NeuroscienceandEarlyChildhoodMathEducation:

ABlueprintforBetterBridgesAssessingtheefficacyofanewresearchdesignforestablishingconnectionsbetweencognitiveneurosciencefindingsandpreschoolmathlearning

JuliaL.Niego

MastersofScienceThesis

NeuroscienceandEducationProgram

BiobehavioralSciencesDepartment

May2011

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“Themoretheschemataaredifferentiated,thesmallerthegapbetweenthenewandthe

familiarbecomes,sothatnovelty,insteadofconstitutinganannoyanceavoidedbythesubject,

becomesaproblemandinvitessearching.”

­JeanPiaget

ProjectDescription

Alargebodyofliteraturedescribestheriftbetweenneuroscienceandeducation,twotheoreticallyrelatedfieldsthathavestruggledtoestablishcommonground.Researchershavepointedtoadisconnectbetweenthepromiseofneurosciencedataandactualapplicationtotheclassroom.Thisprojectconsidersthewaysthatcognitiveneuroscienceandeducationcanforgecommongroundtoamelioratetheseproblems.Buildingontheclaimthataconnectionbetweendataandtheclassroomwillnecessitatebi‐directionalandcollaborativecommunicationbetweenscientistsandeducators,aclinicalinterviewmethodhasbeenchosenasthetoolforuncoveringteachers’experience‐basedmentalmodelsoflearningprocessesintheirstudents’brains.Drawingontheneedforcommonmodelsandlanguage,theseinterviewsarebasedaroundvideosegmentsofchildrenlearningmathintheearlychildhoodclassroom.Theoverarchinggoaloftheprojectistoengendermeaningfuldiscussionbetweeneducationalneuroscienceresearchersandteachersinordertoestablishimportantconnectionsbetweendataonthebrainandlearningasittrulytakesplaceinthepre‐schoolenvironment.Interviewswerecarefullyrecordedandanalyzedinaninterpretivefashiontoidentifyimportantvariablesandobservationcategoriesforfutureresearch.

BackgroundandTheoreticalApproach

NeuroscienceandEducation

Atfirstglance,thefieldsofeducationandneurosciencemightseem

intrinsicallylinked.Afterall,learningtakesplaceinthebrain.Education,perhaps

nowmorethanever,recognizestheneedforaclearerunderstandingofhow

studentslearn.Overthepastdecades,neuroscienceresearchhasmadesignificant

advances,uncoveringnewandexcitingdataonthelearningbrain.

Yet,theliteraturetellsadifferentstory.Neuroscienceandeducationare

theoreticallyrelatedfieldsthathavestruggledtoforgecommonground.Sincethe

90’s,declaredbytheUSCongresstobethe“DecadeoftheBrain,”muchoftheinitial

zealfordirectapplicationofneurosciencedatahasfaded.Earlyattemptstouse

neurosciencetheoriesintheclassroomresultedinmisunderstandingsand

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questionableeducationalpoliciesbasedonhypedideassuchassynaptogenesis,

criticalperiodsandenrichment(Bruer,1997;Mayer,1998).

Thishasledtheresearchcommunitytoreactwithappropriatecautionand

skepticismaboutfurtherattemptstomergeneuroscienceandeducation.Bruerhas

beenattheforefrontofthispositionsincehis1997paper“Neuroscienceand

Education:ABridgeTooFar”(Bruer,1997;Bruer,2006).Hemakestheclaimthat

thetheoreticaldistancebetweenneuroscienceandeducationmaysimplybetoo

great.Thecoreconceptsusedbyneuroscientistsaredifferentfromthoseusedby

psychologistsandclassroomteachers,leadingtoinevitablemisunderstandings.

Brueralsoquestionshowasuperficialfascinationwithsynapsesandbrainimages

causesteacherstooverlookasubstantialbodyoflargelyuntappedcognitive

psychologyresearch(Bruer,2006).Heposesthatresearchersshouldinstead

devoteeffortstoshorterbridgesbetweeneducationandcognitivepsychology,

cognitivepsychologyandneuroscience(Bruer,1997).

