingthechild’s

overt behavior. Thus, underlying the child’s failure to conserve is the strategy of centration—the

tendencytofocusonlimitedamountsofinformation.Third,eachofthestructurespreparesthewayfora

succeedingone.Thus,inthecaseofconservation,theinitialcentrationpreparesthewayforavacillation

amongtheavailabledimensions,andthisinturnleadstothesubsequentdecentration.Inbrief,Piaget

proposes that stages are characterized by invariant sequence, underlying structures, and successive

integrations.

Piagetalsoemphasizedthatdespitetheexistenceofstages,developmentiscontinuous.Thechild

doesnotenteranewstageovernight;instead,thechangesaregradual,andindeedbarelyperceptible

fromclose-up.Piagetexplainedthisintermsofthescaleofmeasurement.Ifwelookcloselyatachild’s

development,observingeverydayandthususinga finescaleofmeasurement, it ishardforustosee

dramaticchanges;fromonedaytothenextwewillnotnoticedifferencesinstages.Butifwestandback,

observing the child infrequentlyand thususinga crude scaleofmeasurement,wewillbe impressed

withchanges;fromoneyeartothenextwewillseeprogressfromonestagetothenext.


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Wehavealreadyreviewedresearchconcerningthenotionsofinvariantsequenceandunderlying

structure. Cross-cultural study demonstrates that the sequence described by Piaget is extremely

widespread,ifnotuniversal.Also,thereseemtobedistinctunderlyingpatternsorstructuresineachof

the major periods under consideration—preoperational and concrete operational. Consider next

Piaget’sthirdconditionfortheexistenceofastage—therequirementthateachstagepreparethewayfor

thenext.Whileitishardtoadduceevidencesupportingthisnotion,itseemstohaveacertainamountof

facevalidity;forexample,afocusontwodimensionsseemsnaturallytofollowfromafocusonone.In

brief, the evidence concerning invariant sequence, underlying structures, and successive integrations

seemstosupportPiaget’spropositionconcerningtheexistenceofmajorstagesofdevelopment.

Atthesametime,thestagenotionsuffersfromanumberofdifficulties.One,alreadyalludedto,is

theexistenceof irregularities indevelopment.Wehaveseen that thechild isnotalways in thesame

stagewithregardtodifferentareasofthought.Thus,hemaybeinstage1withrespecttoclassesand

stage2inthecaseofrelations.Also,thephenomenonofhorizontaldécalageisverystriking:thechildmay

displaydifferentlevelsofachievementinregardtoverysimilarareasofthought.Thus,hemayconserve

substance but not number. The existence of these irregularities seems dissonant with the notion of

distinctunderlyingpatternsorstructuresofthoughtcharacterizingthemajorstagesofdevelopment.If

thepatternsaresostrongandpervasive,whyarethedécalagessostriking?

Anotherdifficultywiththestagenotionisthatthestructurespresumablyunderlyingastagemay

alsobeimplicatedinstagesoccurringearlierinthesequence.ThuswehaverecentevidencebyTrabasso

(1975), for example, to the effect thatunder certain conditions, preoperational children canperform

concreteoperationaltasks.Ifthesamestructuresunderliebehavioratdifferentstages,dowenotthen

have toalterournotionof stages?The issueof stages isextremely complexand isnow the subjectof

considerablerethinking(foranexcellentdiscussionseeFlavell,1985).

Indeed,towardtheendofhislife,Piagetseemstohaverethoughtthestagenotionhimself.Thelast

tenyearsofPiaget’sresearchrevolvedlargelyaroundissuesofcognitivechangeanddevelopmentand

did not employ stage notions to any significant degree. In this sense, Piaget became less of a

“structuralist”(onewhodealswiththeanalysisofmentalstructuresunderlyingthestages)andmoreof

a“functionalist”(onewhodealswiththefactorsdeterminingdevelopment).AsweshallseeinChapter


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6,Piaget’stheoryofequilibrationplacedtheemphasisongradualchangesorineffectonmanyfleeting

substages.WhatwasimportantforthelaterPiagetwasnotaconceptofbroad,stablestages,butatheory

ofthecontinuouschangeanddevelopmentofthechild’sintellectualstructures.

MENTAL IMAGERY

Afterhisbriefexaminationduringthe1920softhecontentofthought,Piaget’smainconcernhas

beenwiththeoperativeaspectofcognition.Thisreferstoactionsusedtodealwithorevenchangethe

world. These actions may be either overt or internal. Examples of overt actions abound in the

sensorimotorperiod.Theinfantkickstoshakearattle,orusesasticktodrawanobjectclose.Thepresent

chapterhascoveredtwomajorsubdivisionsofinternalizedactions:theisolatedandunrelatedactionsof

preoperationalthoughtandthestructuredandcoordinatedonesofconcreteoperationalthought.

Piaget has also shown an interest, albeit a lesser one, in the figurative aspect of cognition. This

referstothreewaysinwhichthechildproducesanaccountofreality.Oneisperception,asystemwhich

functionsbymeansofthesensesandoperatesonanimmediatelypresentobjectorevent.Itisthrough

perceptionthatthechildachievesarecordofthethingsinthesurroundingworld.Thisrecordisoften

inexact, as in the case of the visual illusions. A second subdivision is imitation, by which the child

reproducestheactionsofpersonsorthings. It is truethat imitation involvesactionsonthepartof the

child,buttheseactionsneverthelessfallunderthefigurativeaspectsincetheyproduceacopyofreality

butdonotmodifyit.Athirdportionofthefigurativeaspectismentalimagery.AswesawinChapter3,

mentalimageryreferstopersonalandidiosyncraticinternaleventswhichstandfororrepresentabsent

objectsorevents.Whenwe“picture”toourselvesourfirstbicycle,orthestrollwetooklastweek,thenwe

areusingmentalimagery.Asweseefromthislastexample,thetopicofmemoryiscloselyboundupwith

thefigurativeaspectofthought.Memory(recall)typicallyinvolvesretainingknowledgegainedthrough

thefigurativemode.

In recent years, Piaget has conducted important investigations into two important aspects of

figurative cognition, specifically imagery and memory. His theory stands in stark contrast to the

traditionalempiricistviewofthesematters.Thelatterassumesthatperceptionstampsontheindividual

a literal copy of reality. Given sufficiently frequent repetition of the initial event, a mental image


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mirroring the reality is formed and is stored in memory. If there is no further experience with the

originalevent,thememoryimagegraduallyfades,losingitsfidelitytothereality;itisforgotten.Piaget

criticizesthistraditionalviewonseveralgrounds.Mostimportant,hebelievethatrealitydoesnotsimply

imposeitselfonapassiveorganism.Rathertheindividualassistsintheconstructionofhisownreality.

Hisintellectualactivities—theoperativemodeofthought—servetoshapetheresultsofencounterswith

theenvironment.The resulting figurativeknowledge isnot simplya copyof reality.This theme—the

influence of operative structures on figurative knowledge—dominates Piaget’s discussion of mental

imageryandmemory.Wewillnowconsiderthesetwotopicsinsuccession.

History

Mentalimagerywasoneofthefirsttopicsstudiedbyexperimentalpsychologists.Attheendofthe

nineteenthcentury,theschoolofWundtusedtheintrospectivemethodtoanalyzethenatureofmental

imagery.TheWundtiansbelievedthatimageswerecomposedofabundleofsensationstiedtogetherby

meansofassociation.Atthebeginningofthetwentiethcentury,thestudyofimageryfellintodisrepute

fortworeasons.First,theWurzburgpsychologistsfoundthatmuchofthoughtdidnotseemtoinvolve

imageryatall,andsecond,thebehavioristrevolutionwhichoccurredintheUnitedStatesmaintained

thattheintrospectivemethodwasapoorone.Thebehavioristsfeltthatthedataofintrospection—one’s

impressions of one’s own consciousness—were not public enough. How could another psychologist

determine if an introspectionwere reliable and accurate?As a result of the behaviorist attack on the

methodofintrospection,thestudyofimagerywasconsidered“unscientific”andwaslargelyabandoned.

Recently,however,psychologistshaveshownarenewedinterestintheancientproblemofimagery,and

thetopicisonceagainbecomingcentraltoexperimentalpsychology(Neisser,1976).

Incontrasttomoderninvestigators,Piagethasbeenstudyingimagerysinceatleastthe1930s.In

Chapter3wediscussedPiaget’sworkonimageryintheyoungchilduptotheageof4years.Ifyouwill

recall,thistheoryproposedthatmentalimagesdonotoccuruntilaboutthemiddleofthesecondyear.

Before this timethechilddidnotpossessmentalrepresentationsof theenvironmentand,asaresult,

reactedmainly to events occurring in the present. After imagerymakes its appearance the child can

represent tohimselfbothevents thatoccurred in thepastandobjects thatareno longerperceptually

present. Also, according to Piaget’s theory, imagery results from imitation. At first, the child overtly


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imitatestheactionsofthingsorpeople; later,hisimitationbecomesinternalizedandabbreviated.It is

through this internalactivity that imagesarise.Clearly,Piaget’sviewscontrast stronglywithWundt’s.

Imagesarenotmerelybundlesofsensations,imposedbytheenvironmentandconnectedbyassociation;

rather,theconstructionofimagesinvolvestheactivityofinternalizedimitation.

Later,with Inhelder, Piaget returned to the studyof imagery (1971).His laterworkdealswith

childrenabovetheageof4,andposesanumberofinterestingquestions.Forexample,aretheredifferent

typesof imagesatdifferentstagesof intellectualdevelopment? If so,what is therelationbetweenthe

imagesandthementaloperationsofagivenstage?

Method

Whilethesequestionsareinteresting,thestudyofmentalimagesisverydifficult,especiallyinthe

caseofchildren.Imagesarepersonal,idiosyncraticeventswhichcannotbevieweddirectly.Onecannot

“see”anotherperson’simagery;theinvestigatormust,therefore, infertheirexistenceandnaturefrom

otherphenomena,suchasaverbalreport.Piagethasusedavarietyofmethodstostudyimagery.Oneof

thesemethodsistoaskapersontodescribehisownimages.Butlanguageisnotfullyadequateforthis

task,orevenfordescribingsomethingasconcreteastheimmediateperceptionofanobject.Wearenever

able to convey bywords the precise nature of whatwe see. In our attempt to describe percepts, we

inevitably emphasize certain features and neglect others.We have difficulty in describing shades of

colors,orgradationsof textures.Wecannotgivean impressionof theentireperceptatonce,butmust

describeitsdetails insequence,andtherebyoftenlosetheessenceofthewhole.If languagesopoorly

conveysperceptualeventswhichcontinuetoremainbeforeoureyesforfurtherinspection,howmuch

moredifficultisittodescribementalimageswhichoftenarefleetingandunstable?

Anothermethodof studyingmental images isbydrawing.Here theperson is asked todrawan

objectpreviouslypresented.Sincetheobjectisnolongerpresent,hemustproduceanimageofittoyield

the drawing. The drawing, therefore, gives some insight into the nature of the image, which is the

internal “picture” of the object. The method of drawing, however, presents several shortcomings.

Drawingisnotasimpleanddirectreflectionofimages; italsoinvolvesotherprocesses.Somepersons

havepoormemory.Iftheyhaveforgottentheirimageofanobject,theycannotverywelldrawit.Other


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personssimplycannotdrawwell.Itisnottheirimagethatisatfault,buttheirartisticskill.

A thirdmethodattempts tobypass theshortcomingsoforiginaldrawings.Thesubject isgivena

collection of drawings made by the experimenter, and must select from them the one most closely

correspondingtohisimageofwhathehadpreviouslyobserved.Thismethod,ofcourse,isnotaffectedby

variationsinsubjects’artisticabilitiesandreducesthedifficultiescreatedbyapoorevocativememory.

Buteventhemethodofselectionfromacollectionofdrawingsisnotaltogethersatisfactory.Oneproblem

is that the drawings presented are not likely to be exact copies of the person’s mental image. The

drawingsmayomitdetailsoftheoriginalimageoraddnewfeatures.Ineitherevent,thesubject’schoice

doesnotgiveafullyaccurateindicationofhisimage.

To study imagery, Piaget has used all thesemethods—verbal report, drawing, and selection of

drawings—either alone or in combination. As is customary with the explorations carried out by the

Genevaschool,themethodsweresupplementedbyverbalquestioningcarriedoutintheclinicalmanner.

Major Findings

One experiment was concerned with kinetic images, or the imagery of an object’s movement.

Childrenfromabout4to8yearsofagewerepresentedwithtwoidenticalblocks,oneontopoftheother

(seeFigure13A).Eachsubjectwasaskedtodrawthesituation,andgenerallydidthisquitewell.Then

thetopblockwasmovedsothatitslightlyoverlappedthebottomone,asinFigure13B.Afterthechild

hadhadachancetolookatthisforawhile,thetopblockwasreturnedtoitsoriginalposition(Figure

13A).Thechildwasthenaskedtodrawtheblockinitsdisplacedposition(Figure13B),whichwas,of

course, no longer visible. After this, a collection of drawingswas presented. This contained a correct

rendering of Figure 13B as well as an assortment of incorrect drawings which represented errors

typicallymadebychildrenofthisage.(Thistechniqueissimilartotheuseofcountersuggestionsinthe

interview.)Thechildwasaskedtoselectthedrawingwhichhefeltcorrespondedmostcloselytowhathe

hadseen.Inthefinalstepanothercontrolwasadded.Thetopblockwasonceagaindisplaced,andthe

childwasaskedtodrawthesituationwhileitwaspresent.Ifthechildcouldaccuratelydrawtheblocks

whenpresent,thenanyofhispreviouserrorsofdrawing(whentheblockswereabsent)mustbedueto

faultyimageryormemoryandnottofaultydrawingability.


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FIGURE13Movementofblocks.

Tosummarize,thechildFirstdrewthedisplacedblocksaftertheywerenolongervisible;thenhe

selectedfromagroupofdrawingsoneresemblingthedisplacedblocks;andfinally,whenthedisplaced

blockswereonceagainbeforehim,hedrewthem.

The findings show that before the age of 7 years, children candraw the displacedblocks quite

correctlywhentheyarepresent,butnotwhentheyareabsent;norcanthechildrenchooseadrawing

whichcorrespondstothesituation.Ingeneral,childrenofabout4and5yearsproducedandselected

drawingsofthetypesAthroughE(seeFigure14),whereaschildrenof6yearsmadeerrorslikethoseof

typesFandG.Itwasonlyat7yearsthatover75percentofthesubjectsbothdrewandchosethecorrect

drawings.

FIGURE14Drawingofblocks.

Across-culturalstudyofthisprobleminThailand(Opper,1971)showsthatThaichildrenmake

thesametypesoferrorsasdoSwisschildren,althoughitisnotuntil10yearsofagethat75percentof

theThaisubjectsmakecorrectdrawingsofthetwoblocks.

The responses of the younger child would seem to indicate that he forms only a very general

pictureofthesituation,thatis,thatoneblockhasbeenmoved.Whenaskedtodrawtheexactdetails,heis

unabletodoso.Thechildthereforereproducesthisgeneralimpressionofmovementbydetachingthe

topblockfromthebottom(cf.C),byasymmetricalmovementofshrinkingorenlargementofoneofthe


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twoblocks(cf.DandE),or,finally,bytheretentionofonecommonboundaryoridenticallineforthetwo

blocks, inadditiontomakingchangesontheothersideof theblocks(cf.FandG).His imagedoesnot

appeartocorrespondtotheactualsituation.Thechildseemstocenterononedimension,thatis,onone

particularaspectofthesituation—forexample,theoverlappingofthetopblockindrawingsEandF,or

theoverlappingof thebottomblock indrawingsDandG.However, thechilddoesnotcoordinate the

movementofoneblockwiththefinalstateofthetwoblocks.Apparentlythechilddoesnotanalyzethe

situationinsufficientdetailbutmerelyformsaglobalimpressionofwhathashappened.Heisawarethat

theblockhasmoved,but the intimatedetailsof themovementandtheensuingdisplacementseemto

haveescapedhisattention.Asaresult,hismentalimageisinadequate.

A second typeof imagery is static imagery. In this instance the image reproduces a collectionof

objects,ascene,orapicture—inbrief,anysituationinwhichtheelementsremainunchangedineither

shape or position. Piaget finds that the child is able to produce adequate static imagery earlier than

kinetic.

We have reviewed only a small sampling of Piaget’s experiments on imagery. Their results,

together with those of a great many more studies, have led Piaget to draw the following general

conclusionsconcerningimageryanditsrelationtointelligenceasawhole.First,imagerydevelopsina

gradualmanner.Theevolutionofimageryisnotasdramaticasthatofthecognitiveoperationswhich

display a clear-cut sequence of stages. There appears to be only one major turning point in the

developmentof images.Thisseemstooccurataroundtheageof7or8yearsandcorresponds to the

onsetoftheperiodofconcreteoperations.Beforethebreak,thatis,fromtheageof11/2toabout7years,

thechildseemscapableofproducingwithanydegreeofaccuracyonlystaticimages,andeventheseare

farfromperfect.Thechildcannotrepresentcorrectlythemovementsofanobjectorevensimplephysical

transformations;theimagesproducedforsuchsituationsaregrosslydeformed.

Piagetbelieves that thereason for thisdeficiency isoneaspectofoperativecognition,namely,a

tendencytoconcentrateontheinitialandfinalstatesofagivensituationandtoneglecttheintervening

events which are responsible for the changes. We have already seen this tendency, which is called

centration, operating in the case of conservation. If youwill, recall the situationwhere the childwas

presentedwitha lineofvases,eachofwhichcontainedaflower.Theflowerswereremovedfromthe


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vasesandspreadapart.Whenthisoccurs,theyoungchildusuallybelievesthattherearemoreflowers

thanvases,sincethelineofflowersisnowlongerthanthelineofvases.Hehascenteredonthelengths

andignoredanumberofotherfactors.Hehasfailedtodecenterandtoconsiderthedensityofthelines,

aswellastheirlength,andhehasignoredtheintermediarytransformation(theremovalandspacingof

theflowers).Thus,thechildfocusesmainlyontheinitialandfinalstates(theflowersinthevasesand

the flowersspacedout)and fails to integrate these impressionswithallelse thathasoccurred.Thus,

beforetheageof7or8imageryisextremelystatic.Asaresult,thechildproducesadistortedpictureof

realitycharacterizedbyanemphasisonsuperficialfeatureswhichareeachisolatedfromothersandnot

coordinatedintoacoherentwhole.

Fromabout theageof7yearsonward,however, thechildbecomescapableofproducing images

whichcanreproducekineticsituations.Thisimprovementisduetothefactthathecannowimaginenot

onlytheinitialandfinalstates,butalsotheintermediarytransformations.Hisimageryhasbecomeless

static.Ofcourse,itisneverpossibletoreproducealltheinterveningevents,sinceinsomecases(likethe

pouringofliquid),theyoccurrapidly.Butthechildrecognizesthatasequenceisinvolvedandthatthere

hasbeenaseriesofinterveningstepsbetweentheinitialandfinalstates.

Afinalquestionconcernstherelationbetweendynamicimagesandtheconcreteoperations.Kinetic

imagesoccuratapproximatelythesametimethatthechildbecomescapableoftheconcreteoperations;

whatthenistherelationbetweentheoperativeandfigurativeaspectsofthoughtatthisstage?Onthe

onehand,wehavealreadyseenthatoperativecognitioninfluencesthenatureofthechild’s imagery.

Thus,theconcreteoperationalchild’sdecentrationcontributestothedynamicnatureofhisimagery.In

Piaget’s theory, figurative cognition (here, imagery) is dominated by operative cognition (here, the

concrete operations).On the other hand, images canplay an auxiliary role in thinking. For example,

considerthenumberconservationtaskinvolvingflowersandvases.Theconcreteoperationalchildcan

formaccuratetransformational imagesofthedisplacementoftheflowers.Afterthetransformationhas

beendone,hecorrectlypicturesthewayinwhichtheflowershavebeenremovedfromthevases.The

ability to form imagesof this sortdoesnotguarantee that the child can conservenumber; aswehave

alreadyseen,theprocessesunderlyingconservationarenotsolelyperceptualorimaginal.Nevertheless,

thechildwhohasacorrectimageofthetransformationiscertainlyaheadofthechildwhodoesnot.In

otherwords, images are a useful andnecessary auxiliary to thought during the concrete operational


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stage. By providing relatively accurate representations of the world, images assist the process of

reasoningalthoughtheydonotcauseit.


Images represent absent objects or events. They are “symbols,” in the sense of bearing some

resemblance to the object represented, and are personal and idiosyncratic. Images do not give as

completeanddetailedareproductionoftheobjectasisprovidedbydirectperception.Imagesfirstmake

theirappearancearoundthemiddleofthesecondyearoflife,andtheyarisefromaprocessofimitation

whichgraduallybecomesinternalized.Untiltheageofapproximately7years,thechildisonlyableto

produceapproximatelycorrectmentalimagesofstaticsituations.Heconcentratesonstatesratherthan

ontransformations.Thelimitedimageryofthechildispartlytheresultofimmatureoperativestructures.

Asthesestructuresdevelop,sodoeshisimagery.Aftertheageofabout7years,thechildbecomescapable

ofcorrectkineticimagery.Thisnewabilitypermitsafurtherunderstandingofreality:thechildnowhas

availableamoreaccurateanddetailedrenderingoftheeventsonwhichtofocushisreasoning.

MEMORY

Memory,too,isinfluencedbyoperativecognition.Beforeexploringthis,itisnecessarytobeginby

clarifyingsometerminology.

Definitions

Inordinarylanguage,weusethewords“memory”or“remember”inseveraldifferentsenses.Here

isananecdotetoillustratethepoint.Anadulthasnotriddenabicyclesincechildhood,someyearsago.

Nowhis own child gets a bicycle and askswhether the adult “remembers” how to ride. “Of course, I

rememberhow to rideabicycle,” says theadult.Asked (skeptically) toprove it, theadult geton, and

pedals around a bit. Despite the lack of practice over a long period of time, he is able to ride very

smoothly,muchtothesurpriseofthechildwhoownsthebicycleandwhonowwonderswhetherhewill

gettorideit.Astheadultispedalingdownthestreet,he“remembers”ridingthebicyclewhichheowned

asachild.Hehasafairlyclearmentalpictureofitsoverallshapeandform,aswellastheplacesinwhich


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herode.

This example illustrates two very different kinds of “memory.” In the first kind, the adult

remembers how to do something. Although there has beennopractice formany years, he hasnot lost

general bicycle-riding skills. He “remembers” how to ride not just a specific bicycle, but any bicycle.

