The findings of Swiss scholar Jean Piaget suggest that it can—by helping people achieve a series of four distinct but overlapping stagesof intellectual growth as they search for patterns and relationships.
Robert G. Fuller, Robert Karplus and Anton E. Lawson
The life of every physicist is punctuatedby events that lead him to discover thatthe way physicists see natural phenomenais different from the way nonphysicistssee them. Certain patterns of reasoningappear to be more common among phys-icists than in other groups. These in-clude:• focussing on the important variables(such as the force that accelerates theapple, rather than the lump it makes onyour head);• propositional logic ("if heat were aliquid it would occupy space and a cannon-barrel could only contain a limitedamount of heat, but this is contrary to myobservations, so. . .") , and• proportional reasoning (for example,the restoring force of a spring increaseslinearly with its displacement from equi-librium).In recent studies of the reasoning used bystudents we have discovered among themqualitative differences similar to thosebetween the reasoning patterns of physi-cists and nonphysicists.
How can we understand these qualita-tive differences in reasoning? What roledoes physics play in the way reasoningdevelops in young people?
Along with a group of teachers inphysics and other disciplines, we believethat some of the answers to these ques-tions can be found in the work of devel-opmental psychologists, especially that of
Robert G. Fuller is a visiting professor of physicsat the University of California, Berkeley and aresearch physicist at the Lawrence Hall ofScience while on leave from the University ofNebraska-Lincoln, where he is a professor ofphysics; Robert Karplus is the acting director ofthe Lawrence Hall of Science and President ofthe American Association of Physics Teachers,and Anton E. Lawson is a research associate atthe Lawrence Hall of Science, University ofCalifornia, Berkeley.
the Swiss scholar Jean Piaget. We havehelped start a modest movement, ac-cordingly, to inform others of the relevantfindings and theories of these social sci-entists.
To do so we have extended the psy-chologists' original investigations bydealing with their implications for thepresentation of subject matter at thesecondary-school and college levels.Textbooks, laboratory procedures,homework assignments, test questionsand films may all be examined from thedevelopmental point of view.1
In this article we shall describe thoseideas in Piaget's work that we have foundmost useful; you may judge for yourselfhow valid they are. We shall conclude bysuggesting ways in which you can use yourexpertise in physics and your personalcontacts—whether you teach physics ornot—to encourage others to develop theirreasoning through their observations andanalyses of physical systems.
Student responses to puzzles
To study the differences in reasoningused by studei ts, we have devised anumber of pape-- and-pencil puzzles andgiven them to high-school and collegestudents. Let us examine the followingtypical student responses to two of these,the Ticker-Tape Puzzle and the IslandsPuzzle,2 and discuss the differences inreasoning displayed in them by the stu-dents.
The responses to the Ticker-TapePuzzle (see the Box on page 25) werecollected from engineering and sciencestudents in an introductory physicscourse. Some of them had completed theterm covering newtonian mechanics,others had not. Here are samples:Fred (had used ticker tape)1 B—Dots are spaced equally.2 C—Dots are closing together, cart is
going less distance in the same time.3 A—Dots are getting farther apart, cart
is moving farther in same time (ac-celerating).
4 D—Cart is falling through air; it hasa rapid acceleration.
James (had not used ticker tape)1 B—At constant speed, the same dis-
tance will be covered per unit time.2 E—Deceleration means less velocity,
so less distance per unit time.3 D—Acceleration is exponential, ruling
out A.4 C—Assume a frictionless system, with
brakes momentarily applied betweendots five and six.
The responses to the Islands Puzzle(see the Box on page 26) were collectedfrom a wide variety of adolescents andadults. These two are typical:Deloris (College student, age 17)1 "Yes, because the people can go north
from Island D—because in the clue itcould be made in both directions."
2 "No; I am presuming both directionsdoesn't include a 45° angle from B toC."
3 "Yes, because Island C is right belowIsland A."
Myrna (College student, age 17)1 "Can't tell from the clues given. The
two clues don't relate the upperislands to the lower ones."
2 "Yes; they can go from B to D, andthen to C, even if there are no directflights."