Mayer(1998)pointsoutthatthereisaninherentprobleminthegoalof

tailoringneurosciencefindingsforeducatorsinordertobaseeducationalpractices

onneuroscience.Instead,heposesthatthebridgebetweencognitiveneuroscience

andeducationalpsychologyneedstobea“two‐waystreet,”whereeducational

theoryguidesandinformsneuroscienceresearch.

Yet,neurosciencehascontinuedtoadvance,andeverydaynewfindings

abouthowstudents’brainslearntoread,write,domath–andhandlethestressof

toomuchhomework–areshowinguponbestsellertablesatthebookstore,covers

ofpopularmagazinesandtelevisionscreens.Thelargerfieldofneurosciencehas

branchedandmergedwithotherdisciplines,leadingtosubfieldsofcognitive,social

anddevelopmentalneuroscience.In1999NRCdeclared“Neurosciencehas

advancedtothepointwhereitistimetothinkcriticallyabouttheforminwhich

researchinformationismadeavailabletoeducatorssothatisitinterpreted

appropriatelyforpractice.”

Overthelastdecadethe“neuroscienceandeducationargument”(Bruer,

1997)hascontinuedtoreverberateamongresearchersineducation,psychology

andneuroscienceastheyregardthepromiseofnewdataonthebrainforadvancing

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thescienceofeducationandlearning.Researchershaveposednewsolutionsfor

buildingstrongerbridgesthatcan“spanthechasm”betweenneuroscienceand

education(AnsariandCoch,2006;Goswami,2006,Bruer,2006).

Asoberconsensusremainsinthecurrentliteraturethatdescribinghowdata

onstructuralandfunctionalchangesinthebraincanactuallybeusedtoinform

educationalpolicyandpracticeisadifficulttask(AnsariandCoch,2006;Goswami,

2006,Bruer,2006).Forone,researchersidentifyalackofabilityonthepartof

teacherstoacquireandrecognizerelevantdata,leadingtoacceptanceof“neuro‐

myths”and“Brain‐Based”learningpackagesthatarenotsupportedbyscience.

AnsariandCoch(2006)refertoquestionablemediareportsandoversimplified

claimsaboutleft/rightbrainlearners,“exercising”thewholebrain,and“brain‐

buttons”thatinundatedschoolsoverthelastdecade.

Anotherproblemisteachers’lackofknowledgeandskillsnecessaryto

interpretneurosciencedata.Goswami(2006)notesthattheprogressin

neurosciencelabsislargelytheoretical,andwithoutafirmunderstandingof

hypothesis,theoryandestablishedmodel,teachersarenotabletoestablishhowdata

fitsintothe“bigpicture.”Furthermore,Goswamistatesthatteachersoftenview

scientificresearchastooconcernedwithestablishingrigorinpreciseexperimental

manipulationsandcomplainthatscienceresearcherssimplyprovidetoomuchdata.

EducationalNeuroscience

Takentogethertheseobstaclesstackuptoadifficultproject,yethintsof

promiseareemerginginrecentliterature.Researchershavebeguntocollaborate

acrossthedisciplinesofneuroscienceandeducationandanewinterdisciplinary

fieldhasemerged.Thisisevidencedbythegrowthofnewresearchcentersand

educationalprogramssuchastheCentreofEducationalNeuroscienceatCambridge,

theMBESociety(http://www.imbes.org)andgraduateprograminMind,Brainand

EducationatHarvardUniversity,theundergraduateprograminNeuroscienceand

EducationwithintheEducationDepartmentatDartmouthCollege,andthegraduate

programinNeuroscienceandEducationwithintheBiobehavioralScience

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DepartmentatTeacher’sCollege,ColumbiaUniversitywherethepresentproject

wasdeveloped.