Through experience, he has acquired a physical skill of a general nature, and remembers it. In this

instance,weusethetermmemorytoindicatethatthepaststillexertsaninfluenceonthepresent.The

adult’s ability to ride a bicycle, acquired through a set of earlier learning experiences,was somehow

preserved within him. Note that after childhood this ability existed as a potential, since until this

incident hedidnot actually engage in thebehavior.Note, too, that the element of earlier learning is

crucialtothedefinition.Itwouldnotmakesensetosay,“Irememberhowtosneeze,”sincesneezingwas

neverlearned.Yetitwouldmakesensetosay, ‘‘Irememberhowtokeepfromsneezing”sincethatwas

learned.Inbrief,thisisonevaliduseofmemory:apersoncanretain,overaperiodoftime,abehavioral

potentialwhichistheresultofpreviouslearning.

Theothersenseofmemory isquitedifferent.When theadult ‘‘remembers”ridinghischildhood

bicycle,heisreferringtoaspecificeventandthinginthepast.Hehasaholdonaparticularsliceofhis

own history. He ‘‘remembers” a bicycle with wide tires, and a heavy frame—a Schwinn, in fact. He

remembers riding it up Commonwealth Avenue to a park with a certain kind of path. This kind of

memoryismorespecificandconcretethanthefirst.Inthiskindofremembering,theadultretainsspecific

eventsorthingsfromthepast;intheotherkindofremembering,hepreservesthegeneralskillsacquired

in the past. Often the two types of memory occur together. A person remembers how to type (thus

preservingthegeneralability)andalsoremembersthespecifictypewriterusedinhisearlylessons(thus

retaininginformationconcerningaspecificthingfromthepast).Butthetwotypesofmemorydonothave

tocoexist.Apersonmayrememberhowtotypeandyetmayhavetotallyforgottenthespecifictypewriter

orhisearlylessons.Similarly,apersonmayrememberthetypewriterandlessons,butnotrememberhow

totype.Thus,wehaveusedsomeexamplesofphysicalskillstoillustrateadistinctionbetweentwotypes

ofmemory.

In the intellectual domain, Piaget’s theory (Piaget and Inhelder,Memory and Intelligence,MEM,

1973)proposesasimilardistinctionbetween“memoryinthewidersense”and“memoryinthespecific


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sense.”Theformerrefersto“theconservationoftheentirepast,oratleastofeverythinginthesubject’s

pastthatservestoinformhispresentactionorunderstanding”(MEM,p.1).Moreprecisely,memoryin

thewidersensereferstothe“conservationofschemes,”totheretentionofacquiredpatternsofbehavior

orthought,liketheconcreteoperations.Bycontrast,memoryinthespecificsense“refersexplicitlytothe

past,” to specific eventsor thingsorpersons in an individual’shistory.Anotherwayof lookingat the

distinctionistosaythatmemoryinthewidersenseinvolvestheoperativeaspectofthought:itistheway

inwhichgeneraloperationsorwaysofdoing thingsarepreservedover time.Memory in the specific

senseisgenerallyfigurative: itpreserves information concerning specific things—a face, anobject, an

activity. (These “things” include actions, but only specific actions that are thought to have actually

occurred,notthepotentialforactionsofageneraltype.)

Piagetgoesontoproposesomefurtherdistinctionsconcerningmemoryinthespecificsense.This

typeofmemory—andweshallnowsimplyusethewordmemorytorefertoit—maytakeoneofseveral

forms.Perhapsthemostprimitiveisrecognition.Thisoccurswhenapersonencountersthings(anevent,

person, thing, etc.)previously experiencedand “has the impressionofhavingperceived thembefore

(rightlyorwrongly,fortherearefalserecognitions)”{MEM,p.5).Thus,weseesomeoneknownbefore,

and“saytoourselves”thatthepersonisfamiliar,eventhoughhisnamemayeludeusandwecannot

recallwhereweknewhim.Similarly,thebabyinthesensorimotorperiodrecognizesfacesandplaces

whentheyareencountered.Orthebabyshowsthroughhisabbreviatedschemesthatherecognizesatoy

he has played with. Recognition, then, is one form of (specific) memory, involving an impression of

familiarityuponanencounterwithapreviouslyexperiencedobject.

Recall isamuchmoresophisticatedanddifficultformofmemory.Itinvolvesproducingamental

account of a previously experienced thing in the total absence of that thing. One examplewould be

remembering your childhood bicycle or your first grade teacher.Recall sometimes involves a mental

picture,sometimeswords,sometimesanodor.Thecrucialaspectofrecallisthattheindividualproduces

some kind ofmental representation of the previously experienced event.7 It is evident that recall is

closely linkedwith the semiotic function, alreadydiscussed, since the latter involves the formationof

mentalrepresentationsforabsentthingsorevents.


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The General Hypothesis

Piaget’smaininterestisinthefunctioningofmemoryinthespecificsense—recognitionandrecall.

Howdoesspecificmemoryoperate?

According to some empiricist views, memory works in the following manner. An individual

perceivesanobjectandstoreswithinhimitsreplicaortrace.Themorefrequentlyorrecentlytheobjectis

perceived,thestrongerthetrace,andhencethestrongerandmoreaccuratethememory.Inthisclassic

view,memoryissimplyacopyofsomethingreal,andtheaccuracyofthecopydependsonsuchfactorsas

frequency,recency,andthe like.Notethat intheclassicview,theindividual ismainlypassive:things

imposethemselvesonhim;theymakeanimpressiononhim;theyformatraceinhimasapieceofchalk

leavesarecordonaslate(hencetheexpressiontabularasa,orblankslate).8

Piaget’sview isdifferent.Heproposes that the childdoesnot simply record reality inapassive

manner,storingacopyinthewarehouseofmemory.Instead,asPiagetseesit,thechildassimilatesand

interpretsreality,sothatmemoryisinpartafunctionofthechild’sintellectualoperations.Memorystems

notonlyfromexperiencebutfromintelligence.This,then,isthegeneralhypothesiswithwhichPiaget

beginshisempirical investigations.Giventhis theoretical framework,Piagetgoesonto investigate the

specificwaysinwhichmentaloperationsaffectmemory,especiallyrecall.

Experiments on Memory of a Series

Tostudytheinfluenceofknowingonremembering,Piagetconductedseveralexperiments,oneof

whichinvolvedmemoryforaseries,atopicalreadyreviewedinthischapter.Childrenofvariousages

wereshowntenwoodensticks,alreadyarrangedinacompleteseries,fromsmallesttolargest.Eachchild

was“toldtotakeagoodlookatitandrememberwhathehasseen.’’Thenaboutaweeklater,eachchild

wasaskedtorecalltheseriesbydrawingitorbytracingitoutwithhisfingersonthetable.Afterthis,the

experimenterdeterminedthechild’sstageofdevelopmentwithrespecttoseriationbygivinghimthe

usualtests.Theexperimenteralsoobtainedacheckonthechild’sdrawingabilitybyhavinghimcopya

seriesofsticksavailabletodirectperception.Thiscopycouldthenbecomparedwiththechild’sdrawing

frommemorytodetermineifdistortionsinthelatterstemfrommeredrawingdeficiencies.Inbrief,the

experiment involved (1) determining children’s intellectual level with respect to seriation, (2)


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presentingthemwithacompletedseriestoremember,and(3)measuringrecallbyfingertracingand

drawing.Furthermore,(4)ameasureofdrawingabilitywastakensothatthisfactorcouldbecontrolled.

Whatshouldhappen insuchanexperiment?According to theclassicview, theseries impresses

itselfonthepassivesubject,andtheaccuracyofrecalldependsontheextentofthesubject’sexperience

with it and on similar factors. The child’s drawings should to some degreemirror the realitywhich

impinges on him. Piaget’s view is much different: the child actively assimilates the reality into his

intellectualsystemandthisprocessofinterpretationdeterminesthenatureandqualityofrecall.Inthe

presentinstance,astage1childmaydistorthismemoryoftheseriesinaccordancewithhisimmature

intellectualoperations,andthiswillbereflectedinhisdrawingandtracing.Notethattheresultofthisis

notadrawingwhichissimplyapalecopyofthereality.Rather,itisadrawingwhichissystematically

distortedinlinewiththechild’sintellectualoperations.


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FIGURE15Drawingsofcompletedseries.

Consider a few examples of this. One childmade a drawing like that in Figure 15A, involving

several identical long lines and several identical short ones. This drawingwas similar to the child’s

actual arrangement of the sticks during the test of seriation: hemade one bunch of large sticks and


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anotherbunchofsmallsticks,butdidnotaccuratelyseriatewithineachbunch.Anotherchildproduceda

drawinglikethatinFigure15B.This,too,wassimilartohisactualarrangementofthesticks.Hemadethe

topsofthesticksincreaseinorderofsize,buttotallyignoredthebottoms.(Whenaskedtocopyawell-

formedseriesimmediatelyinfrontofthem,thesesamechildrenproducedfarmoreaccuratedrawings.

Thisallowsustoconcludethatdrawingskillinitselfisnotatissue.)Bycontrast,childreninstage3who

couldaccuratelyseriatewereaccurateinrecall,asindicatedbyveridicaldrawingsandtracings.

ThesefindingscanbetakentosupportPiaget’stheory.Theindividual’smemoryisinfluencedand

organizedtosomedegreebyhisintellectualoperations.Thechildrecallsnotwhathehasseenbutwhathe

knows.Inthepresentinstance,stage1children’srecallisdistortedbytheirimmatureseriationschemes.

(Weshallseecaseslaterwheretheeffectisofadifferentsort.)Atthesametime,Piagetpointsoutthatthe

resultsarenotentirelyclear-cut.Somestage1childrenmakeperfectlyaccuratedrawings.Theirmental

operationsdonotseemtointervenesoforcefullyintheactofrecall. Insteadtheyseemtofocusonthe

appearanceoftheseries—onits“figurativeaspects”—andmanagetorecall itverywell,muchasthey

wouldrecall(anddraw)acircleoratreeorastaircase.Itishardtoexplainwhysomestage1children

showthedistortingeffectsofintellectualoperationswhileothersdonot.

In brief, while there is some variability, the results show that intelligence—the intellectual

operations—structures the child’s recall. Knowledge interacts with perception to produce what is

remembered.

The Development of Memory

According toPiaget, there is a generaldevelopmentalprogression from theearly appearanceof

accurate recognition to the later use of accurate recall.Memory begins in a crude fashion during the

sensorimotorperiod.Atthistime,theinfantshowsevidenceofrecognition.Throughovertorabbreviated

behavior,hedemonstratesthatatoyorapersonisfamiliar.Theinfantdoesnotseemcapableofmore

demandingformsofmemory,especiallyrecall(thisofcourseinvolvesevokingamentalrepresentationof

absentobjectsorevents).Itisonlywiththeonsetofthesemioticfunction,atabout18months,thatthe

childbecomescapableofmentalrepresentationandhencerecall.Earlier,inanothercontext,wecitedthe

exampleofJacqueline,at1;11(11),whouponreturningfromatrip,wasabletoreportoneventswhich


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hadoccurredearlier:“Robertcry,duckswiminlake,goneaway”(Play,Dreams,andImitation,p.222).

Thisisanexampleofrecallinachildwhoisjustbeginningtogiveevidenceoftheuseofthesemiotic

function.Inbrief,infantsshowsignsofrecognitionmemory,whereasrecall,asoneaspectofthesemiotic

function,beginstoappearonlyatabout18months.

Aswehaveseen,oncerecallappears,itsfunctioningisinfluencedbytheintellectualoperations.

Nowweshallseethatthisinfluencecanhavedevelopmentalaspects.Piaget’sexperimentsonmemory

foraseriesshedlightonthisissue.Wealreadyknowthatthechild’srecallafteroneweekisdistortedin

linewithhiscurrentstageofseriation.Butwhathappenstorecalloveralongerperiodoftime,say,sixto

eightmonths?Accordingtotheclassicview,thememorytracesimplyfades,andthisfadingbecomesmore

completeastimegoeson.InPiaget’sview,mattersaremorecomplexthanthat.Inmanycases,theremay

wellbesomedeteriorationofmemoryoveralongperiodoftime.Andyetthereareotherpossibilitiesas

well. Memory, which depends on intelligence, therefore exhibits developmental changes which

correspondtothedevelopmentofintelligence.Indeed,Piaget’stheoryleadstothepredictionthatunder

certaincircumstances,recallmayactuallyimproveovertime.

Inthecaseofseriation,thematterworksasfollows:thestage1childseesawell-orderedseriesand

assimilates it into his intellectual operations. Since these are immature, one week later the child

inaccuratelyrecallsthesticksasacollectionofsmallonesandacollectionoflargeones.Hisintelligence

hasorganizedrecallpoorly.Thenoveraperiodoftime,thechild’smentaloperationsdevelopandhe

enters stage 3. Now, asked to recall the sticks, he remembers a well-formed series. His memory has

improvedovertimebecausehisintellectualstructureshavedevelopedmorefully.

This is indeed precisely the result which Piaget discovered. Of twenty-four stage 1 children,

twenty-twoshowed improvedrecall (asmeasuredbydrawings)when theyadvanced toa later stage

sevenoreightmonthsaftertheinitialtesting.

Severalcommentsshouldbemadeatthispoint.First,independentinvestigatorshavehadahard

timereplicatingthisresult(forexample,Samuels,1976).Agooddealofcarefulresearch,withadequate

controls,needstobedonetopindowntheeffect.Itisparticularlyimportanttoobtaindirectmeasuresof

thechild’sassumed intellectualdevelopment.Second, it is important torecognize thatPiaget’s theory


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doesnotalwayspredictimprovementinlong-termrecall.Improvementcanbeexpectedtooccuronlyif

theinitialrecallwasdistortedbyimmatureintellectualoperationsandiftheseoperationssubsequently

improve.This isaveryspecialcase,however,andoftendoesnotoccur.Forexample, supposeachild

learns someone’snameand tries to recall it ayear later.Memory for thename is likely todeteriorate

regardlessof the child’s stageofdevelopment.The child’s advancement fromstage1 to3of concrete

operationswillhavenoparticularbearingontherecallofnames,sincetherecall ismerely figurative

withnologicaloperationsinvolved.Hereisanotherexample,whichmayseemparadoxical.Supposea

stage1childisshownabadlyformedseries.Afteroneweekheaccuratelyremembersthebadlyformed

seriesbecausehehasassimilateditintohisimmaturementaloperations.Then,overthenextyear,the

child’smentaloperationsadvanceandhehasreachedstage3.Nowwhenaskedtorecallthesticks,he

producesawell-formedserieswhichistheproductofhiscurrentintellectualstructure.Unfortunately,

this is inaccurate recall, since the initial series was badly formed. This example is a case of an

improvement in intellectualstatus leadingtoadeterioration inrecall. (SeveralstudiescitedbyLiben,

1977,actuallyobtainthiskindofresult.)ThemainpointofPiaget’stheoryisnotthatmemorynecessarily

improves over time—it seldom does— but that memory is influenced by developing intellectual

operations,andnotjustbyrealevents.

Summary

Piaget distinguishes between two types of memory. Memory in the wider sense refers to the

individual’sabilitytoretainovertimethepotentialtoexhibitlearnedschemesoroperations.Memoryin

thespecificsensereferstotheindividual’sabilitytoretainovertimeinformationconcerningparticular

events,things,orpersons.Specificmemorymaytakeoneofseveralforms,themostimportantofwhich

arerecognition(animpressionoffamiliarityonanencounterwithapreviouslyexperiencedobject)and

recall(evocationofthepastthroughmentalrepresentations).Piaget’sgeneralhypothesisisthatspecific

memory is influencedby intelligence—the intellectualoperations. Intelligenceserves toorganizeand

shape memory. Piaget rejects the classic view in which events are seen to impress themselves on a

passiveobserver,leavingatraceorasimplecopyofthereality.

Piaget’sexperimentsonmemoryforaseriesdemonstratethatafteroneweek,recallisinfluenced

bytheindividual’sstageofintellectualdevelopment.Presentedwithawell-formedseries,somechildren


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recallnotwhattheyhaveseen,butwhattheyknowabouttheseries.Itisimportanttonote,however,that

there is some variability in these results. According to Piaget, there is a general developmental

progressionfromrecognitionmemorytorecall.Infantsshowsignsofrecognition;recalldoesnotseemto

appearuntiltheonsetofthesemioticfunctionatabout18months.

After it appears, recall is influenced by the development of intellectual structures. The general

hypothesisstatesthatasintellectualstructuresdevelop,theyexertcorrespondingdevelopmentaleffects

onrecall.Indeed,undercertaincircumstances,recallmayactuallyimproveovertime.Piagethasshown

thatinthecaseofseriation,recallbecomesmoreaccurateaschildrenadvancefromoneintellectualstage

to the next. It is important to note, however, that this result is not easily replicated and that Piaget’s

theorydoesnotalwayspredictimprovementinrecallovertime.Instead,themainpointofPiaget’stheory

is thatmemory is influencedandorganized(butnotnecessarily improved)bydeveloping intellectual

operations, and not simply by real events. Memory is the result of an interaction been knower and

known.

CONSCIOUSNESS

Wehaveseenhowthechilddevelopsoperativeandfigurativeaspectsofthought.Bytheageof7or

8years,heachievessomesuccessatclassifyingandorderingobjects,atproducingmentalimages,andat

remembering.Thesecognitiveprocesses,bothfigurativeandoperative,workmainlyonanunconscious

level.NowwewillassumeadifferentlevelofanalysistoconsideranewtopicwhichPiagethasrecently

studied,namely,thechild’sawarenessandverbalizationofhisownthoughtprocesses.

In studying the issueof consciousness,Piaget’s general strategy is first tohave the child solvea

problemandsecondtodeterminehisawarenessofthemethodsofsolution(TheGraspofConsciousness,

GC,1976b).Inoneinvestigation,Piagetusedstandardseriationtasks,involvingsuchmaterialsasasetof

cardsvaryinginheightandwidth,orasetofbarrelsvaryinginbothheightanddiameter.Eachchild’s

taskwastoarrangetheobjectsinorderofincreasing(ordecreasing)size.Hewastold,forexample,to

“makeanicelineofbarrels.”Assoonasthechildbegantodothis,theinvestigatoraskedhimtodescribe

whathewasdoingorwasabouttodo.Sometimesthechildwasasked“howhewouldexplaintoafriend

whatshouldbedone”(GC,p.3OI).Afterthechildcompletedthefirstseries(successfulornot),hewas


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askedtorepeatitandtodescribeandexplainhisactionsashewentalong.Thepurposeofthisrepetition

wastoensurethatthechildknewwhatwasexpectedofhim.

Suppose that a child succeeds at the seriation tasks just described: he produces an accurate

orderingintermsoflengthoftherodsorsizeofthebarrels.Giventhis,wemayinquireintothechild’s

consciousnessorcognizanceofseriation. It is important tobeginbyclarifyingwhat ismeantbyPiaget’s

usageofconsciousnessorcognizance.Piagetuses these termstorefer to thechild’sability toproducea

coherentverbalaccountofthementalprocessesunderlyinghisbehavior.Bythisdefinition,thechildis

consciousorcognizantofhisthoughtprocessesifhesays,forexample,“Ialwayslookforthebiggestone,

then I put it aside and look for the biggest one out of all the ones that are left.” In Piaget’s usage,

consciousnessreferstoanawarenessandverbalizationofone’sownthoughtprocesses.Notonlyisthe

consciouschildabletodosomething;heisalsoexplicitlyawareofhowhedoesit.9NotethatPiagetdoes

notuseconsciousnesstorefertotheelementaryandfleetingperceptionoftheimmediatesituation.Thus

thetermisnotusedtorefertothechild’sawarenessthattherearetoybarrelsonthetableorthathis

handismovingtowardthem,andsoon.Whilesuchelementaryawarenessappearsveryearlyinlifeand

isnodoubthighlyprevalent,itisnotthesubjectofPiaget’sinvestigation.Inbrief,Piagetisinterestedin

the child’s explicit knowledge of his thought processes, and not merely in the crude awareness of

ongoingactivities.

Severalquestionsthenarisewithrespecttoconsciousness.Itisespeciallyinterestingtoinquireinto

the temporal relations between action and cognizance. There are of course several possibilities. One

alternativeisthatactionandcognizanceemergesimultaneously.Asonedevelopssodoestheother,and

it is impossible to determine the direction, or even existence, of causality. A secondpossibility is that

consciousnesscomesfirst,andthusdirectsthesubsequentaction.Perhapsthechildfirstconceptualizes

his action and this helps him to perform it. A third possibility is just the reverse. Perhaps successful

behaviorprecedescognizanceofit.Thechildmaybeablefirsttoperformcertainactions,andonlylater,

uponreflection,doeshebecomeawareofhisbehavior.

ThebehaviorofoneofPiagets’subjects,STO,at6-1,workingatseriation,shedssomelightonthese

issues.Onhisfirstattempt,STOfailedtocompleteasuccessfulseries.Hecouldnotarrangecardsinorder

ofsizeandputthesmallestonesinthecenteroftheline.Hesaid,“I’vemadeastaircasethatgoesupor


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down.”Theexaminerrespondedthatthestaircaseshouldgodownallthetime,“butfirsttellmehoware

yougoingtomakeit?”STOresponded:“I’mgoingtoputthebigone,anotherbigone,anotherbigone,the

middle-sizeone,thesmallermiddle-sizeone,thesmallermiddle-sizeone,andthesmallermiddle-size

one”(GC, p. 312). STO proceeded to produce a good series, with only onemistake, which he easily

corrected.Onsubsequent trials, thesamesortof thinghappened:STOproducedgoodseriesbutpoor

verbaldescriptions.

AccordingtoPiaget,thisexampleshowsthatSTO’sseriationwasfarinadvanceofhisconsciousness

ofit.STOcouldorderthecardsinafairlysystematicwayandyetcouldreferonlyinanimprecisemanner

to“anotherbigone,anotherbigone,”or to “thesmallermiddle-sizeone,andthesmallermiddle-size

one.”Otherchildrenexhibitsimilarbehavior.Forexample,theyuseanextremelysystematicprocedure

forseriation(likeselectingthesmallestandthenthesmallestofallthoseleft)andyetcansayonlythat

theyfirsttookasmallone,thenanothersmallone,andsoon.Piagetconcludesfromdatalikethesethat,

in general, the child’s successful activities—including operative activities like seriation—precede

cognizanceofthem.Thechildcanactandthinkeffectivelybeforehecanverbalizeorbeconsciousofhis

actionsorthoughts.