3 "No, if they could go from C to A, thenthe people on B could go first to D,then to C, and then on to A. But thiscontradicts the second clue, that theydon't go by plane between B and A."
You will notice some similarities be-tween the responses of Fred (to theTicker-Tape Puzzle) and Deloris (to theIsland Puzzle). They both focus on thespecific details of the puzzle. Fred makes
PHYSICS TODAY / FEBRUARY 1977 23
College Teaching and the Development of Reasoning 185
The wheels are turning as these two students compare the angles ofrotation of three intermeshing gears. Their search for numerical rela-tionships will help them develop proportional reasoning and understand
when to apply this pattern of thought. The ability to handle functionalrelationships such as proportionality is a characteristic of formal rea-soning, the fourth of Piagefs stages of intellectual development.
direct correspondence between the ar-rangement of the dots and the physicalexamples given. Although he introducesthe idea of "acceleration," he does notindicate that he has any more than avague general idea of its meaning. In asimilar way, Deloris concentrates on thespatial arrangement of the islands. Herexplanations have more to do with herperception of the physical arrangement ofthe islands than with the clues given inthe puzzle. Both Fred and Deloris appearlimited in their reasoning to the specificdetails of a puzzle, and do not readily re-late the facts of the puzzles to more gen-eral principles.
Consider, on the other hand, the re-sponses of James and Myrna. Both ofthem have made conjectures to facilitateanswering the questions. James, who hadnot previously used a ticker tape, beginshis explanations with generalized con-cepts such as constant speed, decelera-tion, acceleration and a frictionless sys-tem. Even when his explanation is wrong("acceleration is exponential") he dem-onstrates that he is reasoning within asystem of deduction from hypotheses, inwhich a ticker tape can serve as one spe-cific example representative of a moregeneral principle.
Myrna, as she reasons about the IslandsPuzzle, fits the clues into an overallscheme for explaining the air travel be-tween the islands. She suggested a hy-pothetical trip, demonstrating the cor-rectness of her answer by reasoning to acontradiction. James and Myrna displaypatterns of reasoning commonly used byphysicists.
Even in the responses to these simplewritten puzzles, the qualitative differ-ences in student reasoning are vividly
displayed. For an understanding of thesedifferences, let us turn to the work of Pi-aget.
The development of reasoning
Jean Piaget began his research onchildren in about 1920. The results of hiswork of primary concern to us are re-ported in the book, The Growth of LogicalThinking from Childhood to Adoles-cence. a In this book the responses ofyoung people to various tasks concerningphysical phenomena are described.These tasks included physics experimentssuch as those on the equality of the anglesof incidence and reflection, the law offloating bodies, the flexibility of metalrods, the oscillation of a pendulum, themotion of bodies on an inclined plane, theconservation of momentum of a horizon-tal plane, the equilibrium of a balance andthe projection of shadows.
On the basis of the responses, Piagetand his co-workers developed a theory forinterpreting the development of what heconsiders to be universal patterns of rea-soning. Pivotal to this theory is the con-cept of stages of intellectual develop-ment. The stages—there are four in thetheory—are characterized by distinctivefeatures in the patterns of a person'sreasoning. It was hypothesized that eachof Piaget's four stages serves as a precur-sor to all succeeding stages, so that rea-soning develops sequentially, always fromthe less effective to the more effectivestage, although not necessarily at thesame rate for every individual.
Like a concept in any theory, a stage ofintellectual development is a simplifica-tion that is helpful in analyzing and in-terpreting observations, somewhat like apoint particle or a frictionless plane in
mechanics. In this spirit, we should notexpect that most people during their pe-riod of development will exhibit all thereasoning characteristics of, say, stage Afor a certain period of time and thensuddenly change to all the reasoningpatterns appropriate to stage B. Rather,the development of a person's reasoningshould be thought of as gradual, at a par-ticular time showing the features of stageA on some problems while exhibitingcertain features of stage B on others. Thestage concept therefore may be moreuseful for classifying reasoning patternsthan for describing the overall intellectualbehavior of every particular person at agiven time.