Thefieldofeducationalneurosciencehasbecomeanexcitingnewareaof

educationalresearch.Acentralpositionwithinthisfieldistheacknowledgment

thatattemptsatdirectapplicationofneurosciencedatatotheclassroomisindeeda

“bridgetoofar”(Bruer,1997;Goswami,2006).Insteadtheaimofnewinvestigation

isfindingpossiblewaysto“buildstrongbridges”(DeSmedt,Ansari,Grabner,

Hannula,ScheiderandVerschaffel,2010)throughmultiplebi‐directionaland

reciprocalinteractionsbetweenresearchersineducationandcognitive

neuroscience.

ThismodelcanbeseenasincorporatingBruer’s(1997,2006)emphasison

theimportanceofcognitivepsychologytobotheducationandneuroscience,aswell

asMayer’s“two‐waystreet”(Mayer,1997).Theemergenceofcognitive

neuroscienceasasubfieldofneurosciencewasdrivenbythelinkingof

connectionistmodelsofthoughtandbehaviordevelopedbycognitivepsychologists

(seeAnderson,2005forafullreview)withnewneurosciencetechniquesfor

creatingimagesoftheactivebrain.Throughvarioustechniquesinvolving

electromagnetic(MEG,EEG,ERP)andhemodynamic(PET,MRI,fMRI)

measurement,dataiscollectedandusedtobuildmodelsorpicturesofbrain

structures,connectionsandpathways(Campbell,2006).

Educationalneuroscienceresearchersholdthatcognitivepsychology

informedby,andinforming,cognitiveneuroscienceshouldmakeupthecoreof

educationalneuroscience(Berninger&Corina,1998;Bruer,1997;Campbell,2006;

Geake&Cooper,2003).Cognitiveneuroscienceresearchfocusesontheneural

mechanismsunderlyinghumanbehaviorandcognition,whichmatchescloselywith

educationalresearchonlearningandinstruction.Bruer(1997)pointedout,asone

noteofoptimismin“ABridgetooFar,”cognitivemodelscanbeseenasalocusof

similaritybetweenresearchinneuroscienceandeducation.Afterall,cognitive

neuroscienceisbuiltonmodelsofbrainprocessesprovidedbycognitive

psychology,andthesemodelsareasfundamentaltocognitiveneuroscienceasthey

aretotheappliedscienceoflearning.

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Furthermore,inidentifyingsolutionsforbuildingbridgesbetween

neuroscienceandeducation,bi‐directionalcollaborationisavitalelement.Ansari

andCoch(2006)describeaneedfor“practicalmechanisms”tosupportandfoster

meaningfulintegrationbetweenthebrain‐labandtheclassroomsothatteachers

willbemoreinformedconsumers.Thismustbeaccomplishedthroughawareness

andunderstandingofsimilaritiesanddifferencesbetweenresearchinneuroscience

andeducation,andbyestablishingpointsofcontactbetweenscientistsand

educatorsincludingbidirectionaldialogueandcollaborativeexperimentdesign.

Goswami(2006)urgesthatanewgenerationofmulti‐disciplinary

researchersmustdedicatetheircombinedexpertiseinbothneuroscienceand

educationtopresentinghighqualityknowledgeonthebrainindigestibleformand

interpretingneurosciencefromtheperspectiveofandinthelanguageofeducators.

Thisrequiresthatsuchresearchersspendtimewitheducatorsinordertoestablish

waysthatmeaningfulcommunicationcanbeestablished.Commonmodelsof

students’thinkingneedtobeestablishedbetweenresearchersandteachersinorder

tosupportandsustaintrueandequalcollaboration,andtofostersuccessful

exchangeofrelevantdatabetweendisciplines.Anactiveprojectmustalsobe

underwaytodevelopacommonlanguagebetweenneuroscientistsandeducatorsso

thateachunderstandsoneanotherclearly,andsothatneithersideisputoffby

misinterpretedtheoriesorjargon.AsMayer(1998)recognized,drawingon

teachers’experienceandintuitionsaboutstudents’learningpresentsnewhopefor

collaborativedesignofcognitiveneuroscienceresearchthatwillbetrulymeaningful

toeducators.