Howdoesconsciousnessofproblemsolvingdevelop?Piagetproposesthatatfirstthechildisonly

dimlyawareofgoals.Forexample,hewantstomakea“staircase.”Thechildthengraduallydevelops

variousstrategies forachievinghisgoal, forexample,randomplacementorsystematicselectionof the

largest.Atfirst,heisquiteunawareofthesestrategies,justasthe3-month-oldbabyisnotconsciousofthe

procedureswhichheusesforgettinghisthumbintohismouth.Heacts,successfullyorunsuccessfully,

but does not explicitly analyze his actions. With development, however, the child observes his own

activitiesandreflectsonthem.Heinterpretshisactions;hetriesto“reconstruct”themontheplaneof

thought.Atfirst,thisprocessofinterpretationmayleadtodistortionandmisunderstanding.Piagethas

observedmanycasesinwhichtheinitialconsciousnesswasinerror—wherethechilddidnotaccurately

seewhatinfacthehaddone.Butgradually,thereconstructionbecomesmoreandmoreaccurate.The

child’sreflectiononhisownactivitiesallowsthedevelopmentofexplicitknowledgeconcerningbothhis

problem-solving processes and the objects under consideration. In this way, the child learns about

himselfandabouttheobjectssurroundinghim.Hedevelopsabstractconceptsthatcanbeverbalized.


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Piaget’spositionhasmuchtorecommendit.Itseemsusefultomakeadistinctionbetweenatleast

twolevelsofknowledge.Theredoesseemtobeakindof“actionknowledge”or“how-toknowledge”in

whichwesolveproblemsusingmeansofwhichweareunaware.ThusSTOcouldseriate,butwithout

consciousnessofhismethod.Atthesametime,thereisalsoanotherlevelofabstractknowledge,inwhich

wecanexplicitly formulateourmethodsofsolutionandeventheprinciplesunderlyingthem.Thusa

child cannot only seriate but explicitly understands the principles which he uses. The process of

transformingactionknowledgeintoabstractknowledgemaybecrucialforhumanlearning.Thereisa

gooddealofwisdombuiltintoourbehavior,andamajortaskforlearningmayconsistinmakingexplicit

whatinasensewealreadyknowunconsciously.

While these are useful points, Piaget’s investigations in this area seem to suffer from a major

weakness, namely, an overreliance on verbalizations as a source of evidence. In these studies,

verbalizationistakenasthemain,orevenonly,sourceofevidenceforconsciousnessorcognizance.Thus

STOissaidtolackconsciousnessofhisactions,sincehislanguageisinadequate.ButSTO’srepetitiveuse

of vague terms like “the smaller middle-size one” may not accurately reflect the true level of his

consciousness.Seriation ishardtoexpress inwords,andperhapsSTOcouldconceptualize itbutwas

unabletoofferadequatedescriptionsoftheprocess.Piaget’sinterpretationseemsweakinthisregard.At

thesametime,despitethedifficulties,Piaget’sresearchraisesextremelyprovocativeissuesrequiringa

gooddealoffurtherstudy.

GENERAL CONCLUSIONS

Whilecriticismsmayandshouldbemade,andwhilerevisionsarenecessary,Piaget’stheoryisan

enormouslysignificantaccomplishment.Indeed,onreviewingPiaget’slaterworkonthechildfrom2to

11,oneisstruckaboveallbytheincrediblecreativityanddiversityofhiscontribution.Between1940

and1980,Piagetrevolutionizedthestudyof thechild.He introducedascoreof fascinatingproblems

andexperimentaltasks—conservationisonlyoneexample—whichforalongtimedominatedresearch

inchildpsychology.Moreimportant,heofferedanextraordinarilydeepandsubtletheoryofcognitive

development,whichcontinuestoinformourunderstandingofthemind’sgrowth.


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Notes

1SeeH.P.Ginsburg, “TheClinical InterviewinPsychologicalResearch:Aims,Rationales,Techniques,”For theLearningofMathematics,Vol.3(1981),pp.4-11,andS.Opper, “Piaget’sClinicalMethod,” JournalofChildren’sMathematicalBehavior, Vol. 1 (1977),pp.90-107.

2See,forexample,R.GelmanandC.R.Gallistel,TheYoungChild’sUnderstandingofNumber(Cambridge,Mass.:HarvardUniversity,Press,1978),Chap.3.

3 Our exposition of Grouping I is simplified and incomplete: for example, we have defined only one binary operator.We have kept themathematical development at a very informal level. The reader interested inpursuing thematter should see JeanPiaget,TraitedeLogique (Paris:Colin,1949),andalsoj.B.Grize’s formalizationofPiaget’s systemasdescribed inE.W.BethandJeanPiaget,MathematicalEpistemologyandPsychology(Dordrecht,Holland:D.ReidelPublishingCompany,1966).

4 Although it does not seem to help with conservation, counting is far from useless in children’s arithmetic. Hebbeler has shown, forexample,thatyoungchildrenmakeverygooduseofcountingindoingaddition.SeeK.Hebbeler,“YoungChildren’sAddition,”JournalofChildren’sMathematicalBehavior,Vol.1(1977),pp.108-21.

5Strictly speaking, in the caseofnumberPiagetusesa somewhatdifferent logico-mathematicalmodel, called theGroup. The essentialdifferencebetweentheGroupingsandtheGroupisthatthefifthGroupingoperation,tautology(e.g.,A+A=A),isnotusedintheGroup.TautologydoesnotapplytonumbersincethereA+A=2A,notA.Therefore,theGroupmustbeusedfornumber.

6Recently,GelmanandBaillargeon (1983,p.171)haveargued that thephenomenonof invariant sequence isnotas clear-cutasPiagetsuggests.Theydescriberesearchshowingthat insomeareassomechildrendonotexhibitthestagesintheorderpredictedbyPiaget.Thisseemstopresentseriousdifficultiesforthetheory.

7Therecanbeinstancesoffalserecall.Piagethimselffalselyrememberedbeingtheobjectofanabortivekidnapattemptwhenhewasachild.

8 Piaget’s exposition of the classic view probably refers to theorists like Ebbinghaus, who in the nineteenth century invented nonsensesyllablesandspentmanyyearsofhislifememorizingthemhimself.Hewashisonlysubjectanddeservessomesortofprizefor an immense capacity for boredom. In recent years, however, theorists ofmemory have given up both the inclinationthemselves tomemorize nonsense syllables (althoughmay require their subjects to do it) and theoretical accountswhichtreat thesubjectaspassive.Manymoderntheoriesare insubstantialagreementwithPiageton the issueofactivity.ForacomparisonofPiaget’s theorywithothers, aswell asanexcellent critiqueofPiaget’swork, seeL.Liben, “Memory fromaCognitive-DevelopmentalPerspective:ATheoreticalandEmpiricalReview,”inKnowledgeandDevelopment,W.F.OvertonandJ.M.Gallagher,eds.(NewYork:PlenumPress,1977),Vol.I,pp.14-9-203.

9Recently, Flavell andothershavebeen investigating a similar topic,which they term “meta cognition,” andwhich involves the child’sknowledgeabouthisownknowledge.(Forareview,seeJ.H.Flavell,CognitiveDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1985.)Anexampleiswhetherthechildisawareofusingsystematicstrategiestoaidinmemory.


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Learning, Development, and Education

LEARNING AND DEVELOPMENT

We have now described the major periods of intellectual development— sensorimotor,

preoperational, concrete operational, and formal operational—and the stages within them.We have

postponeduntilnowconsiderationofthetransitionmechanisms.Whyisitthatthepreoperationalchild’s

thoughtadvancestoahigherlevel?Whydoestheadolescentdevelopformaloperations?Inshort,what

factorsproducethetransitionfromonestagetothenext?Piagetfeelsthatmentalgrowthinvolvestwo

processes:learninginthenarrowsenseandlearninginthebroadsense,ordevelopment.Thefirstofthese,

learninginthenarrowsense,isprovokedbyexternaleventsandlimitedtocertainsituations;thesecond,

development, is a much wider phenomenon, with broad implications. We will begin by discussing

learninganddevelopmentandthenturntothefourfactorsunderlyingtheprocessofdevelopment.

The Nature of Learning and Development

ForPiaget,theterm“learning”maybeusedintwosenses.Learninginthenarrowsenseinvolvesthe

acquisitionofnewinformationornewresponsesrestrictedtoaspecificsituation.(Notetheparallelwith

memoryinthespecificsense.)Forexample,inschoolgeography,thechildlearnsthenamesandlocations

ofthestatesandtheircapitols.Thiskindoflearningisobviouslyspecifictoparticularculturedcontexts

andisoflittlegenerality.Byvirtueofanaccidentofbirth,theAmericanchildlearnsaboutthefiftystates;

if transported to Canada, the child would then have to learn the names of the provinces and their

capitols.Learningofthistype,then,isimportant—butitisspecificandcannotbegeneralized.

Bycontrast,learninginthebroadsense,ordevelopment,involvestheacquisitionofgeneralthought

structures which apply to many situations. (Note the parallel withmemory in the wider sense.) For

example,thechildacquiressomegeneralwaysofthinkingaboutthestatesandtheircapitols.Learningin

the wider sense is involved when the child develops such notions as that a state cannot be in two

locations at the same time or that the United States must be larger than any individual state (class

inclusion). Learningof this type involves structureswhich are general andwhich canbe transferred


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fromonesituationtoanother.Theyarenottaughtthroughspecificinstruction.

Totakeanotherexample,iftheyoungchildobservesthataballofclayrepeatedlyweighsthesame

despite changes in shape, hemay learn that theweight of this particular clay ball remains constant

(conservationofweight).Thechildmayevenpredictthattheweightwillcontinuetobethesameforany

newchangeinthesameball.Inotherwords,asaresultofrepeatedempiricalobservationsorexternal

reinforcements, the childwillhave learneda law foraparticular situation.Thisdoesnotnecessarily

mean,however,thathehasunderstoodwhytheweightremainsconstant.Also,thechildmaybeunable

to generalize the law to other situations with other objects. It is only when the child develops the

structuresofconcreteoperationalthoughtthatheunderstandsthereasonsfortheconservationofweight

andcangeneralizetonewsituations.Tosummarize,specificlearningmayenablethechildtodealwitha

particularprobleminvolvingweight,butlearninginthewidersense,ordevelopment,isnecessaryfor

him to acquire thought structures capable of generalization. We see, then, that there are important

differencesbetweenlearninginthespecificsenseanddevelopment.

Piagetproposesthat,ofthetwoprocesses,development(learninginthewidersense)isthemore

fundamental.First,aswehavealreadyseen,developmentresultsintheacquisitionofgeneralcognitive

structures as opposed to specific information or responses. Second, development makes possible

meaningful learning in the specific sense. The child can appreciate the meaning of an external

reinforcementorofnewexperiencesingeneralonlywhenhisstructureshavereachedacertainstageof

developmentthroughtheprocessofequilibration.Thechildcanprofit fromexternal information—for

example, reinforcement or an adult’s explanation— only when his cognitive structure is sufficiently

preparedtoassimilateit.

Thus,informationconcerningthestatesandtheircapitolswillonlybearoterecitationunlessthe

childunderstandswhatacapitolisandhowastaterelatestothecountryofwhichitisapart.Similarly,

thespokennumberwords“one, twothree ...”areonlymeaninglesssoundsunless thechildpossesses

somegeneralstructuresofthoughtenablinghimtounderstandthat“one”islessthan“two,”andsoon.

Genuinelearningoccurswhenthechildhasavailablethenecessarymentalequipmenttomakeuseof

newexperiences.When the requisite cognitive structure ispresent,he can learn from theworldand

cometounderstandreality;whenthestructureisabsent,newexperiencehasonlysuperficialeffects.If


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thereistoogreatadisparitybetweenthetypeofexperiencepresentedtothechildandhiscurrentlevel

ofcognitivestructure,oneoftwothingsislikelytohappen.Eitherthechildtransformstheexperience

intoaformwhichhecanreadilyassimilateandconsequentlydoesnotlearnwhatisintended;orelsehe

merelylearnsaspecificresponsewhichhasnostrengthorstability,cannotbegeneralized,andprobably

willsoondisappear.Itisforthisreasonthatthechild’slearning,inschoolorout,cannotbeaccelerated

indefinitely.Therearesomethingsheisnotreadytolearnbecausethenecessarycognitivestructureis

notyetpresent.Ifforcedtodealwithsuchmaterial,thechilddoesnotachievegenuinelearning.

Finally,Piagetmaintainsthatlearninginthespecificsensecannotaccountfordevelopment.Aswe

shallsee, thegeneralcognitivestructuresdevelopthroughacomplexprocess involving four factors—

maturation,experience(physicalandlogicomathematical),socialtransmission,andequilibration—and

consistsoffarmorethanthemechanicalacquisitionofnewinformationorresponses.ForPiaget,learning

inthespecificsensecannotexplaindevelopment.Instead,developmentexplainslearning.

Piaget and his colleagues in Geneva (Inhelder, Sinclair, and Bovet, 1974) have conducted a

number of studies into children’s learning in the broad sense and the possibility of accelerating the

acquisitionofvariouslogicalstructures.Thefindingsshedsomelightontheprocessesofdevelopment.

Thegeneralplanofthesestudieswasfirsttoadministeradiagnosticpretesttodetermineeachchild’s

developmentallevel.Afterthis,thechildrenwentthroughaseriesoftrainingsessionswhichpresented

arangeofproblems,eachofwhichwasdesignedtoelicitadifferentcognitiveoperation.Theaimwas“to

arouse a conflict in the child’s mind” so that he might attempt a coordination among the various

operationsandtherebyachieveahigherlevelofdevelopment.Theinvestigatorscarefullyobservedand

questionedchildreninconflictsituationstoseewhetherandhowlearningoccurred.Sometimelater,the

childrenweregiventwodiagnosticpost-tests,thesecondaboutfourtosixweeksafterthefirsttoidentify

theeffectsoftraininganddeterminewhetherthechangesobservedwerelong-lastingandstable.


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FIGURE16Sticksandhouses.

ConsideroneoftheGenevanstudies.Childrenwerepresentedwithtwostraightlinesofstickswith

smallhousesgluedontoeach(seeFigure16).Thelines(AandB)wereidenticalinlengthandhadthe

samenumber.Eachchildeasilyrecognizedthat lengthandnumberwerethesame.Thenasthechild

watched, line B was rearranged into configuration C, which obviously looks much different. The

experimenterthenaskedaseriesofquestionsconcerningbothlengthandnumber:‘‘Aretherethesame

numberofhouseshereasthere?Isthisroadjustaslongastheother?”Theaimwastoplacethechildin

conflictwithrespecttodifferentaspectsoftheproblem;thechildmightrealize,forexample,thatnumber

doesnotchangewhentheconfigurationistransformed,butatthesametimehemayfailtoconservethe

length.Ifsuchaconflictisproduced,howdoesthechilddeedwithcompetingschemes?Doestheconflict

producelearning?

Throughstudieslikethese,Inhelder,Sinclair,andBovetwereabletodiscoverfinedistinctionsin

thelearningprocess.Inparticularitappearsthatthelearningprocessinvolvesfoursteps.Inthefirst,the

childkeepsthetwomodesofreasoningseparateanddoesnotrealizethataconflictisinvolved.Hesays

thatthereisthesamenumberofhousesinAandCbutthatAismuchlonger.Repeatedquestioningdoes

nothelpthechildtoseethecontradiction.Inthesecondphase,thechildbeginstoappreciatetheconflict.

Heseesthatthetworoads,AandC,whichhethinksareofdifferentlengths,neverthelesshavethesame

numberofsticksineach;nowthechildunderstandsthatthispresentssomethingofaproblem.Oncethe


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childperceivesadiscrepancy,hetriestoreconcileitinsomeway.Thethirdstepinvolves‘‘compromise

solutions.”Here, the childuses an inappropriatemethod to resolve the conflict. For example, hemay

breaka stick inhalf so that the longer row in facthasmore sticksaswell!The fourth step involvesa

legitimatecoordinationof the twoschemes. In thesituationcited, thechildsees thathemustperform

certaincompensations;hesees,forexample,thatalthoughtheendpointsofrowAgobeyondthoseof

rowC,rowChasmorezigzagsthandoesAandthatthesecompensatefortheoverlapofA.

Inhelder, Sinclair, and Bovetmake several general points about their findings. One is that the

child’s ability to profit from training depends on his initial developmental level. These investigators

foundthatchildreninstage1generallyprogressedverylittleornotatallinresponsetotraining;while

thoseat a transitional level showedconsiderableprogress.The reason for thediscrepancy is that the

stage1childrencouldnotperceivetheconflictwhichthetrainingwas intendedto induce,while the

transitional childrenwereable to see it.According to this view, the childwill not experience conflict

unlesshisschemesaresufficientlydeveloped.Iftheyarenot,thennoamountofquestioningthechildor

demonstrating different arrangements of objects will produce conflict and hence intellectual

development.Conflict(andtheresultinglearning)canbeprovokedonlywhenthechildisreadyforit.

Thisperspectivehasimportantimplicationsforeducationandweshallreturntoitlater.

A second point is that amajor form of conflict occurswhen different cognitive subsystems—for

example, lengthandnumber—operatesimultaneouslyandwhenoneof theseschemeshasreacheda

moreadvancedstatethantheother.

Third,thestudieshighlightthecentralroleofthechild’sactivityandinitiative.Inparticular,the

phenomenonofcompromisesolutionsshowsthatstrategiesarenotsimplyimposedonthechild;rather

heplaysamajorroleininventingthem.

Fourth,theinvestigatorssummarizetheirfindingsasfollows:

[Atfirstthereis] . . .anapplicationofexistingschemestoanincreasingvarietyofsituations.Soonerorlater,this generalization encounters resistance,mainly from the simultaneous application of another scheme; thisresults in two different answers to one problem and stimulates the subject seeking a certain coherence toadjust both schemes or to limit each to a particular application, thereby establishing their differences andlikenesses.Thesituationsmostlikelytoelicitprogressarethosewherethesubjectisencouragedtocomparemodes of reasoningwhich vary considerably, both in nature and complexity, but which all, individually, are


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alreadyfamiliartohim.(Inhelder,Sinclair,andBovet,1974,p.265)

Wesee,then,thatdevelopmentinvolvesaconflictamongexistingschemes,thechild’sassimilation

ofnewproblemsintothoseschemes,andaself-regulatedadjustmentorprogressionofthecurrentmodes

ofthought.Piagetreferstothisasequilibration,whichconstitutesoneofthefourfactorsofdevelopment

thatweshallnowdiscuss.

Factors Underlying Development

Maturation.Asyouwillrecall,Piaget’stheoryproposesthatspecificheredityequipsthechildwith

various physical structures which affect intellectual development. Some of these physical structures

resultinautomaticbehavioralreactions.Forexample,whenthelipsarestimulated,thebabysucks;this

occurs because the appropriate reflex is activated through a “prewired” physical mechanism. The

automaticbehavioralreaction isakindof“innateknowledge”;becauseofheredity,whichreflects the

evolutionoftherace,thebabyimplicitly“knowswhattodo”inthefeedingsituation.Reflexes,however,

play aminor role in intellectual development. Inhumanbeings, physical structures givenby specific

hereditytypicallyexertindirecteffectsonintellect.Thus,thebabyisbornwitheyesthatpermithimtosee

only certain frequencies of light, to perceive depth, and to detect objects in front of the body but not

behind.Theeyesdonotprovidethebabywithapreviouslywrittenencyclopediaofknowledge—witha

stockofinnateideas.Instead,theygivethebabywaysofknowing;theybothsetlimitsonandprovide

opportunitiesforintellectualfunctioning.Inbrief,thephysicalstructuresprovidedbyspecificheredity

areorgansofknowingwhichdeterminetheroughoutlinesofintellectualgrowthbutdonotspecifyits

content.

Considernowhowmaturationenters thepicture.Thephysical structures, including the central

nervous system, take time to reach their highest level of development. The brain of the newborn, for

example,issmallerandlighterthanthatoftheadolescent.Itisobviousthatimmaturephysicalsystems

oftencontributetodeficitsincognitivefunctioning.Thesimplestexampleinvolvesmotorcoordination.

Thenewborn’smusclesandotherstructuresarenotsufficientlydevelopedtopermitwalking.Sincehe

cannotgetaround in theworld, thenewbornobviouslycanknowvery littleabout it.Otherexamples

abound. One of the factors underlying the newborn’s inability to speak is undoubtedly an


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underdeveloped articulatory apparatus. One of the variables producing his weakness at abstract

reasoning is in all probability an insufficientlymature brain. It is clear, then, that immature physical

systemscanretarddevelopment.

It is also obvious that the healthy growth of physical systems contributes, at least indirectly, to

intellectual advance, although the details of the process are largely unknown. When leg muscles

develop,thebabybecomesmobileandcanlearnaboutpreviouslyinaccessiblethingsandevents.Alsoin

infancy, “the coordination between grasping and vision seems to be clearly the result of the

myelinizationofcertainnewnervepaths in thepyramidal tract” (Piaget, “Problems inEquilibration,”

1977b,p.7).Inthemostgeneralsense,asthebrainandthecentralnervoussystemmature,theymakeit

possible for the child to use thought and language. In Piaget’s view, the question is not whether

maturationhasaneffect,buthowimportanttheroleofmaturationisandhowitoperates.Someyearsago

Gesellproposedthatmaturationisthechieffactorexplainingdevelopment.Accordingtothishypothesis,

the process of physical maturation is the most important and direct influence on all aspects of

psychologicalfunctioning.Piagetfeelsthatthispositionistooextremeforseveralreasons.

Oneisourlackofunderstandingofthematurationofthecentralnervoussystem.Howcanonebase

a theory onmaturationwhen so little is known about it? Second, it is clear thatmaturation does not

explaineverything.Forexample,childreninMartiniquereachtheconcreteoperationalstageaboutfour

yearslaterthandochildreninSwitzerland.ItwouldseemunlikelythatSwisschildren’sbrainsarefour

yearsmoremature than those of the children inMartinique. Amuchmore likely explanation is that

culturalfactorscontributeheavilytothedifferencesindevelopment.InPiaget’sview,then,physiological

maturationundoubtedlyaffectscognitivedevelopment—ofteninwayswedonotunderstand—butitis

nottheonlyfactor.1

Experience.A second influenceondevelopment is contactwith the environment.To acquire the

notion of object permanence, the infant must obviously experience things disappearing and

reappearing.Toclassifyobjects,thechildmustfirstperceivethem.Tospeakalanguage,theinfantmust

hearpeople talking. Piaget feels that contactwith the environment leads to two types of knowledge:

physical and logicomathematical. On the one hand, physical experience leads to the knowledge of

observables.Observablesreferstothepropertiesandcharacteristicsofobjects,suchasshape,color,size,


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andsoon,thatareperceivedbyaperson.Physicalknowledgeofobservablesisobtainedbyaprocessof

empiricalabstraction(calledsimpleabstraction inPiaget’searlyworks).Thechildencountersanapple

and,throughperceptualactivity,“pullsout”orabstractssomeofitsproperties.Nowthechild“knows”

that it is round and that it is red.Or he lifts a block, and in the process discovers that it is heavy. If,

however,heliftstwoblocksandnotesthatoneisheavierthantheother,thiswouldnolongerbepurely

physicalknowledge.Bycomparingthetwoblocks,hehascreatedarelationshipof“more”or“less”heavy

thatisnotgivendirectlyintheblocksthemselves.Thissecondtypeofknowledgeislogicomathematical.