The first Piagetian stage is called sen-sory-motor. This stage is characteristicof children's thinking from birth to abouttwo years of age. Piaget's work with in-fants provided an explanation for thehumor of the "peek-a-boo" game:
The young infant appears to think thatthe only objects that exist are the objectsthat can be seen. The sudden "creation"of a large person by removing a blanketcovering him does seem to be a funnyevent. Subsequent experiences providethe child with the opportunity to developan awareness of the permanence of ma-terial objects.
The concept of permanence providesthe basis for the child's need for language.If objects do exist when they are out ofsight, then it is useful to have symbols (orwords) to represent them. So the sen-sory-motor stage serves as the precursorfor the next, pre-operational, stage.
During the pre-operational period thechild is learning words and trying to fit hisexperiences of the world together. Thepre-operational child lives in a very per-
2 4 PHYSICS TODAY / FEBRUARY 1977
College Teaching and the Development of Reasoning 186
The puzzle below is a task designed to display the variety of student reasoning patterns usedin a typical physics classroom activity. It is taken from materials for the workshop on PhysicsTeaching and the Development of Reasoning offered at the 1975 AAPT-APS meeting inAnaheim, California (reference 1).
Start End
L
D \2.
E iZ
Many physics labs allow you to study motion by making timer tapes like the five illustratedabove. These are strips of paper attached to a moving object and passing through a timingmechanism that makes a row of small dots by striking regularly at equal time intervals, usuallyfive to ten times per second.• Have you ever used or watched such a device?• Identify the tape that fits each of the examples below and Justify your answers, takingspecial care to mention any tapes that a less experienced student might easily mistake forthe correct one.
1. A student walking through the laboratory at constant speed A B C D EJustification?
2. A cart gradually slowing down on a level plane A B C D EJustification?
3. A cart rolling freely down an inclined plane A B C D EJustification?
4. Explain how one of the two remaining tapes might have been made, and briefly justifyyour hypothesis.
Sparks mark the position of the falling object on the ticker tape. The dot patterns can not beanalysed readily by that third of US adolescents and adults who use only concrete reasoning.
sonal world with his own ego at the center("The Sun is following me!"). He putsfacts together to produce ad-hoc expla-nations, such as, "My dad mows the yardbecause he's a physicist."
The pre-operational child does not usecausal reasoning. Some authors haveused children's pre-causal explanations asthe motif for humorous books. For Pi-aget, such explanations are clues as to howchildren think about the world in whichthey live.
The first two Piagetian stages are usu-ally completed before a person is nineyears old. The child's interaction withphysical systems plays an essential role inhis or her intellectual development duringthe first two stages. The role of physicsin the development of reasoning in theelementary-school years was discussed ina special issue of PHYSICS TODAY.4
Concrete reasoning
To explain the qualitative differencesin the reasoning patterns of older stu-dents' responses to the two puzzles de-scribed earlier we must look to Piaget'sthird and fourth stages of intellectualdevelopment, concrete reasoning andformal reasoning. Certain characteris-tics help identify reasoning patterns as-sociated with these two stages.
Here are some of the characteristics ofconcrete reasoning patterns; illustrativeexamples are added in parentheses:
Class inclusion A person at this stageunderstands simple classifications andgeneralizations of familiar objects orevents (can reason that all aluminumpieces can close an electric circuit, but notall objects that close a circuit are made ofaluminum).
Conservation Such a person reasonsthat, if nothing is added or taken away,the amount or number remains the sameeven though the appearance differs (thatwhen water is poured from a short widecontainer into a tall narrow container, theamount of water is not changed).
Serial ordering The person arranges aset of objects or data Ln serial order andmay establish a one-to-one correspon-dence ("The heaviest block of copperstretches the spring the most").
Reversibility A person using concretereasoning mentally inverts a sequence ofsteps to return from the final to the initialconditions (reasoning that the removal ofweight from a piston will enable the en-closed gas to expand back to its originalvolume).