CognitiveNeuroscienceandMathematics

Amidthegrowingfieldofcognitiveneuroscience,mathematicslearninghas

presentedanareaofparticularpromise.InProceedingsforthe30thConferenceofthe

InternationalGroupforthePsychologyofMathematicsEducationheldinPraguein

2006,Campbelldescribesabuildingfrustrationonthepartofmatheducatorswith

purelytheoreticalmodelsofstudent’learning.Hediscusseshisowndesireasa

matheducatortoseeinsidehisstudent’sbraininordertounderstandhowitis

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changinginresponsetoinstruction,andwhatishappeningwhenbreakdownsin

understandinginevitablyoccur.Campbelloutlineshowadvancesincognitive

neuroscienceholdnewpossibilitiesforfillinginthesegapsineducators’

understandingofstudents’learning.

InarecentpositionpaperbasedonissuespresentedattheEARLIAdvanced

StudyColloquiumonCognitiveNeuroscienceandMathEducation,heldinBelgium

in2009,DeSmedtetal(2010)statethatbringingcognitiveneurosciencetobearon

mathematicslearninghasledtoveryproductiveresearchinrecentyears(Ansari,

2009;Dehaene,2009;Lipton&Spelke,2005;Lemer,Dehaene,Spelke,&Cohen,

2003).Theauthorspointouthowever,thatneuroimagingstudiesaimedat

describingrelationshipsbetweenbrainactivityandinstructionalpracticearestill

scarce.

Inordertoexploresuchconnections,neurosciencemustbeguidedby

educationalandpsychologicaltheories.ReferencingresearchbydeJongetal

(2009),DeSmedtetaloutlinespecificquestionsprominentineducationalresearch

thatcoulddrivefuturecognitiveneuroscienceresearch,suchaslearningfrom

multiplerepresentations,cognitiveloadandtheroleofaffectiveprocessesin

learning.Theauthorsconcludethateducationalresearcherscanplayapivotalrole

byidentifyingimportantvariableswhichneedtobeincorporatedintoeducational

neuroscienceinvestigations.

EducationalNeuroscienceandEarlyChildhoodMath

Math education in the preschool years has been a source of question and

controversyfordecades.In2002,theNationalCouncilofTeachersofMathematics

and theNational Association for the Education of Young Children collaborated to

produceajointpositionstatementrecognizingthefailureofUSstudentstoachieve

mathematicalprowessconsistentwithpeers inothercountriesandadvocatingan

increasedattentiontoearlychildhoodmatheducation(NationalAssociationforthe

EducationofYoungChildren&NationalCouncilofTeachersofMathematics,2002).

Whilemanyeducatorsnowagreethatmatheducationshouldbeginearly,thereisa

lackofunderstandingofhowchildren’smathematical thinkingdevelops, andhow

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besttosupportitintheclassroom(Ginsburg,Jang,Preston,VanEsselstyn,&Appel,

2004).

Agrowingbodyofresearchineducationanddevelopmentalpsychologyhas

investigated the development of mathematical thinking and best practice for

teaching math to young children (Piaget, 1970; Clements, 1999; Ginsburg, Jang,

Preston, VanEsselstyn & Appel, 2004; Seo & Ginsburg, 2004). Ginsburg (1988,

1989,1997,1998,2007)hascontributedmuchtothisburgeoningfieldbybuilding

on Piaget’s method of cognitive clinical interviews as a research tool to assess

children’s mathematical knowledge, problem‐solving strategies and overall

understanding of math concepts at various stages of development. This has

provided researchers and educators with new ways to “enter the child’s mind

(Ginsburg, 1997)” and observe mathematical thinking in order to improve math

teachingandassessment.