In physical experience, then, a child uses empirical abstraction to extract directly from the objects

themselvesaknowledgeoftheirphysicalproperties.

Piaget makes several points about physical knowledge.2 One is that it is a major influence on

development: there isa “vast categoryofknowledgeacquiredbymeansof theexperienceofexternal

objects”(BiologyandKnowledge,BK,p.335).Agoodpartofintellectualdevelopmentislearningwhat

thingsarereallylike.

Second,theprocessofobtainingphysicalknowledgeinvolvesmorethanjustempiricalabstraction.

Piagetmaintainsthat“Itisimpossiblefortheretobedirectandimmediatecontactbetweensubjectand

objects....Anykindofknowledgeaboutanobjectisalwaysanassimilationintoschemes”(BK,p.335).

Thedataofexperiencearealways interpreted in termsofa larger intellectual frameworkofschemes,

concepts,andrelationships.Thechilddoesnotsimplyperceivethepropertiesofaparticularapplein

isolation.Rather,heperceivesandunderstandstheminrelationtoalltheotherappleshehasknown.A

particularappleisperceivedas“red”asaresultofitsassimilationtotheconceptualschemeofapples,of

which redness is one characteristic. Implicit comparisons with other (more or less red) apples

experiencedinthepastgivemeaningtotherednessofthisparticularapple.Buttheactionofcomparing

similaritiesanddifferencesbetweenapresentobjectandaschemethathasbeenconstructedonthebasis

ofpastexperiencescallsformorethanempiricalabstractionalone.

Theabstractionofanyinformationfromanobject...requirestheuseoftoolsofassimilationofamathematicalnature:relationships,oneorseveralclasses(oraction“schemes”atthesensorimotorlevel,whicharealreadyatype of practical concept), correspondences, functions, identities, equivalences, differences, etc. . . . Clearly,these tools . . . are not extracted from the objects. They are therefore due to the person’s own activities.(AdaptationVitaleetPsychologiedeL'Intelligence,AV,p.82,trans.bytheauthors)


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Inbrief,physicalknowledge,ortheknowledgeofobservables,isessentialtodevelopment,butcan

onlybebuiltupwithina larger frameworkbecause it requires certainmental toolswhichhavebeen

createdbymeansofpreviouslogicomathematicalexperience.

Logicomathematicalexperienceinvolvesknowledgeacquiredfromreflectiononone’sownactions,

notfromtheobjectsthemselves.Theconceptoflogicomathematicalexperienceisadifficultone,andwe

shallnowtrytoexplainitbymeansofanexample.

FIGURE17Twosets.

Supposethatachildencounterstwosetsofobjects,asinFigure17.SetAisarrangedinastraight

lineandsetBinacircle.Thechildexaminesthesets,accuratelyperceivingthateachelementisasquare,

thatonesetisarrangedinaline,andtheotherinacircle.Thisisthechild’sphysicalexperienceofthe

sets, and it yields accurate knowledge concerning certain properties of shape, form, and layout. But,

whileessential,physicalknowledgealonedoesnottellthechildsomethingverycrucialaboutthesets:

regardlessofsurfaceappearance,theyhavethesamenumber.Togainthisknowledge,thechildrequires

adifferentkindofexperience,logicomathematicalexperience,inwhichknowledgeisnotadirectresultof

perceiving objects, but of reflecting upon actions performed on objects. To illustrate the

logicomathematicalfactor,Piagetcitesafriend’schildhoodexperience.Attheageofabout4or5years,

hewas seated on the ground in his garden andhewas counting pebbles.Now to count these pebbles he puttheminarowandhecountedthemone, two, threeupto10.Thenhe finishedcountingthemandstartedtocount them in the other direction. He began by the end and once again found he had 10. He found thismarvelous....Soheputtheminacircleandcountedthemthatwayandfound10onceagain.(Piaget,1964,p.12)


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Throughrepetitionsofcountingandrecounting,ofarrangingandrearranging,thechildgrasped

an important property of number: it stays the same despite different orders of counting and despite

differingphysicalarrangements.

HowdidthislearningtakeplaceHowdidthechildcometoknowsomethingabouttheequivalence

ofnumber?Piagetmaintainsthatempiricalabstractionwasnotsufficienttoproducethisknowledge.Ina

sense, the child learned nothing about pebbles: he already knew that they are small, dark, smooth

objects.Thephysicalpropertiesofthepebbleswereknown,andtheydidnot“say”anythingtothechild

aboutnumber.

InPiaget’sview,thechildlearnedaboutnumbernotthroughdirectphysicalexperiencewiththe

pebblesthemselves,butbyconsideringhis

ownactions.Aprocessofreflectiveabstraction(asopposedtoempiricalabstraction)isinvolved.The

childfirstnoticesoneofhisownactions.Inthiscase,heseesthathehascountedtherowinonedirection,

getting10,andthathehascountedtherowintheoppositedirection,alsogetting10.Thisperceptionof

hisownactionsintereststhechild;itsurpriseshim.Next,“theactionnotedhastobe‘reflected’(inthe

physicalsenseoftheterm)bybeingprojectedontoanotherplane—forexample,theplaneofthoughtas

opposedtothatofpracticalaction”(BK,p.320).Thechildreflects(transposes)hisactionofcountingto

theplaneofthought.Thisisonewaythattheprocessisreflective.

Itisreflectiveinanotherwaytoo.Reflectinganactionontoanotherlevelcallsforareorganization

ofmentalstructurestointegratethenewactionwiththosealreadyexistingatthislevel.Thisprocessof

reorganization establishes new relationships and new meanings not found at the lower level. For

example,thechildhastorelatethecountingofthepebblestotheactionofincreasingquantity.Counting

to 10 always gives more objects than counting to 9. He has to relate the counting to the concept of

sequencing: 5 is always counted after4 andbefore6. Countingmust alsobe related to thenotionof

invarianceofnumber.Heseesthatifhecancounttheobjectsinvariouswaysandalwaysgetthesame

result,theymustbethesamenumber.Inasense,thechilddefinesnumericalequivalenceintermsofhis

ownactions.Inreorganizinghisactionsofcounting,hereflectsonthem,orcontemplateshisownactions,

and comes to appreciate their wider implications and significance. In sum, reflective abstraction is


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“reflected”intwoways.Thefirstconsistsofaprojection,orreflection,ofactionsontoahigherlevel,and

the second consists of a reflection upon and reorganization, or reworking, of both the projected and

previousactionsintoanewandbroaderunderstanding.

In his later work, Piaget introduces a third type of abstraction, pseudoempirical abstraction.

Pseudoempirical abstraction is found during the initial stages of the formation of logicomathematical

knowledge,whentheyoungchildneedstouseconcreteobjectsasasupportforsuchknowledge.The

countingofpebblesisanexampleofpseudoempiricalabstraction.Heretheknowledgeisnotabstracted

fromthepebbles,andthusisnotphysicalexperience,butisattributedtothem.Thechildcouldjustas

wellhavegainedtheunderstandingofnumberconservationfromanothersetofobjects,althoughsome

typeofobjectisnecessaryatthisbeginninglevel.Later,whenthechildhasgainedsufficientmasteryof

counting, he will not need the pebbles, or his fingers, or any other objects as a support, and the

abstractionwill become truly reflective. Pseudoempirical abstraction is, therefore, a primitive form of

reflectiveabstractionthatoccursduringtheearlypartoftheconcreteoperationalperiod.

There are several notable aspects of logicomathematical experience. First, it relies on physical

experience,althoughitgoesbeyondit.Intheexamplecited,achildcouldnothavediscoverednumerical

equivalence if he had not accurately perceived the pebbles. Yet perception of the pebbles—physical

experience—initselfwasnotsufficient,andhadtobesupplementedbyreflectionofandontheactions

of counting. Second, logicomathematical experience results in harmonywith the environment. As the

child’s physical knowledge becomes more accurate, his actions, and hence his logicomathematical

knowledge,constructan increasinglyobjective interpretationoftherealworld.Whiletherichness“of

thesubject’sthoughtprocessesdependsontheinternalresourcesoftheorganism,theefficacyofthese

processesdependsonthefactthattheorganismisnotindependentoftheenvironment,butcanonlylive,

act,orthinkininteractionwithit”(BK,p.345).

Althoughdifferentinnature,physicalandlogicomathematicalknowledgearecloselyintertwined,

particularly during the early years. In physical knowledge, the source of knowledge is exogenous or

externaltotheperson.Itisintheobject,oratleastthoseaspectsoftheobjectthatareperceivedbythe

person. Piaget calls these aspects theobservables. Observables, such as shape, color, or size, form the

content of physical knowledge. However, this type of knowledge is extracted within a framework of


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mental instruments—schemes, concepts, and so on—that have been created by an endogenous or

internal source, that of reflective abstraction. These instruments constitute the form of physical

knowledge.Inlogicomathematicalknowledge,thesourceofknowledgeisendogenousandisfoundin

thecoordinationsoftheperson’sownactions,althoughatfirsttheobjectsoftheexternalworldserveas

the basis for this knowledge, as in the process of pseudoempirical abstraction. With development,

logicomathematicalknowledgebecomesmoreandmoreremoved fromreality,asreflectiveabstraction

continuallyleadstotheconstructionofnewoperations,andofoperationsuponoperations.Theformal

theoriesoflogic,mathematics,orphysicsareexamplesoflogicomathematicalknowledgeasitfunctionsin

a“pure”state.But,atthesametimeasbecomingmoredetachedfromphysicalreality,logicomathematical

knowledge provides conceptual tools which are able to grasp a deeper and more profound

understandingofthephysicalenvironment.

Bothphysicalandlogicomathematicalexperienceareimportant,butPiagetfeelsthattheyarenot

sufficienttoexplaindevelopment.Onereasonisbecausetheyomitsocialfactors.

Socialtransmission. A third factor influencing cognitive development is social transmission. This

phraseisusedinaverybroadsensetorefertotheinfluenceofthecultureonthechild’sthought.Social

transmission may refer to a parent explaining some problem to a child, or to a child’s obtaining

information by reading a book, or to a teacher giving instruction in a class, or to a child discussing a

questionwithapeer,ortoachild’simitationofamodel.Certainly,thesocialtransmissionofknowledge

promotescognitivedevelopment.Theaccumulatedwisdomofaculturepassesdownfromgenerationto

generation, and enables the child to learn through the experience of others. Because of social

transmission,thechildneednotcompletelyreinventeverythingforhimself.Thecultureprovideshim

withextraordinarycognitivetools—thecountingnumbers,alanguage,analphabet.Thesetoolsenable

him to do mathematics, to speak, to write—in sum, to participate in higher intellectual activities,

particularlythoseofaliteratenature.

But social transmission itself is not sufficient. Unless the child is prepared to understand the

culturalwisdom,socialtransmissionwillnotbeeffective.Inotherwords,toappreciatetheknowledge

passedonbyotherindividuals,thechildmustpossesscognitivestructureswhichcanassimilateit.The5-

year-old cannot learn the calculus, however well it is transmitted, because he does not have the


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prerequisitestructures.

SomeAmerican andRussian psychologists have proposed that one specific type of social factor,

namely,thechild’sownlanguage,isvitalforthedevelopmentofbehaviorandthought.Inverygeneral

terms,theirthesisisthatatabouttheageof4or5yearsthechildusesinternalspeechtocontroland

organizehisactivities.Language“mediates”betweenexternaleventsandthechild’sresponse.Without

aninternallinguisticsystem,thechild’sresponsesaredirectlycontingentuponexternalevents;butwith

suchasystemthechildcanrepresentexternalevents,delayrespondingtothem,andcantherebycontrol

hisownbehavior.

Piaget’sview,verydifferentfromtheforegoing,attributesalesserroletolanguage.Piagetdoesnot

accept the proposition that language is the sole or primary device by which the child formsmental

representationsof external events.Representation takesmany forms—mental imagery, symbolic play,

drawing—inadditionto language.Thus,mental imagesareoftennonverbal.At18monthsofage, the

infanthasimagesofthingsandeventseventhoughhecanhardlyspeak.AccordingtoPiaget,theinfant’s

imagesandotherrepresentationsderivefromimitatingpersonsandthingsandnotfromlanguage.In

brief,therepresentationalfunction,andgenerally,thefigurativeaspectofthought,neednotinvolveor

dependonlanguage.3

Piagetbelievesthattheoperativeaspectofthoughtalsoneednotinvolvelanguage.Inthecaseof

classification, we have seen that the preoperational child in stage 1 cannot produce a hierarchical

arrangementofobjectsanddoesnotunderstandinclusionrelations.Thisissodespitethefactthatthe

childcanusealloftherelevantwordsinvolved.Hecansay“bluetriangles,”or“redcircles,”or“moreof

these,” or “some of these.” Even though the language is available, the preoperational child cannot

classify.Thisisnot,however,toassertthatlanguageplaysnoroleinthedevelopmentofclassificationor

othermentaloperations.Forexample,thepresenceofnounsinthelanguagemaystimulatethechildto

thinkintermsofdiscreteclasses.Also,theabilitytoverbalizeathoughtstructure,likeclassinclusion,may

helptoconsolidateandgeneralizeit.Nevertheless,forPiaget,thoughtinvolvesmorethanlanguageand

isnotdependentuponit.

ThispropositionisreinforcedbytheresearchofSinclair(reportedinInhelder,Sinclair,andBovet,


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1974).Shebeganbyexaminingthelanguageoftwoseparategroupsofyoungchildren,someofwhom

wereunabletosolveconservationproblemsandsomeofwhomweresuccessful.Shefoundacorrelation

between theability to conserveand theability to talkabout it.Theconservingchildrenusedphrases

comparingthevariables,saying,forexample,thatoneglassofwateris“tallandthin,”whiletheotheris

“short and fat.” The nonconserving children, on the other hand, used “undifferentiated terms” to

describe the situation; they said, forexample, thatoneglassofwater is “big”and theother is “fat.” It

would appear then—perhaps contrary to Piaget’s views—that conservers and nonconservers are

characterizedbydifferenttypesoflinguisticability.

Butdoestheuseofcomplexlanguagecausetheabilitytoconserve?Todiscovertheanswertothis

question,Sinclairtaughtthenonconservingchildrentousethelanguageoftheconserversindescribing

thevariousproblems.Iflanguageiscrucialforconservation,thesechildrenshouldthenhavebeenable

to conserve. Yet the results showed that they could not: the benefits of language trainingwere quite

limited.Itappears,then,thatlanguagedoesnotenablethechildtoconserve.Infact,theoppositeseems

true: thedevelopmentof the thought structuresunderlyingconservationenables thechild toemploy

sophisticatedformsoflanguagetodescribewhathedoesandunderstands.

FurtherevidencesupportingthispropositionderivesfromOpper’s(1979)researchinThailand.

TheThailanguagecontainscertainbuilt-intermscalled“classifiers,”whichsignifythatanobjectispart

ofahigher-order class.Thus theword for lotus specifies both that the object is that particular flower

knownasalotusandthatitbelongstothelargerclassofflowers.Thelanguageitselfvirtuallyannounces

classinclusion.Thequestionthenbecomeswhetherchildrenexposedtosuchalanguageacquireclass

inclusionatayoungeragethanusual.Opperfoundthattheydidnot.Despitethepresenceoflinguistic

mechanisms which would supposedly facilitate this development, Opper’s work showed that Thai

children did not acquire class inclusion earlier than Swiss children, whosemother tongue does not

containsuchmechanisms.ThisevidencealsoseemstosupportPiaget’spropositionthatthoughtinvolves

morethanlanguageandthattheformerisnotfullyshapedbythelatter.4

Considernowtheroleofformalschooling:Isthiskindofsocialtransmissioncrucialforintellectual

development? Some psychologists believe that it is. Some years ago, on the basis of research inWest

Africa,Greenfield(1966)proposedthattheWesternstyleofschoolingisnecessaryforthedevelopment


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ofthestagesofthoughtasdescribedbyPiaget.Themainevidenceforthisassertionwasthediscovery

thatschoolchildreninSenegaldidachievetheperiodofconcreteoperations,as judgedfromatestof

conservation,whereasthosechildrennotinschoolremainedatalowerlevelofthought.Whilethisisan

intriguing finding, the evidence in this area is by no means clear-cut. Some studies are directly

contradictory, showing that schooling is not necessary for the development of concrete operations

(Ashton, 1975; Dasen, 1972). At the present time, the weight of the evidence seems to support the

Piagetian view that schooling, like other forms of social transmission, may accelerate intellectual

development but is not necessary for it. Apparently, individuals growing up in “primitive” societies

without schools nevertheless develop the basic thought structures described by Piaget. Perhaps the

failureofsomeresearcherstoobtainthisfindingcanbeattributedtoproblemsofmeasurementinstrange

cultures,whereWesterntestingtechniquesandtestingmaterialsareofteninappropriate.Inanyevent,

Piaget’sviewisthatschoolingandotherformsofsocialtransmissioncancontributetointellectualgrowth

butdonotfullydetermineit.

Equilibration.Afourthfactoraffectingdevelopmentisequilibration,5whichinawayintegratesthe

effects of the other three factors, none ofwhich is sufficient in itself to explainmental development.

Equilibration refers to the child’s self-regulatory processes, bywhich he progressively attains higher

levels of equilibrium throughout development. The equilibration process is the backbone of mental

growth.

Letusbeginbyreviewingtheconceptofequilibrium.Piagethasborrowedthisnotionfromphysics

andbiologyandhasmodifiedittoapplytohumanintelligence.Theconceptofequilibrium,whichisnot

novelinpsychology,referstoastateofbalanceorharmonybetweenatleasttwoelementswhichhave

previouslybeeninastateofdisequilibrium.Freud,forexample,makesuseofasimilarprinciplewhen

hestatesthatapersontendstowardareleaseoftension.ForPiaget(unlikeFreud)equilibriumdoesnot

have the connotationof a static state of reposebetween a closed systemand its environment.Rather,

equilibrium,whenappliedtointellectualprocesses,impliesanactivebalanceorharmony.Itinvolvesa

systemofexchangesbetweenanopensystemanditssurroundings.Thechildisalwaysactive,anddoes

notmerelyreceiveinformationfromhisenvironmentlikeaspongesoakingupwater.Rather,thechild

attemptstounderstandthings,tostructureexperience,andtobringcoherenceandstabilitytotheworld.

Acognitivesystemisneveratrest,itcontinuallyinteractswiththeenvironment.Thesystemattemptsto


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dealwithenvironmentaleventsintermsofitsstructures(assimilation),anditcanmodifyitselfinline

with environmental demands (accommodation).When in equilibrium, the cognitive system need not

distorteventstoassimilatethem,nordoesitneedtochangeverymuchtoaccommodatetonewevents.

Although the concept of equilibrium was taken from physics, Piaget stresses that physical and

cognitiveequilibriumareverydifferent.Physicalequilibriumseekstomaintainthestabilityofthesystem

withoutchange.Disequilibriumisovercomebyamovementintheoppositedirectionwhichrestoresthe

original state of equilibrium. A thermostat, for example, maintains equilibrium by compensating for

increases or decreases in heatwith actions that restore the system to the original temperature.With

intellectual development, however, there is both stability and change. Cognitive systems, as they

progress, preserve past intellectual achievements but at the same time create new actions and novel

responseswhichallowthepersontogainmoreunderstanding.Equilibriumresultsfromregulationsthat

tendtowardbetter formsofknowledge.There isan increase inknowledgeratherthanareturntoan

originalstate,andthisrequiresadynamicmodelofequilibrium.“Itwouldnotdo,then,toconceiveof

equilibration as a simple process toward equilibrium since it always involves construction oriented

towardbetterequilibrium’’(EquilibrationofCognitiveStructures,ECS,p.26).

For Piaget, cognitive development consists of a succession of alternating equilibria and

disequilibria. Each successive level of equilibrium reaches a better form of knowledge through the

additionandreorganizationofcognitiveelements.Thesequantitativeandqualitativechangesresultin

new relationships, new understandings, and the solving of certain problems, but also open up the

possibilityofnewquestionsandproblems,ofnewimbalancesanddisequilibria.Toreconcileboththe

stabilityandthechangesthatoccurincognitivedevelopmentandtoemphasizethedynamicaspectof

this process, Piaget refers to it as optimizing equilibration (équilibration majorante). Optimizing

equilibration is the process that leads to the successive improvements in equilibrium that occurwith

development.Eachnewequilibriumbecomesmorepowerful in itsabilitytocomprehendthephysical

characteristicsandrelationshipsoftheobjectsintheenvironment,andalsotoattributecausal, logical,

andmathematicalpropertiestothem.

Piaget describes three types of equilibrium, all ofwhich contribute toward achieving a balance

betweenthepersonandhisenvironment.Thefirstistheequilibriumbetweenapersonandanobjector


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event of the environment. Here the person encounters an object, assimilates it to a scheme, and

accommodatestheschemetotheparticularobject.Iftheschemeisappropriate,thereisequilibrium;if

not,therewillbedisequilibrium.Achildwhoonlyhasschemesforappleandorangeswouldhaveno

troublewhenencountering instancesof these fruits,butwouldbe indisequilibriumwhenpresented

withherfirstexperienceofapineapple.Thistypeofequilibriumdependsupontheinteractionbetween

apersonandtheenvironment,thatis,betweenassimilationandaccommodation.

Anothertypeofequilibriumisbetweenthevariouscognitivesubsystems.Here,theequilibriumis

internalratherthanexternal.ExamplesofthiscanbefoundintheresearchbyInhelderandcolleagues

into learning, discussed in the previous section, which indicated that very often the lack of

understandingofaproblemiscausedbyanimbalanceduetodifferencesinthespeedofacquisitionof

differentcognitivesubsystems.Forexample,atacertainstageofdevelopmentthechild’sacquisitionof

thesubsystemofnumberisinadvanceofthatoflengthandthiscreatesadisequilibrium.Onlywhenthe

twosubsystemsreachthesamelevelandareinequilibriumisthechildabletounderstandconservation

oflengthproblems.Assimilationandaccommodationarealsoinvolvedinthissecondtypeofequilibrium,

buttheyarecarriedoutinternallybymeansofreciprocalassimilationandaccommodationofthevarious

cognitivesubsystems.