Concrete reasoning enables a personto• understand concepts and simple hy-potheses that make a direct reference tofamiliar actions and objects, and can beexplained in terms of simple associations("A larger force must be applied to movea larger mass.");• follow step-by-step instructions as ina recipe, provided each step is specified(carry out a wide variety of physics ex-
PHYSICS TODAY / FEBRUARY 1977 25
College Teaching and the Development of Reasoning 187
The puzzle below is a written task designed to display the variety of deductive-logic strategiesused by adolescents (reference 2).
There are four islands in the ocean, Islands A, B, C and D. People have been travelling theseislands by boat for many years, but recently an airline started in business. Carefully readthe clues about possible plane trips at present. The trips may be direct or include stopsand plane changes on an island. When a trip is possible, it can be made in either directionbetween the islands. You may make notes or marks on the map to help use the clues.First clue: People can go by plane between Islands C and D.Second clue: People can not go by plane between Islands A and B.• Use these clues to answer Question 1. Do not read the next clue yet.1. Can people go by plane between Islands B and D?
Yes No Can't tell from the two clues Please explain your answer.Third clue (do not change your answer to Question 1 now!): People can go by plane betweenIslands B and D.• Use all three clues to answer Questions 2 and 3.2. Can people go by plane between Islands B and C?
Yes No Can't tell from the three cluesPlease explain your answer.
3. Can people go by plane between Islands A and C?Yes No Can't tell from the three cluesPlease explain your answer.
periments in a "cookbook" laboratory),and• relate his own viewpoint to that of an-other in a simple situation (be aware anautomobile approaching at 55 mph ap-pears to be travelling much faster to adriver moving in the opposite direction at55 mph).
However, persons whose reasoning hasnot developed beyond the concrete stagedemonstrate certain limitations in theirreasoning ability. These are evidenced asthe person:• searches for and identifies some vari-ables influencing a phenomenon, but doesso unsystematically (investigates the ef-fects of one variable without holding allthe others constant);• makes observations and draws infer-ences from them but without consideringall possibilities (fails to see all of the majorsources of error in a laboratory experi-ment);• responds to difficult problems by
applying a related but not necessarilycorrect algorithm (uses the formula s =at'212 to calculate displacement, evenwhen the acceleration is not a constant),and• processes information, but is notspontaneously aware of his own reasoning(does not check his conclusions againstthe given data or other experience).
The puzzle responses given by Fred andDeloris are examples of concrete rea-soning.
Formal reasoning
The following are characteristics offormal reasoning patterns and examplesfrom the history of physics to illustratethem:
Combinatorial reasoning A person sys-tematically considers all possible relationsof experimental or theoretical conditions,even though some may not be realized inNature (for example, using the spectralresponse of the eye to develop the three-
element theory of color vision),Control of variables In establishing the
truth or falsity of hypotheses, a personrecognizes the necessity of taking intoconsideration all the known variables anddesigning a test that controls all variablesbut the one being investigated (for ex-ample, changing only the direction of thelight to detect the possible existence of theether),
Concrete reasoning about constructs Aperson applies multiple classification,conservation, serial ordering and otherreasoning patterns to concepts and ab-stract properties (for example, applyingconservation of energy to propose theexistence of the neutrino),
Functional relationships A person rec-ognizes and interprets dependencies be-tween variables in situations described byobservable or abstract variables, andstates the relationships in mathematicalform (for example, stating that the rate ofchange of velocity is proportional to thenet force),
Probabilistic correlations A person rec-ognizes the fact that natural phenomenathemselves are subject to random fluc-tuations and that any explanatory modelmust involve probabilistic considerations,including the comparison of the numberof confirming.and disconfirming cases ofhypothesized relations (for example,arguing from the small number of alphaparticles scattered through large anglesfrom gold foil to suggest a nuclear modelfor the atom).
Formal reasoning patterns, taken inconcert, enable individuals to use hy-pothesis and deduction in their reasoning.They can accept an unproven hypothesis,deduce its consequences in the light ofother known information and then verifyempirically whether, in fact, those con-sequences occur. Furthermore, they canreflect upon their own reasoning to lookfor inconsistencies. They can check theirresults in numerical calculations againstorder-of-magnitude estimates. Jamesand Myrna, in their responses to thepuzzles, gave evidence of using formalreasoning.