Inrecentyearstherehasbeenacallforpreschoolmathcurriculathatare

researchbased(Clements,2007;Clements&Samara,2007).Questionshavearisen

regardingtheappropriatenessofteachingmathematicstoveryyoungchildren,the

bestmodeofinstruction,andtheroleofconcretemanipulativesinmathlearning

(Ginsburg,BoydandSunLee,2008).Finally,despitemisinterpretationofearly

discoveriesaboutneuronsandsynapses,cognitiveneuroscienceconfirmsthatthe

earlyyearsoflifeareveryimportantinachild’smathematicaldevelopment,serving

asafoundationonwhichshewillbuildsubsequentknowledge(Baroody,2007,

Spelke&Dehaene,1999,Xu,Spelke,&Goddard,2005).Clearly,matheducatorsand

educationalneuroscienceresearcherswanttoachieveafullerandmoreaccurate

understandingofhowtheyoungbraindevelopsmathematicallyinordertoknow

howtobestsupportbothtypicalandatypicalmathlearning.

Evenso,thereisalackofcognitiveneuroscienceresearchleadingto

insightfulexplanatorymodelsofchildren’slearningprocessesthathaveproven

relevantforapplicationintheearlychildhoodmathclassroom.Partofthereason

forthisisthatthesemodelsdonotresultfromthecarefullycontrolledexperiments

favoredbycognitivepsychologyandneuroscience.Asanypreschoolmathteacher

willtellyou,3and4‐yearoldsarespontaneous,unpredictable,andficklelearners.

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Higher‐levelcognitiveprocesses,evenintheadultbrain,arebynaturenon‐linear,

fulloffeedbackloopsandprocessesthatcompeteandcoordinate.Modelsofthese

processesthatcanbeunderstoodandusedbyteachersmustbetrueexplanatory

modelsthatareiconicandanaloginnaturebeingbuiltupfrom“moreprimitiveand

familiarnotions(Clement,2000).“

Inconclusion,whileeducationalneuroscienceresearchdoesnotasyet

provideafullorapplicablemodelofchildren’smathlearning,thefieldismuch

closertothispossibilitythanever.Withinthecurrentliteratureisablueprintfor

newresearchmethodsthatcanbeginconstructingthismodel.Itisclearthatsuch

researchmustinvolve(1)bi‐directionalcollaborationbetweenearlychildhood

mathteachersandeducationalneuroscienceresearchers(2)involveopportunities

foropendiscussion,reflectionandexchangeofideasand(3)createcommonground

formeaningfulcommunicationaboutresearchquestions,includingashared

languageandtheoreticalframework.

ProjectAim

Theaimofthisprojectwastodevelopandassesstheinitialefficacyofa

researchmodelfordetermininghowandinwhatwayscognitiveneuroscience

researchcanbemademeaningfultoearlychildhoodmatheducators.Thespecific

goalsoftheprojectwere:

(1) Todesignaresearchmodelthatwouldincorporaterecommendationsinthe

currentliteratureforbi­directionalcollaboration,commonmodelsand

commonlanguageinordertofostermeaningfulcommunicationbetween

educationalneuroscienceresearchersandteachers

(2) Togatherpilotdataontheefficacyoftheresearchmodelforengagingor

changingteacher’scurrentmentalmodelsofstudent’slearning

(3) Toidentifyimportantvariablesandobservationcategoriesforuseofthe

researchmodelinfutureinvestigation

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ResearchModelDesign

Theprimarygoalofthisprojectwasthecarefulconstructionofaresearch

designthatcouldexplorehowcognitiveneuroscienceonchildren’smathlearning

couldeffectivelyengageteachers.

Bi­directionalCollaboration

Thefirsttaskwastochoosearesearchtechniquethatwouldallowcollection

ofdataonteachers’authenticthoughtsandideasthroughbi‐directional

communicationbetweenresearcherandteacher.