Athirdtypeofequilibriumisbetweenanoverallcognitivesystemanditscomponentsubsystems,

thatis,betweenthewholeanditsparts.Theoverallsystem,byintegratingthevariouselements,assumes

variouspropertiesofitsownwhicharenotfoundintheindividualsubsystems.Thesesubsystemsdonot

ceasetoexistbyvirtueofbeingintegrated,butcontinuetoretaintheirownspecificcharacteristicsand

thusbedifferentiatedfromeachother.Oneexampleisthehierarchicalclassinclusionofanimals.The

category of animals integrates the various subcategories of lions, tigers, cats, dogs, and so forth. It

incorporatescertaincharacteristicsofeachofthese,buthasabroaderapplicationthananyofthem.The

subcategories are clearly differentiated from each other even though they may have certain

characteristicsincommon.Theintensionandextensionoftheclassofanimalsdoesnotduplicateentirely

thoseofanyofthesubclasses,justastheintensionandextensionofeachoftheseisdistinctfromthoseof

any other subclass. Another example is the coordination at the level of formal operations of the two

earliertypesofreversibility,negationandreciprocity,withintheoverallINRCsystem.TheINRCgroup

provides more possibilities than either of the two types of reversibility encountered earlier in


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development although these continue to exist as distinct processes even when they have become

integratedintotheINRCsystem.Thisthirdtypeofequilibriumisbetweentheprocessesofintegration

anddifferentiation,butalso involvesassimilationandaccommodation. Integration isaccomplishedby

assimilation,whereasaccommodationisresponsiblefordifferentiation.

One fundamentalquestion regarding thedynamicsof thisprocessofoptimizingequilibration is

this:Whatarethetransitionmechanismsthatenable theprogression fromone levelofequilibriumto

another more powerful type of cognitive structure? Piaget believes that a major factor is reflective

abstractionin itsdual formsofprojectionandreorganization.Piagetalsoproposessomemorespecific

principles to explain conceptual development: differentiation and integration, the relativization of

concepts,andthequantificationofrelations.

Differentiation and integration are two complementary processes that play a major role in

conceptualdevelopment.Differentiationistheprocessofconstructingnewschemesorelementsonthe

basisofexistingonessoastomeettherequirementsofexperience.Asaresult,finerandfinerdistinctions

aremadebetweenandwithin schemesor concepts. Integration is theprocessof establishing linksor

connectionsbetweentheseelementssoastomaintaintheirunity.

Whenfacedwithafamiliarobjectorexperienceforwhichhealreadyhasaschemeavailable,the

childusesthisschemetoassimilatethefamiliarexperience.If,however,heencountersanovelobjector

event,forwhichexistingschemesareinadequate,anewschemewillneedtobeconstructed.Thisnew

schemewilleitherbederivedfromanexistingonethatbearssomesimilaritytothenewexperience,or

may result from the reciprocal assimilation of two or more schemes that separately contain the

characteristics of this experience. The new differentiated schemes that are created do not exist in

isolation, but become related to, or integrated with, existing schemes into higher-order ones. By

introducingnewrelationshipsandcharacteristicstoconcepts,differentiationandintegrationallowfor

thesubsequentassimilationofmorevariedexperiencesandhenceopenupthepossibility for further

differentiationandintegration.

Differentiationandintegrationarecloselyrelatedtotheintensionandextensionofconcepts.Recall

thattheintensionofaclassorconceptreferstothecharacteristicsorpropertiesofthatclass.ForPiaget,


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thismeanstheactionsthatapersoncancarryout,ortheschemesthatapersonhasavailable,relatingto

thatclass.Theintensionofanapplereferstotheavailableschemesofred,round,orsweet.Extension

referstothemembersoftheclass,itsfieldofapplication,ortheobjectstowhichtheseschemesapply.In

thechild,orinanadultforthatmatter,intensionandextensionarenotstatic.Onthecontrary,theyare

constantlychangingastheresultofexperience,anditistheprocessesofdifferentiationandintegration

that underlie these changes. The first characteristics to be differentiated are the obvious superficial

aspectsofthephysicalenvironmentthatcanbedirectlyperceived.Theserefertophysicalexperience.

Gradually,asthechildreflectsonhisexperiencesoftheseobjects,hegoesbeyondmerelyapprehending

observable characteristics to draw inferences from them. Since inferences are processes of a

logicomathematical nature, differentiation and integration now occur within a logicomathematical

framework. Thus, knowledge moves from the periphery to the center of objects, from exogenous to

endogenousprocesses.Inthiswaydifferentiationandintegrationleadtoanincreasinglycomplexand

deeperunderstandingoftheworld.

Thedevelopmentof the “cat” concept can serveas an illustration. For theveryyoung child, the

conceptof “cats” initially refers to theactualcats thatheencountersathome, inhisneighborhood,or

even in stories. At this stage his cat scheme is very general, and indeed there is often an

overgeneralizationofschemes. Its intensionmightbesomethingwith four legs,a tail,and fur,and its

extensionmayevenincludesquirrels,badgers,orotherfour-leggedcreatureswithatailandfur.With

additionalexperienceofcatsofdifferentcolorssuchasginger,black,ortabby,orwithdifferenteyecolors,

blue, green, or yellow, he will construct or differentiate subschemes of cats to account for these

differences. Each subscheme has its own characteristics distinct from the others, but they are all

interrelatedandintegratedwithintheoverallschemeofcats.

Suchdifferentiationandintegrationcouldcontinueindefinitely,dependingupontheexperiences,

interests,andmotivationoftheperson.Thechildstartswiththeirphysicalcharacteristicsortheactions

thatcanbetakenwithcats,suchasstrokingorfeeding.Later,thepersonconsidersfeaturessuchasbreed,

personalitytraits,orgenesthatarenotdirectlyobservableandrequireinferences.Thusajudgeatacat

show,whoneedstogofarbeyondjustasuperficialknowledgeoftheobservablecharacteristicsofcats,

wouldhaveahighlydifferentiatedandintegratedconceptofcats.


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Piagetreferstothis increasinglywidenetworkofrelationsor linksthatareestablishedbetween

schemesandtheirelementsbymeansofdifferentiationandintegrationastherelativizationofconcepts.

The child initially understands objects, situations, or events in terms of a limited number of broad,

undifferentiated categories or schemes. As she begins to create additional subschemes or elements to

account for new differentiated characteristics, she establishes relationships and interdependencies

between these elements.With an increased number of elements comes an increase in the number of

compositions,andhenceofpossibleinterrelationshipsbetweenthem.Theserelationshipsmaycoverthe

observablecharacteristicsofactionsandobjects,theirphysicalfeaturessuchasshape,size,orcolor.Or

theymaycovercoordinations, that is, inferencesdrawnfromtheperson’sactionsthatconstructspatial,

causal,andlogicomathematicalrelationshipswithotherobjectsintheenvironment.Therelativizationof

conceptsunderliesamovement froman initial, superficial,andundifferentiatedunderstandingofan

objecttoadeeperandmorevariedgraspofitsvariousproperties,functions,andrelationships.

Considertheseriationofstickstaskasanexampleofrelativization.Theveryyoungchilddivides

thesticksintothetwobroadundifferentiatedschemesof“large”and“small.”Relationshipsbothwithin

and between the schemes are somewhat limited. The slightly older child begins to distinguishmore

characteristicsoflengthandcreatesanewschemeof“mediumsize.”Alreadymorerelationsneedtobe

constructedbecauseofthelargernumberofschemes.Laterthechildwillbeabletoseriatethesticks,first,

in a tried-and-error fashion, and thenmore systematically.When the seriation is finally grasped, the

childisabletosetuprelationsandinterdependenciesbetweeneveryelement.Eachofthesticksbecomes

linkedor related toeveryotherone inanordered systemof graded lengths ranging fromshortest to

longest.

Onetypeofrelationthatthechildslowlyconstructsisquantification.Thequantificationofrelations

refers to the child’s progressivemove from an initial focus on the qualitative features of a concept to

reasoning on its quantitative aspects. For example, in seriation, the young child first focuses on the

qualitiesof“bigness”or“smallness.”Alltheelementsinthe“large”categoryareviewedasbeingsimilar

toeachother,theyarealllargeanddifferentfromthoseinthe“small”one.Theconstructionofathird

“middle-sized”categoryisstillaqualitativeapproach,althoughitisamovetowardquantification.The

additionofthemiddlecallsforcomparisonsamongthethreecategoriesinwhichthechildfocusesmore

specificallyon,andbecomesmoresensitiveto,thedifferencesinlengthbetweenthesticks.


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Withincreasingsensitivitytothesedifferences,thechildcomestorecognizethat,evenwithineach

category,thesticksareperhapsnotquiteassimilarasfirstbelieved.Indeed,therearedifferencesamong

the various “large” sticks. Eventually, the child understands that all the sticks are related in a

quantifiablemanner.Eachstick,whencomparedwiththeothers,isalittlemore,orless,“long”or“short.”

Theyareallnowviewedasvariationsalongthesingledimensionoflength.Theimplicationisthatthe

childhasnowconstructedacontinuumwithunlimitedpossibilitiesofincludingnotonlyactualobjects

presented,butalsoanyotherpossiblevariationalongthatsamecontinuum.Forexample,thechildcould

envisagethepossibilityof includingsticksthatwillneveractuallybepresentedbutareonlymentally

conceived.

Thiscontinuumisalogicomathematicalconstructionofwhichtheactualstickspresentedformonly

onepart.Furthermore,atthispoint,thechildalsounderstandsthat“more”and“less”arereciprocally

related.Asthesticksbecomelonger,or“morelong,”theyalsobecome“lessshort.”Amoveinthepositive

directionof“morelong”implicitlyinvolvesacorrespondingmoveintheopposite,negativedirectionof

“lessshort.”

Forpurposesofsimplicity,thepresentexamplehasconcentratedonthequantificationofasingle

property,the“long-short”dimensionoflength.Inreallife,ofcourse,thesituationisfarmorecomplex.

Objectsvaryalonganumberofdimensions.Applesarenever identical.Each individualapplecanbe

quantifiedalonganumberofdimensions:size,color,texture,sweetness,tonamebutthemostobvious

characteristics.All thesedifferences canbeplacedalongquantifiable continua thatdonotnecessarily

develop at the same pace. As quantification proceeds for these various differences, it allows for the

possibilityofanincreasingnumberofrelationships,andinthiswaynotonlycontributestowardamore

objectiveunderstandingofreality,butalsotowardbetterandbetterformsofequilibrium.

Inevitably, the study of equilibration and the successive levels of equilibrium along the path of

development leads to the reverse of the coin, disequilibrium. As Piaget states, the existence of any

positiveinstancenecessarilyimpliestheexistenceofitsnegation.Consequentlythestudyofequilibrium

leads to the study of disequilibrium. Piaget holds that disequilibrium is of crucial importance in the

processofequilibration,sinceitistheprimemotorofintellectualdevelopment.Disequilibriummotivates

thesearchforbetterformsofknowledge,andthusprovidesthelinkbetweenonelevelofequilibrium


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andthenext.

Disequilibrium,orimbalance,occurswhenapersonencountersanobjectoreventthatheisunable

toassimilateduetotheinadequacyofhiscognitivestructures.Insuchsituations,thereisadiscrepancyor

aconflictbetweenthechild’sschemesandtherequirementsoftheexperience.Thisisaccompaniedby

feelings of unease. Piaget refers to this situation as a disturbance, perturbation, or conflict. Generally

speaking, a disturbance is anything that prevents the person from assimilating an experience or

achievingagoal.Sinceassimilationisinvolvedindisturbances,andassimilationalwaysoccursrelativeto

anassimilatoryscheme,theconceptofdisturbanceisarelativeone.Whatmaybeadisturbancetoone

person,becauseof thenatureandtypeofschemesavailable,maynotbeso foranotherperson,either

becausehisschemesarenotsufficientlydevelopedforhimeventoperceivetheeventasdisturbing,or

becausehisschemesaresowellorganizedthataparticulareventorexperienceisrapidlyassimilated.In

theconservationofliquidstask,theveryyoungchildstateswithnofeelingofuneaseorconflictthatthere

ismoreliquidwhenitispouredintoatallthincontainerthanwhenitisinashortfatone.Forhim,the

situationisnotdisturbing.Thissamesituationwill,however,produceconflictintheslightlyolderchild,

who feels unease at stating that the same water is more, or less, depending upon the shape of the

container.Theevenolderchildagainfeelsnoconflictbecausehecanexplainthesituationinalogical

way.

When faced with a disturbance, the person reacts with responses that attempt to regulate the

conflict.Theseresponses,orregulations,willdifferdependinguponwhatschemesareavailable.Inmost

ofthestudiescarriedoutinGeneva,threetypesofreactionstodisturbanceshavebeenfound,andPiaget

callsthemalpha,beta,andgamma.

Alphareactionsaregenerallyfoundintheveryyoungpreoperationalchildwhooften,becausehe

doesnotperceivetheeventasdisturbing,simplyignoresit.Ifheperceivesitatall,itwouldbeasaminor

disturbancethatrequiresonlyslightmodificationofhisstructures.Ontheotherhand,hemaydeformthe

eventcompletelysoastofithisschemes.Inbothcases,verylittlechangeoccurstothecognitivesystem.

Alpha reactions, therefore, either modify the disturbing element so as not to interfere with existing

cognitivestructuresorignoretheconflictaltogether.Theyoungchildwhohasonlyschemesforsquares

andcirclesmayassimilateanovelshapesuchasatriangleintothesquarescheme,therebycompletely


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deforming the experience. Similarly, a child who, during the early stages of language development,

refers to all animals as “dogs,” is not disturbed by feelings of unease. She assimilates all four-legged

creaturesintoherunderlyingschemeofdogs,regardlessoftheextenttowhichrealityisdeformedtodo

this.

With beta reactions, which are usually found during the later preoperational and concrete

operationalstages,thechildseekstoincorporatetheconflictingeventintohiscurrentcognitivesystem.

Todothis,hemodifiesandreorganizesthissystemsoastotakeaccountofthedisturbance.Thechildof

thislevelnotonlydistinguishescirclesfromsquares,butwillcreatenewschemeswhenheencounters

triangles,rectangles,andsoon.Thedisturbance introducesvariations intothesystembycausingnew

schemestobecreatedthatwillexistalongsidetheoriginalones.Thevariationsarepartialbecausethe

child is able to create only a limited number of new schemes or subcategories. Beta reactions are

neverthelessanimprovementonalphaonesbecausetheyattempttoadaptthesystemtodisturbances

perceivedintheenvironment.

Finally,gammareactions are foundat the formaloperational level.Here theperson constructs a

systemthatallowshimtoanticipateallpossiblevariationsbymeansofinferences.Thesystembecomesa

closedoneandthelikelihoodofdisturbanceisreduced.Theoriginaldisturbingelementbecomesone

possible variation within a whole system of possible transformations. The child at this level can

anticipate the possibility of all sorts of shapes, both regular and irregular, even before he actually

perceivesthem.

The alpha, beta, and gamma reactions are not necessarily confined to particular stages of

development.Piagetbelievesthatthesametypesofreactionsaretobefoundinanyareaofknowledge,

sothatifanadultwereexposedtoatotallynewtopic,shetoowouldexhibitthesamesequenceofalpha,

beta,andfinallygammareactionswhenshemasterstherelevantknowledge.

In sum, disequilibrium, a major cause of cognitive development, is caused by disturbances,

perturbations,or conflicts thatoccurwhen there isadiscrepancybetween thechild’s schemes,which

determinewhatsheisabletoassimilate,andtherequirementsofcertainexperiences.Disequilibriumis

relativetothechild’sdevelopmental level.ThechildreactstotheconflictbyregulationswhichPiaget


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categorizesasalpha,beta,orgamma,dependingupontheschemesavailable.

Contradictions.Closelyrelatedtocognitiveconflictanddisequilibriumisthenotionofcontradiction

(seePiaget,ExperimentsinContradiction,1981a).Oneexampleistheconservationofliquidstask,where

liquid appears to bemorewhen in a tall thin container than in a short fat one. The person starts to

question this contradiction and, to resolve it, tries to discover its reasons or causes. In an attempt to

explorethenatureofcontradictionandrelateittotheequilibrationprocess,Piagetandhiscolleagues

havecarriedoutanumberofstudiesinthisarea.

Inoneofthetasks,thechildrenwerepresentedwithaseriesofsevendisks,referredtoasAtoG,

eachofwhichwasimperceptiblylargerthanthepreviousone.Thediskswereattachedtoaboardsothat

anysingleonecouldonlybecomparedwiththoseimmediatelybeforeandafterit.ThusdiskAcouldbe

comparedwith B, Bwith C, and so on. The last and largest disk, G, was not attached, and could be

compared with any other disk of the series. Since each disk was only very slightly larger than the

previousone,thedifferencebetweeneachofthesixattacheddiskswasimperceptible,althoughitwas

evident that G was larger than A. The child was asked to explain the contradictory situation of an

apparentequalitybetweenthefirstsixdisks,A=B,B=C,andsoon,andthenonequalitybetweenGand

A.

Inthisandotherstudiesofthesamenature,threestageswerefoundinthechild’sunderstanding

of contradiction. During an initial stage, the young child is not aware that there might be any

contradictioninthesituation,inthiscaseofadmittingthatthefirstsixdisksareequal,thatFisequaltoG,

andthatGislargerthanA.HealsoappearstofeelnouneaseatstatingatonepointintheinterviewthatF

is the same size as G and later at another point that G is larger than F. Either he forgets his former

statement, or he does not relate the two statements together, and thus does not recognize the

contradiction.Childrenwhoremembertheirpreviousstatementsattempttoreconcilethecontradiction

butdosowithinappropriateactions.SomeofthemsaythatGisthesameasF,thatFisthesameasA,and

thatGislargerthanA.Aswehaveseenintheprevioussection,thesearealphareactions.

Atthesametimeasexhibitingalackofawarenessofmanycontradictions,theyoungchildofthis

initial stage provides examples of what Piaget calls pseudocontradictions, that is, he interprets as


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contradictory certain relationships or situations that are not so to the person at a higher level of

development.Forexample,intheseriationtask,ayoungchildfindsitcontradictorythatastickcanbe

simultaneously larger(thanprevioussticks)andsmaller(thantheonestofollow)orthatahalf-filled

glasscanbehalffullaswellashalfempty.Hebelievesthatastickiseitherlargeorsmall,aglasseither

emptyorfull,butnotbothatthesametime.

Duringasecondstage,thechildbeginstobeawareofthecontradictionsinhisstatements.Hewill

search for solutions, but since he does not yet have the ability to overcome these contradictions, his

solutionswillbecompromiseones.Intheearlierdisksexperiment,hewillsetuptwodistinctclasses:the

“small”disks,A,B, andC, and the “large”ones,E, F, andG, but thenhemighthave troubledeciding

whether theboundarydisk,D,shouldbe in the“small”or“large”categoryandwillmove itbackand

forthbetweenthetwo.SomechildrenbelievethatdiskGchangesinsize,andfirstsayitisthesamesize

asF,butthenthatitbecomeslargerwhencomparedwithA.Otherchildreninthisstagemaycreatethree

classes,withanintermediatesizebetweenthesmallandlargecategories.Forexample,AandBwouldbe

small,C,D,andEintermediate,andFandGlarge.Allthesedifferentreactionsconstitutebetabehavior,

orthecreationofvariationswithinthesystem.

Finally,ataround11to12years,thestage3childunderstandsthatthedisksformaseriation,with

imperceptible differences between each successive disk. He has quantified the size relationship. By

doingthishehascreatedanewcognitivestructurethatisabletoassimilatethedisturbingelement.This

understanding of the situation resolves the imperceptible differences problem. It allows the child to

explaintheapparentcontradictionandtoanticipatethepossibilityofanunlimitednumberofdisks.

Piaget states that the child’s initial unawareness of contradiction occurs because he first

concentrates on the observable features of a situation or the results of an action, onaffirmations, and

neglectsthenonobservables,orwhathasbeenexcludedbytheaction,thenegations.Thecommonfeature

oftillcontradictionsisanincompletecompensationbetweenaffirmationsandnegations.Fortheyoung

child,affirmationspredominateovernegations.Thisisbecauseitiseasiertoapprehendpositivesthan

negatives.Theperceptionofanabsentobjectorcharacteristicinvolvesexpectations thatgobeyondthe

informationactuallyprovidedbytheobjects.Wecanspontaneouslythinkofredobjects(affirmations),

but we need to construct or infer the category of nonred ones (negations) since they are not given


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perceptually.Negationrequiresinference,thatis,aninternalconstruction,andthechildneedstimeto

buildtheseinternalconstructions.

Onlywhen the intension and extension of a concept have become sufficiently differentiated to

cover negations will the child be able to overcome contradiction. The awareness of contradiction

presupposes theability todraw inferences. In the foregoing task, theyoungchildconcentrateson the

observablesoraffirmationsthat“AisthesameasB,”“BisthesameasC,”andsoon,until“Fisthesameas

G”and“GislargerthanA.”Tofeelcontradictionandtoovercomeit,thechildmustbeabletoinfertwo

things.First,hemustrealizethattherelationship“GislargerthanA”(affirmation)impliesthat“Aisnot

equaltoG”(negation).Second,andmorecomplex,thechildmustbeabletoinfer,byusingaschemeof

transitivity,that“AisthesameasF.”Sinceonlyadjacentdiskscanbecompared,thiscannotbeobserved

directlyandisalsoanegation.Itisonlyatquiteanadvancedstageofdevelopmentthatthechildacquires

transitivityandhencebecomescapableofconstructingthisnegation.

All this may seem contrived, artificial, and irrelevant to the study of normal intellectual

development, but that is not so. On the contrary, Piaget believes that the concepts of affirmation and

negationareof tremendous importance to thewholeof cognitivedevelopment.This isbecauseevery

actionnecessarilyandimplicitlycontainsbothapositiveandanegativeaspect,bothanaffirmationanda

negation.Theclassofredobjectsimpliesalltheobjectsexcludedfromthisclass,ortheclassofnonred

objects.Additionimpliessubtraction,andsoon.Affirmationsandnegationsarefoundateverylevel,in

perception, sensorimotor actions, and mental operations. Initially, the young child grasps only

affirmations.Onlyslowlyandlaboriouslydoesheconstructnegations.Hisnegationsaresystematically

graspedonlywhen thechild is able to construct reversibleoperational structures inwhich there is a

completecompensationofaffirmationsandnegations.

AlthoughPiagetreachedtheseconclusionsonaffirmationsandnegationsduringthelatterpartof

hiscareer,hefeltthattheyweresuchanimportantexplanatoryframeworkforintellectualdevelopment

asawhole thathe returned tomanyofhis earlier studies, inparticular the conservation tasks, inan

attempttoexplainpastfindingsintermsofthechild’sinitialprimacyofaffirmationsandhissubsequent

constructionofnegations.