In the table on page 28 we summarizesome differences between reasoning at theconcrete and formal levels. It is quiteclear that a successful physicist makes useof formal reasoning in his area of profes-sional expertise. In fact, formal reasoningis prerequisite for producing quality workin physics.
Many theoretical and experimentalissues relating to Piaget's work are stillbeing investigated. Piaget's original no-tion was that all persons use formal rea-soning reliably by their late teens. Yetrecent studies strongly suggest that, al-though almost everyone becomes able touse concrete reasoning, many people donot come to use formal reasoning reliably.These persons often appear to be rea-soning at the formal level and/or com-prehending formal subject matter when
26 PHYSICS TODAY / FEBRUARY 1977
College Teaching and the Development of Reasoning 188
Workshops that focus on physics teachingand the development of reasoning have beenoffered at professional meetings and on in-dividual college campuses. The workshopmaterials for examing instructional aids invarious subject areas are available fromseveral sources:• Physics Teaching and the Developmentof Reasoning Workshop Materials, AAPTExecutive Office, Graduate Physics Building,S.U.N.Y., Stony Brook, N.Y. 11794;• Biology Teaching and the Developmentof Reasoning Workshop Materials, LawrenceHall of Science, Berkeley, Cal. 94720;• Science Teaching and the Developmentof Reasoning Workshop Materials (includesphysics, chemistry, biology, general scienceand earth sciences), Lawrence Hall ofScience, Berkeley, Cal. 94720, and• College Teaching and the Developmentof Reasoning Workshop Materials (includesanthropology, economics, English, history,mathematics, philosophy and physics ma-terials), ADAPT, 213 Ferguson Hall, Universityof Nebraska-Lincoln, Lincoln, Neb 68588.
Another such workshop is being spon-sored by the American Association ofPhysics Teachers at the joint APS-AAPTmeeting in'Chicago this month.
College students are being encouragedto develop their reasoning in several pro-grams, including:• physical-science programs, such as thoseled by Arnold B. Arons, University of Wash-ington (Amer. J. Phys. 44, 834; 1976) andJohn W. Renner, University of Oklahoma(Amer. J. Phys. 44, 218; 1976);• the introductory physics laboratory coursefor engineering students developed by RobertGerson, University of Missouri-Rolla, and• two Piaget-based multidisciplinary pro-grams for college freshmen, ADAPT at theUniversity of Nebraska-Lincoln and DOORSat Illinois Central College, East Peoria.
they are actually only applying memor-ized formulas, words or phrases.
The development of formal reasoningrepresents an extremely worthwhile ed-ucational aim. Formal reasoning is fun-damental to developing a meaningfulunderstanding of mathematics, the sci-ences and many other subjects of modernlife. The finding, by a wide variety ofstudies,5 that more than one third of theadolescents and adults in the UnitedStates do not employ formal reasoningpatterns effectively presents a real edu-cational challenge. What can be doneabout the significant fraction of the pop-ulation that appears to be stuck at thestage of concrete reasoning?
Self-regulation
As physicists, we can see the advan-tages to our profession of more wide-spread use of formal reasoning patterns.To see the role that physics would have toplay in creating the necessary atmosphere
u4l.it I
By comparing the extensions of a coil spring at various points, these students are gaining insightinto proportionality; such formal-reasoning patterns are attained through self-regulation.
for this, let us turn to another concept inPiaget's theory of intellectual develop-ment, that of self-regulation.
Self-regulation is the process wherebyan individual's reasoning advances fromone level to the next, an advance that isalways in the direction toward more suc-cessful patterns of reasoning. Piagetconsiders this process of intellectual de-velopment as analogous to the differen-tiation and integration one sees in thebiological development of an embryo, aswell as analogous to the adaptation ofevolving species.
A person develops formal reasoningonly through the process of self-regula-tion. Concrete reasoning thus is a pre-requisite for the development of formalreasoning.