Acognitiveclinicalinterviewmethodwaschosenastheresearchtechniquethat

wouldbestaccomplishthisgoal.SinceitwasdevelopedbyPiaget(1955,1975)todescribe

internalthoughtstructuresinchildren,theclinicalinterviewmethodhasbranchedintoa

varietyoftechniquesforresearchinpsychologyandeducation(Strauss,1993),including

matheducation(Clement,2000;Ginsburg,1989,1997;Ginsburg&Opper,1988;Ginsburg,

Jacobs&Lobez,1998;Ginsburg,Jang,Preston,VanEsselstyn&Appel,2004;Ginsburg,

Boyd,&SunLee,2008).Thestrengthoftheclinicalinterviewmethod,asopposedtonon‐

clinicaldatagatheringtechniques,isthatitcanbeusedtocollectandanalyzedataon

mentalprocessesatthelevelofasubject’sauthenticideasandmeanings,andtoexpose

hiddenstructuresandprocessesinthesubject’sthinkingthatcouldnotbedetectedbyless

open‐endedtechniques(Clement,2000).

Astheclinicalinterviewmethodisbynatureanopen‐endedtechnique

severalissuesregardingreliabilityofdatawillbeaddressed.Clement(2000)

outlinesimportantconsiderationsforresearchersusingthetechniqueinorderto

fosterreliability.First,hesuggestspreparingsetprotocolsforinterviewsthatcan

beusedwithrepeatedsubjects.Second,videotapinginterviewscreatesarich

recordofverbalandbehavioraldatathatcanbereexaminedandshared.Finally,a

combinationofgenerativeandconvergentinterviewmethodsallowsinterviewsto

befirstanalyzedinanexploratoryfashionsothatobservationcategoriescanbe

developedforlatercodingofdata.

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Inhisownresearchconstructingmodelsofproblemsolvinginalgebra

students,Clementurgestheneedtobeginwithgenerative,interview‐basedcase

studies.Theseareanalyzedandtheoreticalhypothesestaketheformofmodelsthat

aregroundedinnaturalisticobservationofbehaviors.Asdataiscollectedand

analyzed,theseinitialmodelsarerevisedinabi‐directionalresearchtechnique

incorporatingbothbottomup(inductive)andtop‐down(deductive)methods.

Throughthisprocess,investigatorsbecomesensitizedregardingwhattolookfor,

andobservationcategoriescanbedevelopedforfuturedata,providingthe

foundationforthedesignofconvergentstudies.

Basedontheserecommendations,thefollowingelementswereincorporated

intotheresearchdesign:

Threesetprotocolsweredevelopedforeachclinicalinterview.Thechoiceof

questionsfortheprotocolsdrewontheseminalworkofPiaget(1975),aswell

adaptationsofthesemethodsdevelopedbyClement(2000),Strauss,(1993)and

Ginsburg,(1989,1997).Thefirstprotocol,(Interview1)wasdesignedtocollect

teachers’uniquepathtoteaching,educationalbackground,andpersonalphilosophy

orapproach.Thesecondprotocol(Interview2)includessixquestionsthatrelateto

discussionofaspecificteachingmoment.Thefinalprotocol(Interview3)asksa

seriesoffourquestionsthatinviteteacherstorelatefindingsofcognitive

neurosciencetotheteachingmoment,theirownclassroomsandpersonal

philosophies,aswellastodescribewaysthattheneuroscienceinformation

impactedorchangedtheiropinions/beliefsaboutearlymathlearning.Itis

importanttonotethat,whilequestionsfortheseprotocolswerepre‐set,the

interviewerwasabletoreactresponsivelytoanswersastheywerecollectedby

askingfollow‐upquestionstoclarifyandextendtheinvestigation(Clement,2000).

TheseprotocolsandquestionswillbediscussedinfurtherdetailintheMaterials

andMethodssectionofhispaper.Ascriptforeachprotocolisalsoincludedinthe

Appendix.

Eachclinicalinterviewwasvideorecorded.Repeatedreviewofrecorded

interviewswouldallowdatatobeinitiallyanalyzedinanopen‐endedexploratory

fashioninordertodevelopobservationcategoriesforfutureanalysisandcoding.

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CommonModels

Thesecondtaskinthegoalofassemblingtheresearchdesignwastoidentify

commonmodelsofstudentlearninginordertoallowmeaningfuldiscussion

betweenresearcherandteachers,andguidetheincorporationofneurosciencedata

intothisdiscussion.