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Toendthissectiononequilibration,letuslookathowPiagetincorporatestheconceptsofempirical

and reflective abstraction, optimizing equilibration, equilibrium, and disequilibrium, into a model of

cognitivedevelopmentwhichhecallsthespiralofknowing.Thisspiralofknowingissymbolizedbyan

invertedcone,asshowninFigure18.Theinnerspiralofthecone,A,representsinternalconstructionsin

theformofreflectiveabstractionwithitssuccessiveprojectionsandreorganizationsthatarecarriedout

withintheoptimizingequilibrationprocess.Theouterlayers,EandE',representinteractionswiththe

environmentintheformofempiricalabstractionwithintheframeworkofpreviousreflectiveabstraction.

These two processes, A and E/E', are in constant interaction as new projections and reorganizations

result from interactions with the environment. Three vectors, a, b, and c, determine the progress of

cognition.Vectorarepresentsthehierarchicalsuccessionofcognitivestructures,startingwithreflexes,

moving throughsensorimotorschemes,preoperational structures, concreteoperations, finally toreach

prepositionaloperations.Vectorbrepresentsthemodificationsofthestructuresanddis-equilibriathat

result from interactions with the environment. Vector c represents explorations of the environment

whichleadtopartiedorcompletereorganizationofthestructures.

FIGURE18The spiral of knowing. From Adaptation Vitale et Psychologie de I’Intelligence: Selection Organique etPhénocopie,byJ.Piaget.Copyright1974byHermann,Paris.ReprintedbypermissionofHermann,Paris.

Theever-wideningbutopencirclesofspiralArepresentthreemajorcharacteristicsofequilibrium.

First,thereistheunderlyingpoweroftheequilibrium.Thisreferstothenumberofactionsthatcanbe


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carried out and hence to the number of schemes available, or the field of application of the cognitive

structures. As the field of application extends and schemes becomemore differentiated,more actions

becomepossible,andequilibriumbecomesmorepowerful.This increase inschemes,or in the fieldof

application,isreflectedinthewideningofthecircles.

Theyoungchild’sclassificationsystem,forinstance,wouldberelativelyundifferentiatedwithfew

classesandsubclasses.Withonlyafewschemesandsubschemesavailable,itwouldnotbepossiblefor

himtocarryoutmanyactions,ortoestablishmanylinksorrelationshipsbetweenthem.Thisequilibrium

wouldnotbeverypowerful.Fortheolderchildwhohasalreadyconstructedahierarchicalclassification

system with numerous subclasses, the possibility of links and relationships becomes boundless. The

equilibriumisthereforeinfinitelymorepowerful.

Thepowerofaparticularlevelofequilibriumisdirectlyrelatedtothedegreeofrelativizationand

quantification of concepts as well as to differentiation and integration. Understanding becomes

increasingly coherent as relationships and connections between schemes increase. Consequently an

increaseinpowerofequilibriumisaccompaniedbyagrowthincoherence.

Anothercharacteristicofequilibriumisstability,whichisdefinedasthecapacitytocompensateby

actions ormental operations for changes in the environmentwithout disturbing thewhole structure.

When a system is stable, the introduction of new elements does not destroy it. The structure easily

incorporates the new elements and does not change. Stability is achieved when any action in one

direction (affirmation) can be compensated for or canceled out by an action in an opposite direction

(negation).Withastableequilibrium,affirmationsarebalancedbynegations.Inseriation,forinstance,

the young child who is able to construct a series only by trial and error will, when presentedwith

additional sticks to insert, find it necessary to destroy thewhole series and start from the beginning

again, whereas the child with amature seriation structure can incorporate an unlimited number of

additionalstickswithoutdistortingtheseries.Thelatterhasamorestableequilibrium.Perfectstabilityis

achieved when the person is able to anticipate disturbances or conflict before they are actually

encountered.

Athirdcharacteristicofequilibriumisitsopenness,whichreferstotheabilitytoincorporatenew


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ideasandraisenewquestionsandproblems.Thesewill lead tonovelactionsandresponses to solve

theseproblems.Thisopennessisreflectedintheupwardmovementofthespiral.Eachsuccessivelevelof

equilibrium in the equilibration process solves previous problems and provides answers to previous

questions,butat thesametimeopensupthepossibilityofnewproblemsandnewquestions. It is this

opennessthatensuresthatcognitioniscontinuallydeveloping.Thesethreecharacteristicscombined—

power, stability, and openness—ensure that the equilibration process continually conserves past

understandingandconstructsnewknowledge.

POSSIBILITY

Piagetwasgreatlyconcernedwiththeconstructionofnewknowledge,aproblemunderlyingthe

equilibrationprocessand thespiralofknowing.Howdoes thechildcreatenewresponsesoractions?

What accounts for the openness of the spiral toward new possibilities of disequilibrium and re-

equilibration?

In a number of studies designed to investigate the development of the concept of possibility,

childrenwererequiredtocomeupwithasmanysolutionsaspossibletocertainproblems.(SeePiaget,Le

PossibleetleNecessaire,1981b,1983.)Forexample,theywereaskedtoindicateallthedifferentways

theycouldthinkoftoplacethreediceonapieceofcardboard,tomakeatoycargofrompointAtopointB,

ortocutupapapersquare.

Findingsof this typeofstudyshowedthreemainstages inthedevelopmentofpossibilities.The

youngchildof4 to5yearscomesupwitha limitednumberofpossiblesolutions,oneor twoatmost.

These few possibilities are often accompanied by a strong feeling of necessity, which Piaget calls

pseudonecessity.Thisisthefeelingthatitisimpossibletochangerealityortheimpressionthatbecause

this is how things are, this is how they necessarily have to be. Reality, as given in the few solutions

suggested,isfeltofnecessitytobetheonlypossibility.

Inthestudywiththethreedice,theveryyoungchildrenof4to6yearswereabletocomeupwith

onlyafewsuggestions,andthesewereoftengeneratedbyaprocessofanalogy.Forexample,onechild

placedthethreediceinthethreeanglesofthesquarepaper.Whenaskediftherewereotherways,he


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movedoneofthedicetothefourthangle, thenmovedthethreedicearoundthevariousangles,each

timeleavingadifferentanglewithoutadie.Childrenofthislevelalsobelievethatthebestsolutionsare

thosethataresimilartothefirstoneproposed.

Atthenextstagetheolderchildrenareabletoincreasethenumberofpossiblesolutionssuggested,

andcomeupwitharangeof“co-possibles,”thenumberofwhichincreasewithage.Childrenof7to8

yearsproducefourtofivepossiblesolutions,whereasby9to10yearstheycanenvisagethirtyormore

solutions,eventhoughtheythemselvesarenotalwaysabletodescribeallthesepossibilities.Withthe

dice problem, children of 7 to 10 years suggested numbers ranging from twenty to ten thousand,

althoughwhentheexperimentersuggestedtenthousand,onechildfeltthatthisnumberwastoohigh.

Theyrealizethatthesemanysolutionsexistasabstractco-possibleswhichsomeoneelsemaybeableto

describe,eventhoughtheythemselvescannot thinkofallof them.At thisstage, thebestsolutionsare

consideredtobethosethatdifferthemostfromtheonesthathavealreadybeensuggested.

Finally, around 11 to 12 years, children infer more or less immediately that the number of

possibilitiesisunlimited.Thechildrealizesthatanysolutionproposedisonlyasampleofsuchavast

numberofsolutionsthatitwouldnotbepossibletothinkofthemall.Atthispoint,anunlimitednumber

ofpossibilitiesisconceptuallydeducedratherthanactuallyobserved.

The idea of an unlimitednumber of possibilities is obviously not something the child is able to

observe in theenvironment,but is something thatheconstructs internallybymaking inferences from

whatisactuallygiveninasituation.Aswehaveseen,inferencesrequireaninternalconstructionthat

goes beyond observables. This explains why it takes so long for a child to acquire the concept of

possibility.

Piaget maintains that the conquest of possibilities is a crucial mechanism of the equilibration

process.Eachnewpossibilityopensupafieldofvirtualorpotentialnewpossibilities.Asthechildsolves

problemshebeginstodiscoverothers,andtorealizethateachproblemcangenerateahostofpossible

solutions,notallofwhichheisabletodescribe.Itisthiscreationandmultiplicationofpossibilitiesthat

providestheopennessofequilibration,andexplainstheproductionofnoveltywhichisoneofthebasic

questionsraisedbyPiagetinhisgeneticepistemology.


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Studies were also conducted into the feeling of necessity in the child. Their results show that

necessity follows a parallel development to possibility. Young children start with the feeling of

pseudonecessity,whichwasfoundinthestudiesofpossibility.Olderchildrenproduceasmallnumber

ofco-necessitiesandgrasptheideathateachoftheco-possibilitiesorsolutionstoaproblemisequally

necessary.Finally,around11to12years,thechildexplainsthatthereareanunlimitednumberofco-

necessities.

Inhisdiscussionsontherelationshipamongpossibility,necessity,andreality,Piagetstatesthatin

the early stages of development, there is a lack of differentiation among these threemodalities. The

youngchild,owingtohislimitednumberofschemes,believesthattheonlypossibilitiesarethosethatare

observable.Moreover,theseareconceivedofasbeingnecessary,whichisinfactapseudonecessity.Asthe

child’sschemesmultiply,andasmoreconnectionsbetweenthemareestablished,hebecomescapableof

goingbeyondobservablesandofdrawinginferencesaboutreality.Itistheseinferencesthatleadtothe

construction of a larger number of co-possibilities. Possibilities are the result of the differentiation of

schemes. At the same time, with development, the initial regulations are changed into reversible

operations.Operationsareaccompaniedby feelingsofnecessity.Aswehaveseen in theconservation

tasks,necessityisonecharacteristicoflogicalreasoningprocesseswhichresultsfromtheintegrationof

schemes and their transformation into operatory structures. Operations represent a synthesis of the

possible and the necessary, as well as a synthesis between integration and differentiation which is

characteristicofthethirdtypeofequilibrium.

Summary and Conclusion

Piaget distinguishes between development and learning in the narrow sense. Development is

influencedby four factors.Physical structuresboth limit certain aspects of cognitive development and

make others possible, butmaturation in itself is not sufficient to explainmental development, partly

becausethereareobviousculturaleffectsoncognitivefunctioning.Asecondfactorisexperience.Physical

experience involves gaining knowledge of objects by observing them directly. Logicomathematical

experience involves an internal coordination of the individual’s actions which at the outset are

performedon theobjects, but laterdonot require this physical support.However, these two typesof

experiencearenotsufficienttoexplaindevelopment,becausetheyomit,amongotherthings,theeffects


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of social influences. A third factor, socialtransmission, refers to the acquisition of knowledge by such

techniques as reading or instruction. This factor is also insufficient to explain development, partly

becauseitignorestheroleofthecognitivestructureswhichmakesocialinfluencesefficientorinefficient.

Afourthfactorisequilibration.Thisconceptinvolvesthechild’sself-regulatoryprocesseswhichleadhim

throughprogressivelymoreeffectivestatesofequilibrium.Thenotionofequilibriumreferstoasystemof

exchangesbetweenanopensystemand its surroundings. It impliesasystemthat is inactivebalance

withitsenvironment.Thedegreeofequilibriumisdefinedbyasystem’spositiononthreedimensions:

fieldofapplication,stability,andopenness.Thegreaterthedegreeofthesequalities,themoreperfect

the equilibrium. Research stresses the central role of internal conflict in promoting equilibration. As

equilibrationproceeds,thechildcomestoappreciatetherolesofpossibilityandnecessity.

Piagetdistinguishesbetweenlearninginthenarrowsenseandlearninginthewidersense.The

former involves the mere acquisition of specific responses to particular situations. Such learning is

superficial:itisunstable,impermanent,andunlikelytogeneralize.Learninginthewidersenseinvolves

theacquisitionofgeneralcognitivestructures.Indeed,theseareusedtogivemeaningtospecificlearning

andoftenmakeitpossible.Thus,developmentexplainslearning.Further,developmentoccursthrougha

self-regulatoryprocessinvolvingthefourfactors,notthroughtheacquisitionofspecific informationor

responses.Learningthereforecannotexplaindevelopment.

Piaget’s theory makes an enormous contribution in focusing on the processes of self-regulated

development.Piagetcontinuallystressesthechild’scontributiontothedevelopmentalprocess.Itisthe

childwhotriestoassimilatetheconservationproblemintoalreadyavailablestructures,anditisthechild

who feelsa subjective lackof certaintyabouthis solution.Thechilddoesnot simply react toexternal

events,buttakesanactivepartinhisowndevelopment.Piaget’snotionofself-regulationisextremely

valuable. It seems to capture a goodpartof the realityof children’sdevelopment. It also serves as an

alternative to human engineering views which stress the external shaping of responses and the

modificationofbehavior.

EDUCATION

Inthepresentsection,wewillconsidersomeimplicationswhichPiaget’sviewsholdforeducation.


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WhilePiagethasdevoted relatively little attention toproblems in this area,hiswork canmake three

typesofcontributionstoeducationalpractice.First,Piaget’stheoryprovidessomegeneralprinciplesfor

theconductofeducation.Second,Piaget’sstudiesof thedevelopmentofspecific logical,mathematical,

andphysicalconceptsinthechildcanassistthedevelopmentofcurriculaandteachingpracticesinthese

areas.Third,Piaget’sclinicalinterviewingtechniquecanproveavaluablediagnosticandevaluativetool

fortheteacher.ThissectionthereforewilldescribePiaget’sthoughtswithrespecttoeducationandwill

discuss these three types of potential contributions. The section closes by considering possible future

directionsforaPiagetianapproach.

Itshouldbeemphasizedattheoutsetthatour intentionisnottoproposeparticularcurriculaor

instructionalpracticesonthebasisofPiaget’swork.AsSinclair(1976,p.11)putsit,

I’m not sure thatmuch can be donewith application of Piaget’s theory in a detailedway by the Piagetianpsychologist. . . .Thereareabsolutelyno [direct]practical indications in theworkofPiagetwith respect toeducation....Piagethasverylittletosaywithrespecttospecificproblemssuchashowtoteachreadingandwriting,andvariousothereducationaltechniques.

Hence,wewillbeconcernedwiththemajorguidingprincipleswhichemergefromPiaget’swork.

LikePiaget,wefeelthattheimplementationoftheseprinciplesrequiresthespecialskillsoftheeducator,

whounderstandsthedistinctiveconditionsoftheschoolsetting,ratherthanthepsychologist.

A Child-Centered Approach

OneofPiaget’smostsignificantcontributions ishisnotionthat theyoungchild isquitedifferent

fromtheadultinseveralways:inmethodsofapproachingreality,intheensuingviewsoftheworld,and

intheusesof language.Piaget’s investigationsconcerningmatterssuchastheconceptofnumberand

verbal communication have enabled him to produce a change—indeed, one might almost say a

metamorphosis—in our ways of understanding children. As a result of his work we have become

increasingly aware that the child isnot just aminiature although lesswiseadult, but abeingwith a

distinctivemental structure that is qualitativelydifferent from the adult’s. The child views theworld

fromauniqueperspective. For example, the childbelow the ageof7 years trulybelieves thatwater,

whenpouredfromonecontainertoanother,gainsorlossesinquantity,dependingontheshapeofthe

secondcontainer.Orinthecaseofnumber,theyoungchild,althoughabletocountto20ormore,hasno


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conception of certain fundamental mathematical ideas. He may think, for example, that a set of five

elements is largerthanasetofeightelements if thephysicalarrangementof thesetstakesoncertain

forms.

Theseandmanyotherunexpecteddiscoveries leadtothesurprisingrecognitionthatthechild’s

worldisinmanywaysqualitativelydifferentfromthatoftheadult.Onereasonforthechild’sdistinctive

viewofrealityisadistinctivementalstructure.Theyoungchild(belowabout7or8yearsofage)centers

hisattentiononlimitedamountsofinformation;heattendstostatesratherthantransformations;heis

egocentric,failingtotakeintoaccountotherpointsofview;hisconceptsarerelativelyundifferentiated;

andheisincapableofformsofthought,suchasreversibility,whichallowsymbolicmanipulationofthe

dataofexperience.Eventheolderchild(between7and11years)isstronglytiedtoconcretesituations

although he is capable of fairly subtle mental operations. The child reasons best about immediately

presentobjectsandfailstoappreciatethecontradictionsorpossibilitiesinherentinasituation.

Oneresultofthechild’scognitivestructureisaviewofrealitywhichtotheadultseemschaoticand

unnatural.Anotherconsequence is that theyoungchild’suseof language isdifferent fromthatof the

adult.That is, thewords that thechildusesdonothold thesamemeaning forhimas theydo for the

adult. Adults often overlook this point. We usually assume that if a child uses a particular word, it

automaticallyconveysthesamemeaningthatitdoeswhenanadultusesthatword.Adultsoftenbelieve

thatonceachildhaslearnedthelinguisticlabelforanobject,hehasavailabletheunderlyingconcept.

ButPiagethasshownthatthisoftenisnotthecase.Thechilddoeslearnhiswordsfromtheadult,but

assimilates them into his ownmental structure,which is quite different from the adult’s. Thewords

“sameamounttodrink,”forexample,areinterpretedinonewaybythe4-year-old,andinanotherway

by the adult. Only after a period of cognitive development does the child use these words and

understandtheminthesamewayasthemorematureperson.

Theimplicationofthisverygeneralproposition—thattheyoungchild’sthoughtandlanguageare

qualitativelydifferentfromtheadult’s—isalsoverygeneral:theeducatormustmakeaspecialeffortto

understandtheuniquepropertiesofthechild’sexperienceandwaysofthinking.Theeducatormusttry

to adopt a child-centered point of view, and cannot assume that the child’s experience or modes of

learningare thesameashisown.Forexample,while theeducatorhimselfmay learnagreatdealby


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readingabookorlisteningtoalecture,similarexperiencesmaybefarlessusefulfortheyoungchild.The

educatormayprofit froman orderly sequence ofmaterial, but perhaps the child does not.While the

educatormayfeelthatagivenideaissimpleandindeedself-evident,thechildmayfinditdifficult.In

short, it is not safe to generalize from the adult’s experience to that of the child. The educator’s

assumptions,stemmingastheydofromanadultperspective,maynotapplytochildren.Theeducator

needstoimprovehisowncapacitytowatchandlisten,andtoplacehimselfinthedistinctiveperspective

ofthechild.Sincethemeaningexpressedbythechild’slanguageisoftenidiosyncratic,theadultmusttry

tounderstandthechild’sworldbyobservinghisactionsclosely.Therearenoeasyrulesorproceduresto

usetounderstandthechild.Whatisnecessaryisconsiderablesensitivity—awillingnesstolearnfrom

thechild,tolookcloselyatthechild’sactions,andtoavoidtheassumptionthatwhatistrueorcustomary

fortheadultisalsotrueforthechild.Theeducatorneedstointeractwiththechildinaflexiblewayto

gaininsightintothelatter’scurrentleveloffunctioning.Withthisattitude—awillingnesstoobservethe

childandtolearnfromhimtheeducatorcanbegintounderstandthechildandtotailortheeducational

experiencetothechild’sneeds.Educationmuststemfromachild-centeredperspective.

Activity

Theconceptthatchildren—orindividualsofanyage—learnbestfromself-initiatedactivityisvital

fortheguidanceofeducation.ThroughoutthisbookwehaveseenthatPiagetplacesmajoremphasison

theroleofactivity—bothphysicalandmental—inintellectualdevelopment.InPiaget’sview,“toknow

anobject,istoactonit”(Piaget,“DevelopmentandLearning,”1964,p.8).Almostfrombirth,theinfant

touchesobjects,manipulatesthem,turnsthemaround,looksatthem,andthroughsuchactivitiesgains

an increasingunderstandingof their properties. It is through action, notpassiveobservation, that he

developsanunderstandingoftheworld.Indeed,thereisasenseinwhichthechildconstructsreality.

For the older child, too, the essence of knowledge is activity. Thus, when the preoperational child

attempts to remember (retain his knowledge over time), he actively organizes the material by

assimilatingittoavailableschemes.Often,thechild’sunderstandingisnotonaverballevel,whichinfact

usually takes a long time to develop. The adolescent’s knowledge also involves activity: in trying to

understandphysicalphenomena,heactivelygenerates combinationsofhypotheticalpossibilitiesand

transformstheminthought.Hedoesnotsimplyrespondtotheimmediatepresent.Tosummarize,inall


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cases—whetherbehavioralschemes,concreteoperations,orformalstructuresareinvolved—theessence

ofknowledgeisactivity.

Topromotegenuineunderstanding, the teacher should therefore encourage the child’s activity.

Whentheteacherattemptstobypassthisprocessinvariousways—forexample,bylecturingataclassof

youngchildren—theresultisoftensuperficiallearning.Perhapsthisisonereasonwhysomuchofwhat

is taught in school is immediately forgotten after the school year ends. By contrast, genuinely active

learningcanleadtoamoresolidandlong-lastingunderstanding.

Awordofcautionisneededinconnectionwiththisemphasisonactivity.Sometimesteacherstakeit

to refer solely tophysicalactivity; theybelieve that themanipulationofobjectsautomatically leads to

learning. This may be true in some situations, but it is not always the case. Take, for example, a

preschooler who is actively engaged in playing with the toys provided at school—swinging on the

swings,orbuildingcastlesinthesandpit.Thischildwillprobablylearnsomethingabouttheproperties

oftoys,swings,orsand,andabouthisownrelationshipstotheseobjects.Thisisimportantknowledgefor

the child at this stage.Take, on theotherhand, the caseof ahigh school student following a science

lesson.First, the teachercarefullydemonstratesaparticularexperiment to theclass.Theteacher then

asks thepupils to carryout the sameexperiment, forwhich theprocedure is given stepby stepona

certainpageofthetextbook.Isthepupilwhocarriesoutthecorrectphysicalactionsasdescribedinthe

bookreallylearning?Notnecessarilyso,oratleastheisnotalwayslearningthethingsthattheteacher

intendedhim to learn. If thepupil’sphysicalactionsarenotaccompaniedbyparallelmentalactivity,

suchasthinkingofalternativetypesofresultsandtheirmeaning,itisunlikelythatmuchrealandlasting

learningwill occur. At this stage, simply tarrying out physicalmanipulationswill not producemuch

learning.

AsPiaget(ScienceofEducationandthePsychologyoftheChild,1970c)putit,“althoughthechild’s

activity at certain levels necessarily entails the manipulation of objects, ... at other levels the most

authenticresearchactivitymaytakeplaceinthespheresofreflection,ofthemostadvancedabstraction,

andofverbalmanipulation(providedtheyarespontaneousandnotimposedonthechild)”(p.68).