The process of self-regulation is one inwhich a person actively searches for re-lationships and patterns to resolve con-tradictions and bring coherence to a newset of experiences. Implicit in this notionis the image of a relatively autonomousperson, one who is neither under theconstant guidance of a teacher nor strictlybound to a rigid set of precedents.
Self-regulation can be described asunfolding in alternating phases, beginningwith assimilation. The individual'sreasoning assimilates a problem situationand gives it a meaning determined bypresent reasoning patterns. This mean-ing may or may not, in fact, be appropri-ate. Inappropriateness produces what iscalled "disequilibrium," "cognitive con-flict" or "contradiction," a state that, ac-cording to Piaget, is the prime mover ininitiating the second phase—accomoda-tion.
Accomodation entails
• an analysis of the situation to locate thesource of difficulty and• formation of new hypotheses and plansof attack.Just how this is done varies from personto person and depends upon his analyticaland problem-solving abilities. The re-sults of these reflective and experimentingactivities are new reasoning patterns thatmay include new understandings. Interms of assimilation and accommoda-tion, self-correcting activities (accom-modation) are constantly being tested(assimilation) until this alternation ofphases produces successful behavior.The whole self-regulation process, di-rected at a stable rapport between pat-terns of reasoning and environment, isoften called "equilibration" by Piaget.
Recall the self-regulation process thatCount Rumford recounts in his essays onheat.6 In Piaget's terms, Rumford ex-perienced cognitive conflict by the ex-traordinary ability of apple pies to retaintheir heat, by the fact that heat had noeffect upon the weight of objects and bythe intense heat of the metallic chipsseparated from the cannons he bored. Hecould not assimilate these experienceswith the caloric theory of heat, so he re-jected that theory. He accommodatedhis reasoning to experience by developingthe idea that heat was excited and com-municated by motion.
The development of reasoning has tworequirements: Exploratory experienceswith the physical world, and discussionand reflection upon what has been done,what it means and how it fits, or does notfit, with previous patterns of thinking.This suggests that experiences gainedthrough physics can play a key role in the
PHYSICS TODAY / FEBRUARY 1977 27
College Teaching and the Development of Reasoning 189
Let us examine how physics could beused to foster self-regulation in a person.Two factors appear to be required:• He must be faced with a physical sit-uation that he can only partially under-stand in terms of old ideas and• he must have sufficient time to grapplementally with the new situation, possiblywith appropriate hints, but without beingtold the answer—people must be allowedto put their ideas together for them-selves.
The ideal situation would be one inwhich the problems experienced are feltto be solvable. The Piaget hypothesis isthat a challenging but solvable problemwill place persons into an initial state ofdisequilibrium. Then, through their ownefforts at bringing together this challengewith their past experiences and what theylearn from teachers or peers, they willgradually reorganize their thinking andsolve the problem successfully. Thissuccess will establish a new and morestable equilibrium with increased un-derstanding of the subject matter andincreased problem-solving capability, thatis, intellectual development.
One example of such a use of physics isan exhibit of a spring scale and an equal-arm balance mounted on the wall of anelevator in a public building.' The ridersin the elevator noticed that the "weight"of the object on the scale varied while thebalance remained stationary, a paradoxthat gave rise to some cognitive conflict.A small card beside the exhibit askedquestions and offered hints to encouragethe riders to accomodate to this experi-ence.
Physics programs, done properly, canbe effective means of promoting intel-lectual development. Such develop-mental-physics programs are not aimedat producing more physicists, but at en-abling people to develop their potentialfor formal reasoning. This reasoning canserve them well in many aspects of ourtechnological society.
If physics is an essential element in thegrowth of reasoning, why are persons soturned off by physics? It seems to us thatthe physics community has chosen toisolate itself from individuals using pri-marily concrete reasoning patterns. Ithas been suggested that all of the juniorand senior high-school physics curriculathat have been developed in the last 25years have been intended for studentswho typically use formal reasoning.
True, modern secondary-school physicscourses, such as PSSC Physics and theProject Physics course, have directedstudents toward laboratory experiments.Yet many of the experiments can only beunderstood within the hypotheticalstructure of the formal laws of physics.For example, the use of stroboscopic
Concrete versus formal reasoning
In concrete reasoning, a person• needs reference to familiar actions, objects and observable properties;• uses classification, conservation, serial ordering and one-to-one correspondence inrelation to concrete items above;• needs step-by-step instructions in a lengthy procedure, and• is not aware of his own reasoning, inconsistencies among various statements or con-tradictions with other known facts.
In formal reasoning, a person• can reason with concepts, relationships, abstract properties, axioms and theories;• uses symbols to express ideas;• applies combinatorial, classification, conservation, serial ordering and proportionalreasoning in these abstract modes of thought;• can plan a lengthy procedure to attain given overall goals and resources, and• is aware of and critical of, his own reasoning, and actively checks on the validity of hisconclusions by appealing to other information.
From Module 9 of the Science Teaching and the Development of Reasoningworkshop materials (see the Box on page 27).
photographs to analyze the collisions oftwo objects appear to be at least as de-manding as the Ticker-Tape Puzzle; yetwe have seen that the solution to theTicker-Tape Puzzle was inaccessible tostudents who used only concrete rea-soning.
In short, our fixation on the formal as-pects of physics instead of its concreteexperiences has made physics unneces-sarily difficult and dry. We have re-moved the sense of exploration and dis-covery from the study of physics for themajority of students. Several generationsof public-school students have beenalienated from physics.8'9
What can you do to make the study ofphysics less a slave to the formal structureof the discipline and more of a servant tothe development of reasoning? Youcan• become more familiar with the appli-cations of Piaget's ideas to learning fromphysics;• learn about the present attempts tooffer Piaget-based programs for largenumbers of students;• encourage your school or college toinitiate some programs that focus on thedevelopment of reasoning rather than themastery of content;• assist service clubs and other groups topresent physics to the citizens by meansof displays, exhibits and media, and• develop your skills as a facilitator ofself-regulation in others.10
The Box on page 27 lists some sourcesof workshop materials, as well as currentcollege programs based on the Piagetconcepts.
The human potential
As a result of our professional experi-ences, we of the physics community maypossess a valuable insight: that carefullyplanned interactions of persons with theexperimental systems and concepts ofphysics can contribute vitally to the full
human potential. Perhaps our efforts toincrease the appropriate people-physicsinteractions are as important to the futureof mankind as our continuing efforts toincrease our fundamental understandingof physical systems.
This material is based upon work done as apart of AESOP (Advancing Education throughScience-Oriented Programs), supported bythe US National Science Foundation underGrant No. SED74-18950. The opinions arethose of the authors and do not necessarilyreflect the views of the Foundation.
References1. Proceedings of the Workshop of Physics
Teaching and the Development of Rea-soning (Anaheim, Calif. January 1975),American Association of Physics Teachers,Stony Brook, N.Y. (1975).
2. E. F. Karplus, R. Karplus, School Sci. andMath. 70, 5(1970).
3. B. Inhelder, J. Piaget, The Growth ofLogical Thinking from Childhood toAdolescence, Basic Books, New York(1958).
4. PHYSICS TODAY, June 1972.5. D. Griffiths, Amer. J. Phys. 14, 81 (1976);
G. Kolodiy, J. Coll. Sci. Teach. 5,20 (1975);A. E. Lawson, F. Nordland, A. DeVito.J.Res. Sci. Teach. 12, 423 (1976); J. W.McKinnon, J. W. Renner, Amer. J. Phys.39, 1047 (1971); J. W. Renner, A. E. Law-son, Phys. Teach. 11, 273 (1973); C. A.Tomlinson-Keasey, Dev. Psychol. 6, 364(1972).
6. The Collected Works of Count Rumford(S. C. Brown, ed.), Harvard U. P., Cam-bridge, Mass. (1968).
7. L. Eason, A. J. Friedman, Phys. Teach. 13,491 (1975).
8. P. de H. Hurd, School Sci. and Math. 53,439(1953).
9. M. B. Rowe, The Science Teacher 42,21(1975).
10. A. B. Arons, Amer. J. Phys. 44,834 (1974).
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