Acceptance of the principle of active learning requires a considerable reorientation of beliefs


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concerningeducation.Teachers(andthepublicatlarge)usuallyconsiderthattheaimofeducationisto

impartexistingknowledge,oftenofafactualtype,asefficientlyaspossibletothepupil,whowillthen

absorb it in the form presented. In this view, if students were allowed to design and conduct

experiments, there would not only be chaos in the classroom, but there would also be no learning.

AccordingtoPiaget’stheory,thesebeliefsandattitudesareerroneousforseveralreasons.Teacherscan

infactimposeverylittleknowledge.Itistruethattheycanconvincethechildtosaycertainthings,but

these verbalizations often indicate little in the way of real understanding. Moreover, it is seldom

legitimate to conceiveofknowledgeas a thingwhich canbe transmitted.Certainly the childneeds to

learnsomefacts,andthesemaybeconsideredthings.Sometimes,drillorprogrammedinstructionmay

assistinlearningofthistype.Butoftenthechilddoesnotlearnevenfactswhenimposed;thestudent

mayhavetodiscoverthemhimself.

Inaddition,factsarebutasmallportionofrealknowledge.Trueunderstandinginvolvesaction,on

boththemotoricandconceptual levels.Consider forexampletheunderstandingofclassproperties.A

traditional viewmightpropose that the child can simplybe taught some facts about classification, for

instance,thatasquareisageometricform.Piaget’sview,ontheotherhand,arguesthatunderstandingof

classificationconsistsofasequenceofactivities.First,thechildphysicallysortsorotherwisemanipulates

objects.Hefeelsvariousformsandinthisway(amongothers),perceivesthedifferencesamongthem.He

mayputdifferentformsindifferentplaces.Later,hecansorttheobjectssolelyonamentallevel;nowthe

child does not need to separate things physically. Later still, he can perform inclusion operations on

imaginedclassesofobjectsandcanconsiderthatahypotheticalclass includesand is“largerthan” its

constituentsubclass.Thus,knowledgeofclassificationdoesnotmerelyinvolvefactsbutactionsaswell:

physical sorting, mental sorting, mental inclusion operations. Furthermore, most of these actions are

nonverbal.

Since learning occurs through the child’s activity, structured teaching methods, such as

programmedlearningoraudiovisualaids,shouldbedeemphasizedinfavorofmore“active”methods.

Instead of attempting to impart truths, teachers should set up situationswhichwill lead the child to

question,toexperiment,andtodiscoverfactsandrelationships.Childrenneedtobeencouragedintheir

exploratory frame of mind. This occurs naturally in the very young child, who is constantly

experimentingwithobjects,language,andsituationstounderstandmoreabouttheworld.Yetoncehe


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startsgoingtoschool,heseemstoceasebeinganexperimenter.Whathashappenedtoextinguishthis

desirefordiscovery?Inschool,explorationisoftendiscouragedentirely.Andwhenitdoestakeplace,the

teacher—notthechild—isusuallytheexperimenter.Underthesecircumstances, thechild learnsvery

little, becomes disinterested, and losesmotivation. Teachers should therefore present the child with

materialsandsituationsthatencouragethedesignofhisownexperiments.Thiswill inturnleadtoa

deeperandmorelong-lastingknowledgethanwillarotememorizationoffactspresentedbyteachersor

intextbooks.

WehaveseenthatPiaget’stheorystressestheroleofactivityineducation.Itshouldbeclearthat

Piaget’sintentionisnottoglorifyactivityforitsownsake.Instead,it istopointoutthatactivity,when

channeledincertaindirections,leadstothegoalofgenuinelearning.Asweshallseenext,thenotionof

reinventionprovidesanunderstandingofthegoal,genuinelearning.

Reinvention

Supposethatthechildhasbeenencouragedtoengageinactiveexplorationandthattheeducator

has taken pains to guide the process of equilibration in a manner sensitive to the child’s cognitive

abilitiesandneeds.Thegoadofallthisactivityistoproducegenuineunderstanding.Aswehaveseen,

thisdoesnot involve themere repetitionof simple facts.Genuineunderstanding is insteada process of

reinvention.AsPiagetputsit,“readcomprehensionofanotionortheoryimpliesthereinventionofthis

theorybythesubject”(Piaget,“CommentsonMathematicalEducation,”1977a,p.731).

Piagetdescribesthereinventionprocessasfollows.Atfirst,thechildengagesinconcreteactivities

involvinganotionlikecardinalnumber.Forexample,hemayspontaneouslycountalineofobjectsfirst

from left to right and then from right to left.Activities suchas these, spontaneously generatedby the

child,leadtotheunderstandingofkeyprinciples.Hefinds,forexample,thatifyoucountasetfromright

toleft,yougetthesamenumberaswhenyoucountfromlefttoright.

In thePiagetian view,we can say that the child has reinvented a key aspect of the principle of

cardinality.Thenotionofreinventionisusedsincetheconceptwasnotsimplytransmittedfromteacher

tochild;instead,thechildwasputinapositionwherehisownspontaneousactivityledtothecreationof


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the concept. Thus, when the child gets the same number regardless of the direction of counting, he

concludesonhisownthatdirectionalitymakesnodifferenceforcounting.This“concludingonhisown”is

theessenceofreinvention.

The understanding which results from reinvention, Piaget maintains, is more genuine and

powerfulthanisthatprovidedthroughstructuredteachingandpassivelearning.Oneindicationofthe

reinventedconcept’spoweristhatthechildspontaneouslyusesitinnewsituations,asifheistestingits

generality. The childwho receives the concept in a passive fashion is less likely to engage in active

generalizationofthistype.

Atthesametime,Piagetpointsoutakeylimitationtothechild’sreinventedunderstanding:“the

pupilwillbefarmorecapableofdoingandunderstandinginactionsthanofexpressinghimselfverbally

... a large part of the structures the child uses when he sets out actively to solve a problem are

unconscious”(Piaget,1977a,p.731).Sothechild’sreinventionleadstoagenuineunderstanding,but

onethatisnotyetcapableofexpressiononaconscious,verballevel.

Theachievementofahigherlevelofunderstandingshouldbedelayeduntilalatertime.AsPiaget

putit,“formalization[inmathematics]shouldbekeptforalatermomentasatypeofsystematizationof

thenotionsalreadyacquired.Thiscertainlymeanstheuseofintuitionsbeforeaxiomatization”(inPiaget,

1977a, p. 732). In otherwords, formalization should be introduced only after the child has become

comfortablewithhis“informalnotions”andonlywithmuchassistanceonthepartoftheteacher.Indeed,

one of the teacher’s main responsibilities is to help the child achieve an explicit consciousness,

expression,andformalizationofhis“intuitiveknowledge.”Inalatersection(oncurriculum),weshall

explore the process of helping the child to make a transition between these different levels of

understanding.

Individualized Learning

Piaget’s theory stresses that current cognitive structuresandnewexperiences interact toarouse

interest and stimulate the subsequent development of understanding. Interest and learning are best

facilitatediftheexperiencepresentedtothechildbearssomerelevancetowhathealreadyknows,butis


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atthesametimesufficientlynoveltopresentincongruitiesandconflicts.Inotherwords,Piagetproposes

thatthechild’sinterestisarousedwhenanexperienceismoderatelynovel(recallthediscussionofthe

moderatenoveltyprincipleduringinfancy).Thismeansthattheexperienceisnotsoradicallynovelthat

the child cannot assimilate it into current cognitive structures, and it is not so familiar as to be

immediatelyandeffortlesslyassimilated,andthusoflittleinterest.Theprincipleisrelativistic:byitself

an event does not possess some degree of interest. Rather, interest is derived from the interaction

between the state of the child’smind and theproperties of the thing to be known.At the same time,

moderatelynovelexperiencespresentthechildwithcognitiveconflict.Andaccordingtothetheoryof

equilibration,theseconflictsserveasthebasisforreorganizationofcognitivestructuresandsubsequent

development.

The situation with regard to interest and conflict is complicated by the fact that there is

considerablevariationamongchildrenofthesameageintheirrateofdevelopment.Wehaveseenthat

somechildrenwithinagivencultureacquireconservation,forexample,atage5andothersnotuntil8.

Consequently,inanyclassofthirtytofiftychildren,therearewidedifferencesamongchildreninlevels

ofcognitivefunctioning.Becausetheselevelsvary,thechildren’sinterests,whicharedeterminedbyan

interactionbetweenthecurrentlevelofcognitivefunctioningandexperience,willalsovary.Theteacher

isthereforeinevitablyfacedwithawidevariationamongstudentsinbothcognitivelevelandinterest.

Todealwiththis,theremustbeextensivechangesinclassroompractice.First,teachersshouldbe

aware of the child’s current level of functioning. To some extent the teacher can rely on Piaget’s

discoveriesforthisinformation.ButPiaget’sworkcoversonlyalimitednumberofthosetopicsusually

studiedinschool.Therefore,theteacherhimselfmustmakeanassessmentofhisstudents’capabilities.

Onceobtained,thisknowledgewillhelptheteachertocreatesituationsintendedtoprovokethechildto

questionandexperiment.Theteachermayalsoselectsuitablecounterargumentswhichwillencourage

thechildtoclarifyhisthinking.Knowledgeofstudents’functioningwillalsohelptheteachertopresent

theconflictsituations that,aswehaveseen fromthe trainingresearchcarriedout inGeneva,areone

importantmechanismofconceptualgrowth.

Theassessmentofintellectuallevelisnotaneasytask.Theevaluationmustbedifferentfromthe

usualstandardachievementtestswhichoftenmeasureonlysurfaceknowledge,rotememory,andother


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superficial aspects of learning. The teacherwill have to evaluate not only the products of thought—

correct or incorrect answers—but the process of students’ thinking aswell. The teacherwill need to

observethechildrencarefullyandattempttodiscoverboththeircompetenciesandtheirweaknessesin

anyarea.Withoutsuchevaluation,theteacherwillfinditdifficulttojudgebetweenwhatismoderately

novelandthuslikelytoarouseinterest,betweenwhatisalreadyknownortooadvancedforthepupilat

thisstageofdevelopment,andbetweenwhatisorisnotaconflictsituationforeachindividualstudent.

Oncetheteacherrecognizesthechild’scurrentleveloffunctioninghecancreateexperienceswhichwill

promoteinterest,arouseconflict,andfacilitatedevelopmentforthestudent.

Second,teachingshouldbeorientedmoretowardtheindividualstudentthantheoverallgroup.

Sincetherearegreatindividualdifferencesinalmostallareasofcognitivedevelopment, it isunlikely

thatanyonetaskorlessonwillarousetheinterestoforpromotelearninginallmembersoftheclass.For

somechildren,aspecifictaskmaybetooeasilyassimilatedintocurrentmentalstructures,whileforother

studentsthesameproblemmayrequiretoogreatadegreeofaccommodationforthemattheirpresent

stage of development. The result is boredom for the first group and confusion for the second. Third,

childrenmustalsobegivenconsiderablecontrolovertheirownlearning.Somemayneedmoretimethan

otherstodealwiththesamematerial;similarly,childrenmayapproachthesameproblemindifferent

ways.

Topromoteinterestandlearning,then,theteachershouldtailorthecurriculumtothelearnerand

trytoindividualizeteachingasmuchaspossible.Thismeansthatthelargegroupshouldeffectivelybe

disbandedasthesoleclassroomunit,thatchildrenshouldoftenworkonindividualprojects,andthat

theyshouldbeallowedadegreeoffreedomintheirownlearning.Severalobjectionsareusuallyraised

tothissortofaproposal.Underanindividuallearningarrangement,wouldnotchildrenwastetheirtime

orengage inmereplay?Onemaycounter thisargumentbynotingthat the teachermaydependona

certainamountofspontaneousintellectualmotivationinchildren,particularlyyoungerones.Piagethas

shownthatthechildisquiteactiveinacquiringknowledge,andthathelearnsaboutimportantaspectsof

realityquiteapart frominstruction in theschools. In the first twoyearsof life, forexample, the infant

acquiresaprimitiveunderstandingofcausality,ofthenatureofobjects,ofrelations,oflanguageandof

manyotherthings—largelywithoutthebenefitofformalinstructionoradult“teaching.”Oneneedonly

watchaninfantforashortperiodoftimetoknowthatheiscurious,interestedintheworldsurrounding


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him,andeagerto learn.Thesamecanalsobesaidofolderchildrenandissupportedbythefactthat

someschoolsmanagetooperateindividualizedprogramswithagooddeadofsuccess.Inaddition,one

mustrememberthatindividualizedinstructiondoesnotrequiretheabrogationofresponsibilityonthe

partoftheteacher.Indeed,themoreindividualizedthelearning,theheaviertheburdenontheteacher.

The teacher must assess the student’s level, assign relevant learning experiences, and generally

supervisetheentirelearningprocess.Gettingchildrentowork“ontheirown”requiresaconsiderable

contributiononthepartoftheteacher.

Indeed, the burden is so heavy that teachers often feel that the provision of individualized

instructioninlargeclasses(betweentwentytofiftychildren)isanentirelyunrealisticandimpractical

solution.It istruethat in largeclassesnosingleteachercaneffectivelytailoracurriculumtomeetthe

specificcognitiveneedsofeverypupilateverymomentoftheteachingday.Andfromanotherpointof

view,itmightnotevenbeagoodideatohavetwenty,thirty,orfiftyindividuallearners,all“doingtheir

own thing’ ’ since some of the advantages of group learningwould be lost in the process. Yet,when

covering topics where there are obvious differences among children in their understanding of the

material,teacherscandividetheclassintosmallgroupsofchildrenatapproximatelythesamelevel.For

othertopics,allchildrencanworkindividuallyattheirownlevel,whileforstillothertopicstheentire

class canbe joined together.Theessentialpoint is that teachingneeds tobe flexible; the teacher can

employacombinationofgroupandindividualinstruction.

What the student needs, then, are opportunities to learn in a rich environmentwhich contains

manypotentiallyinterestingelements.Thestudents’needsateacherwhoissensitivetohisaffectiveand

cognitiveneeds;whocanjudgewhatmaterialswillchallengehimatagivenpointintime;whoisableto

evaluate his level of functioning and present new ideas at a level consistent with the student’s

intellectual and linguistic development; who can present this knowledge in a way that arouses the

child’s interestandactivity;andwhocanhelpthestudentswhennecessaryandwhohasfaith inthe

child’scapacitytolearn.

Social Interaction

InPiaget’s view, physical experience and concretemanipulation are not the only influences on


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learning.Anotherfactorthatleadstothedevelopmentofknowledgeissocialexperienceorinteraction

withotherpersons.WhilePiagethasnotwrittenextensivelyonthistopic,hisworkcontainsanumberof

importantimplicationsconcerningtheroleofpeersintheeducationalprocess.

The effects of social experience, although almost negligible during the first fewmonths of life,

become increasingly important as the child grows older.Wehavepointed out earlier that one of the

primedeterrents toanobjectiveunderstandingofreality is thechild’segocentric thought.At first, the

childcannotviewpeople,objects,orevents inthesurroundingworldobjectivelybecausehecanonly

perceivethemastheyrelatetohimself.Theveryyoungchildassimilatesexternaleventsdirectlyintohis

ownactionschemes.Objectsoreventsareonlyrelevanttotheextentthattheyconcernthechild’sown

privatepreoccupations.Hecannotviewobjectsoreventsfromanyperspectiveexcepthisown,andthis

egocentrismofcoursepreventshimfromgaininganobjectiveviewofobjectsorofpersons.Gradually,as

thechildbecomescapableofdecenteringhisattention,ashebeginstofocussimultaneouslyonvarious

aspectsofreality,andashecomestounderstandanotherperson’spointofview,thenhegainsamore

objectiveknowledgeofreality.

Onemethodwhich promotes the relinquishment of egocentrism is social interaction.When one

childtalkstoanother,hecomestorealizethathiswayofviewingthingsisnottheonlyperspective.The

childseesthatotherpeopledonotnecessarilysharehisopinions.Socialinteractioninevitablyleadsto

arguments and discussion: the child’s views are questioned, and he must defend and justify his

opinions. This action forces the child to clarify his thoughts, for if hewants to convince others of the

validityofhisownviews, thechildmustpresentthemclearlyand logically. Inaddition,otherpeople

maynotbeastolerantofhisinconsistenciesasisthechildhimself,andtheydonothesitatetopointthem

out.Thussocialinteractionhelpsthechildtorecognizetheshortcomingsinhisthinkingandforceshim

toseeotherpointsofviewwhichmayconflictwithhisown.Suchconflictsinschemesorideasareoneof

themechanismsofprogress.Therefore,weseethat,inadditiontothemorecommonlystressedaffective

sideofsocialinteraction—theneedtogetalongwithotherpeople—thereisalsoanimportantcognitive

component.Socialexperiencenotonlyhelpspeopletoadjusttoothersatanemotionallevel,butitalso

servestoclarifyaperson’sthinkingandultimatelyhelpshimtobecomemorecoherentandlogical.

Itshouldbemadeclearthatsocialexperience isnot independentofphysicalexperience.Verbal


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exchangeofopinions,forexample,isnotfeasibleoncertainsubjectsuntilthechildhastheexperienceof

manipulatingobjects.Duringtheearlystagesofdevelopment,physicalexperienceisespeciallycrucial.

Yet once the child has acted on an object or a situation, language can then serve as amajor tool to

internalizetheexperienceintoacompactcategory.Thechildcanalsouselanguagetocommunicatean

understandingof experience to others. Indeed, the very attempt to communicatepermits the child to

makeexplicitcertainaspectsofexperiencewhichwereatfirstunderstoodonlyatthelevelofaction.The

child’s activity andexperience areofparamount importanceduring the early stagesofdevelopment;

laterverbalcommunicationandsocialinteractionhelptodefineandconceptualizethisexperience.

TheimplicationofPiaget’sview,therefore,isthatsocialinteractionshouldplayasignificantrolein

theclassroom.Childrenshouldconverse,shareexperiencesandargue,fortheseareallmajortoolsinthe

acquisitionofknowledge.

Curriculum

Intheprecedingsections,wehavereviewedvariouseducationalprinciples.Mostrefertogeneral

aspects of the learning process and in themselves do not represent a completely novel approach to

education.Manyofthesepointshavealreadybeenemphasizedbyeducationalphilosophers.Theroleof

activityinlearningwasdiscussedbyRousseauandDewey,andtheprincipleofindividualizedlearning

hassomecommonalitywithSkinner’sconceptsofprogrammedinstruction.Piaget’sresearchaddsnew

empiricaldatainsupportoftheseprinciples,buttheeducationalprinciplesthemselvesarenotnew.The

uniqueness of Piaget’s contribution to education lies in other areas, particularly in his detailed

descriptionof thedevelopmentofnumerousphysical, logical, andmathematical concepts inchildren,

andinhisaccountofthegeneraldevelopmentofthinking.Thistypeofknowledgewasnotavailableto

other educational theorists such as Rousseau or Dewey. A number of the concepts which Piaget has

investigatedareparticularlyrelevanttoeducation,sincetheyaretaughteitherdirectlyorindirectlyin

schools.Forexample,whileconservationoflengthisnotusuallytaughtinschools,itisaprerequisitefor

theunderstandingofmeasurement,whichistaught.Knowledgeofthechild’scognitivelevelandofthe

child’sunderstandingofparticularconceptscanbeusedtofacilitateeducationinseveralways.

Limits.Ontheonehand,researchconcerningthechild’scognitiveleveldemonstratesthatthereare


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limitationsonwhat the child can learn.Thechild’s thoughtdevelops througha seriesof stages, each

showingbothstrengthsandweaknesses.Anyonestageischaracterizedbytheabilitytoperformcertain

actionsand,ontheotherhand,bythepropensitytocommitparticularerrors.Oneimplicationofthestage

theoryisinaway“pessimistic.”Sinceintellectualdevelopmentseemstofollowanorderedsequence—a

sequencewhich,untilproof to the contrary, appears tobeuniversal—theyoungchild is incapableof

learningcertainkindsofconcepts.Itwouldservenopurpose,forinstance,totrytoteachachildofthe

preoperationalperiodtheprincipleofinertia,oranyotherabstractnotionwhichrequirestheexistence

ofreasoningataformaloperational level.Somethingscannotbetaughtatanylevel,regardlessofthe

methodadopted.Itisofcoursepossibletoacceleratesometypesoflearningthroughtheuseofsuitable

environmentalstimuli.Forinstance,ifachildofthepreoperationalperiodisfairlyclosetoachievingthe

structureofconcreteoperations,suitablephysicalexperiencemayexpeditetheprocess,withtheresult

thatthestructuremaybeacquiredsomewhatearlierthanifnosuchexperiencehadbeenpresented.But

aswehaveseen,suchaccelerationispossibleonlyifthechildisinatransitionalstage.

Given these limitations on children’s learning, the educator can respond in several ways. One

strategyistodelaytheteachingofcertainsubjectsuntilchildrenarepresumed“ready”tounderstand

them.Tosomeextent,thisstrategyisobviouslyreasonable:itmakesnosensetoteachcalculustothe5-

year-old.Ontheotherhand,thisapproachcanbeappliedinanoverly-zealousmanner.Thus,onemight

proposethatsinceelementaryschoolchildrencannotemployformaloperations,scienceshouldnotbe

taught until adolescence, when it is possible to reason in a hypothetico-deductive manner. Such a

practicewouldbeunfortunatebecauseevenyoungchildrencanunderstandsomethingofscienceona

level appropriate to their own cognitive abilities. For the concrete operational child, science could

involveagooddealofphysicalexperiencewhichmightleadtoformaloperationalthought.Similarly,in

mathematics,whilepreoperationalchildrencannotfullyunderstandequivalence,theycanprofitfrom

considerableexperienceinthecountingofconcreteobjects.Oftensuchconcreteactivityisaprerequisite

formoreabstractunderstanding.Inbrief,whilelimitationsinchildren’scognitiveabilitiespreventthem

fromlearningcertainconcepts,oneshouldnotforgetthatpreparatorywork,usuallyofaconcretenature,

isoftendesirableandevennecessaryforlaterunderstanding.Hence,despitethelimits,oneshouldnot

giveuponyoungchildren’s learningof certain concepts,but should searchoutappropriateways for

themtoengageinpreparatoryactivities.6


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Strengths. At the same time, there is amore “optimistic” side to Piaget’s theory. At each stage of

development,thechildiscapableofcertainformsofthought,ofspecificconcepts.Forexample,Piagethas

found that concepts of topological geometry (distinctions between closed versus open figures, etc.)

develop in the childbefore thoseofEuclideangeometry (measurementof angles, distances, etc.) and

projective geometry (measurement of perspectives, coordinates, etc.). Understanding of topological

notionsappearsfairlyearlyinlife,whereasthechildonlybeginstounderstandthenotionsofEuclidean

and projective geometry at around 7 years of age. Thus, while the 5-year-old may be incapable of

learning projective concepts, he has already developed an intuitive understanding of topological

notions.Eachstageofdevelopmentischaracterizedbystrengthsaswellasweaknesses.Knowledgeof

thestrengthsaswellasofthelimitationscanbeusedtoimproveeducationinseveralways.Onepossible

improvementisadetailedevaluationandmodificationofexistingcurricula.Thistypeofworkisbeing

carried outmore andmore extensively in several countries. For example, Shayer (1972; 1974) has

workedwithanumberof science courses (chemistry,physics, biology) commonlygiven in theUnited

Kingdom.Hehas tried, for each topic covered, to assess theminimumconceptual level required for a

pupiltobeinterestedinandtograsptheparticularconceptinvolved.Shayerattemptstodeterminehow

suitablethecoursesandspecificconceptsareinrelationtothedevelopmentallevelsofthestudents.Asa

result of these investigations, he suggests that many learning problems may be due to a mismatch

betweentheconceptuallevelofthemajorityofpupilsandtheconceptsbeingpresented.Suchwork—

assessingstudents’strengthsandweaknessesinrelationtothematerialtaught—caneventuallyleadto

thedevelopmentofnewandmoreeffectivecurricula.

Knowledgeofstudents’ intellectualstrengthscan leadto the improvementofeducation inother

ways,too.Inparticular,itcanproduceanoptimisticviewconcerningstudents’potentialandthecreation

of new learning opportunities. Piaget’s theory shows that by the age of 5 or 6, when they are

simultaneously entering school and theperiodof concrete operations,most childrenhavedeveloped

remarkably sophisticated intellectual processes. By this age, most children already possess the

intellectual prerequisites for understanding a good deal of what is taught in elementary school. For

example,children’sspontaneousconceptofnumberissuchthattheyshouldhavenoparticulardifficulty

withthemostnotoriousofschoolsubjects,namely,arithmetic.Asaresultofnaturaldevelopment,they

understand ideasofone-to-onecorrespondence,equivalence,additivity—that is, theconcepts forming


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thefoundationforagooddealofschoolarithmetic.Inotherwords,Piaget’stheorysuggeststhatvirtually

allchildrenpossessthecognitiveequipmentfordoingstandardacademicwork.Whatistaughtinschool

should easily be assimilated into the existing cognitive framework. Piaget feels that it is difficult to

understandhowstudents“whoarewellendowedwhenitcomestotheelaborationandutilizationofthe

spontaneous [patterns] of intelligence can find themselves handicapped in the comprehension’’ of

academicsubjects(Piaget,

ScienceofEducation,1970c,p.4).Theteachershouldthereforeseriouslyconsiderthenotionthat

theeducationofchildrencanrelyonsomealreadyexistingintellectualassets.Problemsinlearningare

notlikelytostemfromfundamentalintellectualdeficitsinthechild.Giventhisnotion,theeducatorcan

devisecurriculawhichattempttoexploitthechild’sstrengths.If,forexample,thepreoperationalchildis

capableofunderstanding“functions,” thentheeducatormayelaborateonthisconcept. If theconcrete

operationalchildcandealwithcomplexformsofequivalence,thentheeducatormaytrytoexploitthis

informalknowledge.Thenaturalcourseofdevelopment—thespontaneousappearanceof intellectual

capabilities—provides important opportunities for the fostering of academic knowledge and should

therefore exert a strong influence on the nature of curriculum. The educator should also expect that

children will have little difficulty in mastering school work because of their natural intellectual

strengths.

Intuitionandconsciousness.Weallknowthatdespitechildren’sintellectualstrengths,theteaching

ofcertainsubjectsdoesnotgoassmoothlyasitmight.Arithmeticisaprimeexample.Althoughchildren

already possess spontaneous notions of basic mathematical ideas, they usually have a terrible time

learningschoolarithmetic.Whyshouldthisbeso?Thereare,ofcourse,manydifferentkindsofreasons,

butperhapsPiaget’snotionofdifferentlevelsofunderstandingcanshedsomelightontheissue.

Thefirstoftheselevelsismotoricorpracticalunderstanding.Thisisthelevelofaction.Thechild

canactdirectlyonobjectsandmanipulatethemcorrectly,makingtheobjectsdowhattheyaresupposed

to do. All this indicates that the child has “understood” objects at the level ofmotor responses. This

knowledge is preserved in the form of schemes, which allow the actions to be repeated in identical

situationsandgeneralized tonewones.Another levelofunderstanding isconceptualization.Here the

childreconstructsinternallytheactionsthatwerepreviouslyperformeddirectlyonobjects,andatthe


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same time adds new characteristics to these actions. He organizes themental activities and provides

logicalconnections.Atthesametime,muchofthechild’sintellectualworkremainsunconscious.Aswe

sawinreviewingPiaget’sworkonconsciousness,thechildisoftencapableofmentaloperationsthathe

isnotawareofandcannotexpress.Athirdlevelofknowledgeinvolvesconsciousnessandverbalizations.

Now the child can dealwith concepts on an abstract level and can express hismental operations in

words.Thechildcanreflectonhisownthought.

At all stages of intellectual development, children find it easier to act—either behaviorally or

mentally—thantoachieveconsciousnessoftheiractions.Consciousnessandverbalizationarerelatively

latedevelopments,andtheiremergencemaydependonpriorunderstandingatthelowerlevels.

The existence of different levels of understanding—practical, conceptual, and conscious—has

importantimplicationsforeducation.Wehavealreadyseenthatateverystageofcognitivedevelopment

thechildpossessesbasicintellectualstrengths.Usuallytheseinvolveunderstandingattheunconscious

levels,thatis,motoricandconceptualunderstanding.Bycontrast,schoollearningtypicallyoperatesatan

exclusively verbal and formalized level. The child’s spontaneous mathematics is informal and

unconscious;thearithmetictaughtinschoolisformalandhighlyverbalized.ForPiaget,then,oneofthe

key problems of education involves “finding the most adequate method for bridging the transition

between these natural but nonreflective structures [that is, understanding of the first two types] to

consciousreflectionuponsuchstructuresandtoatheoreticalformulationofthem”(ScienceofEducation,

1970c,p.47).Piagetrecommendsgraduallybuildingonwhatthechildalreadyknows—onthechild’s

actionsorunverbalized“intuitions”—toachieveasubsequentformalization.

Perhaps there is a paradox here: to foster true abstraction and consciousness, one must first

encourage the concreteandunconscious.Of course, thisdoesnotmean that all learningmustalways

involvethemanipulationofconcreteobjects.Theadolescentinthestageofformaloperationsmayprofit

fromverbalorwrittenmaterial,providedthatinthecourseofdevelopmenthehasalreadyacquireda

gooddealofmotoricandconceptualknowledgecorrespondingtotheabstractioninquestion.If,however,

theformaloperationallearnerencountershighlyabstractmaterialwithwhichhehashadnorelevant

previousexperience,thenforhim(liketheyoungerchild)lowerlevelsofunderstandingmayhelpto

serveasafoundationforconsciousness.Formostofus,trulyabstractunderstandingcanbeachievedonly


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throughimmersionintheconcrete.Inbrief,oneofthechieftasksofeducationistheeliminationofthe

gapbetweenthechild’sinformedmodesofunderstanding,whichPiagethasdescribedinsomedetail,

andtheformalitiestaughtinschool.

A caution. A word of caution is necessary with regard to the use of actual Piagetian tasks or

experiments in the school curriculum.Since conservation is an indicator that the childhas reacheda

certainstageofdevelopmentorhasacquiredacertaincognitivestructure,someeducatorsbelievethat

thedirectteachingofconservationwillautomaticallypromotethedevelopmentofthechild’sunderlying

cognitivestructure.Piaget’stasksarethereforebeingusedasteachingdevices,asbasicsubjectmatterin

thecurriculum.Thisseemstomakelittlesense.Learningthecorrectresponsestocertainspecifictasks

doesnotmeanthatachildwill reach thesame intellectual levelasanotherchildwhospontaneously

gives the correct responses to the same task. The only result of instruction in Piagetian concepts is

generally that the child acquires some very localized learning in the narrow sense, which does not

promotegeneralprogressinotherareasofcognition.Suchinstructionisthereforeofratherlimitedvalue,

especiallysincethecognitivestructuresnormallydevelopinaspontaneousfashion,quitewithoutthe

“benefit”ofeducation.

Clinical Method

AswehaveseeninChapter1,itwasveryearlyinhiscareerthatPiagetrejectedstandardtestsasa

useful tool for the studyof cognitivedevelopment. Such tests, he felt, fail to give a good indicationof

underlying cognitive processes. Piaget now feels that standard tests are not particularly useful for

educational purposes, either. Indeed, he considers the tests to be a “veritable plague on education”

(quoted by Elkind, 1976, p. 192). For Piaget the preferred method is the clinical interview. This

technique isnotmerelypreliminary, nor is it sloppyorunscientific. It is instead themostuseful and

“valid”methodcurrentlyavailableforthestudyofthinking.Theclinicalmethodhasanimportantroleto

play in education, too, particularly in the areas of assessment and diagnosis. By the use of suitable

probing questions that attempt to reveal the underlying reasons for a child’s initial statement or

judgment, by presenting countersuggestions to the child’s arguments, and by providing conflict

situations, the teacher who employs this method can discover a great deal about a child’s cognitive

functioning. In theclinicalmethod, the interviewermustobserveand listento thechildcarefullyand


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mustadaptboththepaceandthelevelofthequestioningtotheindividualchildwhois interviewed.

Standardizationmustbeavoided.Itisnotthepurposeoftheinterviewtofindoutonlywhetherachildis

abletoansweracertainquestioncorrectlyornot,buttouncoverunderlyingcognitiveprocesses.Incorrect

answers in particular provide the interviewer with an indication of the child’s current state of

knowledge.

Theclinicalmethodneednotbe restricted toPiagetian tasks, likeconservationor seriation.The

method can be used in any situation inwhich the objective is the exploration of the child’s thought

processes.Hence,itisquiteappropriate,andwethinkveryuseful,toemploythemethodtoexaminethe

child’s understanding of academic subject matter. For example, clinical interviewing has proved

successfulintheinvestigationofelementaryschoolchildren’sproblemsinlearningarithmetic(Ginsburg,

1982).Teachersattemptingtoassesstheirpupils’functioningmightthereforefindthemethodauseful

diagnostictoolinmanyareasofclassroomlearning.Thetechniqueisparticularlyvaluableinidentifying

theintellectualdifficultieswhichunderlielearningproblems.

Anotherandmoreindirectuseofthemethodmightbemadeinprogramswhichattempttotrain

prospective teachers in questioning skills for use in teaching situations. There aremany similarities

betweentheclinicalinterviewandthe“Socratic”questioningtechniqueintheclassroom.Forinstance,in

agrouporindividualsetting,askillfulteacherdoesnotsimplyaskquestionswhichrequiretherecallof

correctanswers;evenmoreimportant,heasksprovocativequestionsthatstimulatethepupil tothink,

and to become aware of underlying causes. This requires questions that probe into the “whys” of

situations.Inaddition,teachersneedtoadaptthelevelandpaceoftheirquestionstotheunderstanding

ofpupils;teachersneedtobeabletolistenandobservetounderstandthemeaningofaresponse.These

skillsofquestioning,sensitivity,andinterpretationareallstressedintheclinicalinterview.

These, then,are twoways inwhichPiaget’sclinicalmethodcanbeused ineducation: first,asa

meansofassessmentdifferentfromstandardtestsinbothitsflexibleprocedureanditsaimofassessing

cognitivestructure,and,second,asameansofdevelopingintheprospectiveteacherasensitivitytoward

learnersandthequestioningskillsessentialforinstruction.


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Future Directions

During the period from 1960 to 1980, psychological and educational researchers carried out

numerous studies based on the structural aspects of Piaget’s theory, that is, the stages of cognitive

development,conceptsofconservation,classification,orseriation.Educatorsinparticularbelievedthat

anoveralltheoryofhumanintellectualdevelopmentshouldbeabletoprovideinsightsthatwouldhelp

them in their teaching in the classroom.These studies have resulted in a certain amount of perhaps

predictabledisenchantmentanddisappointment.Expectationsweretoohigh.Itisdifficulttoseehowa

theorythatemphasizesfourbroadstagesofdevelopmentcouldprovideusefulinsightsforateacherwho

teaches childrenover the relatively shortperiodofoneyear, just as it isdifficult to imaginehow the

studyofconservation,whichisnotaconcepttaughtinschool,couldbeofanydirectbenefittotheteacher.

Piaget’s laterworkintotheprocessesofcognitivedevelopmentandthemechanismsof learningoffers

more scope for both cognitive psychology and education. This later functional approach to cognitive

development, however, like the early structuralwork, doesnothavedirect applications to education.

Beforeitcanhelptheteacherintheclassroomsetting,agreatdealofresearchisneeded.Butitprovidesa

frameworkforthestudyandanalysisoftheprocessesbywhichlearnersacquirewhatitisteachersare

tryingtoteachandcouldresultininsightsintoclassroomteachingandlearning.Threemainareasofthis

laterworkhavepotentialapplicationstoeducation.

The first is related to Piaget’s distinction among three types of knowledge: social, physical, and

logicomathematical.Thedifferentnatureofeachtypecallsfordifferenttypesofteachingmethods.Social

knowledgecallsfordidacticmethods;physicalknowledgeisbestpromotedthroughthemanipulation,

exploration, and discovery of objects; and logicomathematical knowledge requires construction,

reinvention,andreflectiononactionsandcoordinations.Atpresent,teachershaveatendencynotonlyto

treat all knowledge as if it were of the same type, but in many cases to treat it as if it were social

knowledge and best promoted through errorless learning. While this type of learning may be

appropriateforsocialknowledge,itmaynotnecessarilybesuitablefortheothertwotypes.If,asPiaget

claims, it is disequilibrium, disturbance, or conflict that motivates the search for better forms of

knowledge, thenthe learningofphysicaland logicomathematicalknowledgewouldcall forsituations

withsomeelementofconflict.


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Ifaparticularsubjectmattercouldbeanalyzedintermsofthesethreetypesofknowledge,andthe

kindsofconflictlikelytoleadtolearning,thenteachingappropriatetoeachtypecouldbedesigned.This

mightresultinmorevaried,interesting,andeffectiveteachingmethodsthanthosecurrentlyadopted.

AnotherareaofPiaget’stheorywithindirectapplicationtoeducationisthatofthealpha,beta,and

gamma reactions to disturbances. Here again, specific subject matters could be analyzed with these

concepts in mind and appropriate teaching methods and situations designed for each level. Alpha

reactions would require situations which enable the learner to become more aware of disturbing

elements.Learnersatthebetalevelneedsituationsthathelpthemtoexploreandconstructvariations

and compromise solutions,whereas learners at the gamma levelneed tobehelped to integrate their

morematureunderstandingofoneparticularareaofknowledgewithotherareas.

ThethirdareainwhichPiaget’sworkcanprovideaheuristicframeworkforeducationalresearch

coversspecificprinciplesof theequilibrationprocess, suchasdifferentiationand integration,and the

relativization and quantification of concepts. For any specific area of academic learning, researchers

couldidentifytheprocessesinvolved,suchasthetypeofdifferentiationsandintegrationsthatoccur,the

sequenceandnatureofrelativizations,thecharacteristicsthatarequantifiedforanyparticularconcept,

theinterrelationshipsbetweenthesequantifications,andsoon.Understandingofthedynamicsofthese

processes for an academic subject could then help educators to set up appropriate teaching-learning

situations.

Thisapproachtoteachingandlearningwouldbearadicalchangefrompastpractices.Ifadopted,

theeducator,ratherthanlookingatteachingfromthepointofviewoftheacademicsubjecttobelearned

oratwhathasprovedsuccessfulinthepast,wouldapproachtheteaching-learningsituationfromthe

pointofviewofthe learnerandhowthis learnerspontaneouslyacquiresknowledge.Webelievethat

this constructivist, genetic epistemological approach to the classroom setting, based on the functional

aspects of Piaget’s theory, could prove to be an extremely fruitful method of collaboration between

psychologyandeducationandcouldleadtoimportantcurriculumdevelopmentsinthefuture.


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WehavereviewedsomeofthemajorimplicationsofPiaget’sviewsforeducationalpractice.While

Piagethasnotbeenmainlyconcernedwithschools,onecanderivefromhistheoryanumberofgeneral

principleswhichmayguideeducationalprocedures.Thefirstoftheseisthatthechild’slanguageand

thoughtaredifferentfromtheadult’s.Theteachermustbecognizantofthisandmustthereforeobserve

childrenverycloselyinanattempttodiscovertheiruniqueperspectives.Second,childrenneedtoacton

thingstolearn.Formedverbalinstructionisgenerallyineffective,especiallyforyoungchildren.Activity

constitutesamajorportionofgenuineknowledge;themerepassivereceptionoffactsorconceptsisonly

aminorpartofrealunderstanding.Third,childrenaremostinterestedandlearnbestwhenexperience

ismoderatelynovel.Whenanewevent isboth familiarenoughso that itmaybeassimilatedwithout

distortionintocurrentcognitivestructure,andnovelenoughsothatitproducessomedegreeofconflict,

theninterestandlearningarepromoted.Sinceatagivenagelevelchildren’scognitivestructuresdiffer,

allchildrenwillnotfindthesameneweventinteresting,norwilltheylearnfromit.Thisimpliesthat

successfulgroupinstructionisalmostimpossible.Childrenshouldworkindividually,withfreedom,at

tasks of their own choosing. Piaget finds, too, that an important aspect of learning is self-regulation.

Beforeenteringschool,andwithoutadult instruction,thechildlearnsinmanyways.Fourth,children

shouldhavetheopportunitytotalkwithoneanotherinschool,toargueanddebate.Socialinteraction,

particularlywhenitiscenteredonrelevantphysicalexperience,promotesintellectualgrowth.

Fifth,oneofPiaget’smajorcontributionstoeducationliesintheprovisionofextensivedataonthe

developmentinchildrenofbasicmathematical,logical,andscientificconcepts,andthusonthegeneral

developmentof thinking.This informationcanbeusedtodeterminethe limitsonchildren’sability to

learn, toevaluatecurricula, todevelopnew learningexperiences, and toeliminate thegapsbetween

intuitionandconsciousness.Sixth,Piaget’sclinicalmethodcanbeusedasaneffectiveaidindiagnosis

and assessment, and in helping teachers acquire thequestioning skills useful for promoting genuine

learning in the classroom. Finally, Piaget’s theory of equilibration has implications for the conduct of

teaching.

It should be clear that these views are at variancewithmany of the assumptions of traditional

education.According toPiaget’sevidenceandtheory,studentsofagivenage leveldonotandcannot


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learn essentially the same material; they learn only in a minor way through verbal explanation or

writtenexposition(concreteexperiencemustcomefirst);theycananddoexertcontrolovertheirown

learning;andtheyshouldtalktooneanother.Itshouldalsobeclearthattheseideasarenotparticularly

new.The “progressive”educationmovementhasproposedsimilarprinciples formanyyears.Piaget’s

contributionisnotindevelopingneweducationalideas,butinprovidingavastbodyofdataandtheory

whichprovideasoundbasisfora“progressive”approachtotheschools.

Wewouldalsoliketopointoutthattheseeducationalideasarenotonly“idealistic,”butpracticalas

well.ManyprimaryschoolsinGreatBritainandintheUnitedStateshavebeenapproachingeducationin

linewiththeprinciplesdescribedabove,andhavedrawndirectlyonPiaget’sworkfortheirinspiration.

These schools represent a very promising experiment in educational innovation and have already

achievedagoodmeasureofsuccess.

Wewill close this section on education, and this book,with a quotation fromPiaget, stating his

educationalgoalsandatthesametimedescribinghisownaccomplishment.

Theprincipalgoalofeducationistocreatemenwhoarecapableofdoingnewthings,notsimplyofrepeatingwhat other generations have done—menwho are creative, inventive, and discoverers. The second goal ofeducation is to formmindswhichcanbecritical,canverify,andnotaccepteverythingtheyareoffered.Thegreatdangertodayisofslogans,collectiveopinions,ready-madetrendsofthought.Wehavetobeabletoresistindividually, to criticize, to distinguish betweenwhat is proven andwhat is not. Sowe need pupilswho areactive,wholearnearlytofindoutbythemselves,partlybytheirownspontaneousactivityandpartlythroughmaterialwesetupforthem;wholearnearlytotellwhatisverifiableandwhatissimplythefirstideatocometothem.(Piaget,“DevelopmentandLearning,1964,p.5)

Notes

1Lenneberghasproposedasophisticatedtheoryofmaturationtoexplainthedevelopmentoflanguage.Thistheory,whichisfarsuperiortoGesell’s, is in many respects congruent with Piaget’s and deserves to be taken seriously indeed. See E. H. Lenneberg,BiologicalFoundationsofLanguage(NewYork:JohnWiley&Sons,Inc.,1967).

2 Piaget himself has given relatively little attention to physical experience, despite his estimate of its importance. In developmentalpsychology, this topic isusually treatedunder the rubricofperceptualdevelopment,and themost important theory in theareaisE.J.Gibson’s.SeeE.J.Gibson,PrinciplesofPerceptualLearningandDevelopment(EnglewoodCliffs,N.J.:Prentice-Hall,Inc.,1969).

3Today,manypsychologistsarecomingtoagreewithPiaget’sthesisthatthoughtshapeslanguagefarmorethanlanguageshapesthought.See,forexample,J.McNamara,“CognitiveBasisofLanguageLearninginInfants,’’PsychologicalReview,Vol.79(1972),pp.1-13.


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4Theseassertionsconcerningtheroleoflanguagehavenotgoneunchallenged.Beilin(1977)inparticularhasdemonstratedthattraininginverbal rules can accelerate the pace of conservation, and in an address (“Language and Thought: Thistles Among theSedums,”PiagetSociety,1977)haselaboratedontheroleoflanguageinthedevelopmentofthinking.

5Piagetrevisedhisconceptofequilibrationonseveraloccasions.Thepresentdescription isbasedonhis last revisioncontained inworkswrittenbetween1970to1980andinparticularinTheEquilibrationofCognitiveStructures(1985).

6Oneimportantissueregardstheteachingofreadingtotheyoungchild.OnthebasisofPiaget’stheory,whatcanoneconcludeconcerningthedesirabilityof teaching4-or5-year-oldstoread?Webelieve that the theoryhas little ifanythingtosayaboutreading,since Piaget has not studied it directly and since it is not clear how the intellectual skills which he has studied relate toreading. Our own experience is that there is no cognitive limitation which would prevent preoperational children fromlearningtoreadiftheyaremotivatedtodoso.


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