Itisnoteworthythatevenwithallthenewdatacomingfromresearch,there

isamarkedlackofinsightfulexplanatorymodelsofstudents’learningprocesses.

Partofthereasonforthisisthatchildren’scognitiveprocessesarecomplex,highly

influencedbyenvironmentandexperience,andfullofinteractionsbetween

development,instructionandsocialandemotionalfactors.Furthermore,teachers’

experienceswiththeseprocessesarenotderivedfromstudyofdevelopmentand

cognition,butontheirtimespentintheclassroom,teaching,observingand

assessingtheirstudents.

Clementassertsthatsubjects,inthiscaseteachers,dohavepre‐existing

knowledgestructuresandreasoningprocessesthatguidetheirthoughtsandbeliefs

aboutstudents’learning.Thesementalmodelshavestrongeffectsonteachers’

ideasandapproaches.Strauss(1993)claimsthatwithoutdeterminingthenatureof

teachers’mentalmodelsaboutchildren’smindsandlearning,newinformationwill

notbeabletoengageorchangethesemodels.Usingasemi‐structuredclinical

interviewtechniquehecollectedandanalyzedteachers’answerstoquestionsabout

whattheywoulddoinspecificteachingsituations,uncoveringmentalmodelsthat

hecouldthenconnecttoinformationprocessingmodelspresentedbycognitive

psychology(i.e.workingmemory,elaborativeprocessing).

Inasimilarway,thisprojectaimedtouseclinicalinterviewtofirstaccess

thesepre‐existingmodelssothattheycouldbeutilizedindiscussionofstudent

learning,andlaterconnectedtomodelspresentedbycognitiveneuroscience.In

ordertoguidemeaningfuldiscussionofstudents’learning,aproblemspaceneeded

tobeestablishedwithinwhichbothresearcherandeducatorcouldobserve,reflect

onandanalyzestudentinstruction,behavior,strategy,andperformance.By

incorporatingtheelementsthatteachersnaturallychosetodescribelearning

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processes,newinformationcouldbeintroducedonthelevelofateachers’unique

model.

Acase‐basedresearchapproachwaschosenasthetechniquethatwouldbest

accomplishthisgoal.Widelyusedinteachereducationandeducationalresearch,

case‐basedinstructionisapractice‐anchoredlearningpedagogythatcanbeusedto

provideteachercandidatesandresearcherswithmultipleopportunitiestoconsider

complexitiesofteachingandlearning(Andrews,2002;Kilbane,2008;Rosen,2008;

Steinkuehleretal,2002).Kilbane(2008)emphasizesthatcasesillustratelifeinthe

classroomasitactuallyis,notasitshouldbe.Recentresearchonthecase‐based

methodhasrevealedthatcomputercaseswhichoffervideovignettesoflearning

momentscombinedwithinteractivediscussionquestionshavethegreatestimpact

onthequalityofteacher’sreflectivenarratives(Rosen,2008).Teachersareasked

towatchandreflectonvideo‐recordedteachingmomentsastheyhappeninreal

time,thusallowingthemtodescribelearningprocessesontheleveloftheirown

personalmodelsoftheseprocesses.

Videovignettesofearlychildhoodmathteachingmomentswerechosenfrom

theVITAL(videointeractionsforteachingandlearning)archivesofTeacher’s

College,ColumbiaUniversity.Lee,GinsburgandPreston(2009),intheir

descriptionoftheproject,statethatimprovingearlychildhoodteacherpreparation

isthemostpressingneedforearlychildhoodmathematicseducationintheUnited

States.VITALprovidesprospectiveteacherswith“engagingandintellectually

stimulatinghands‐onandminds‐onlearningexperiencesthatsupplementthe

traditionaltextbookandreadings."ThepresentdesignextendstheuseofVITALas

atoolforcollectingdataonteachers’knowledge.

Thequestionsforthesecondprotocol(Interview2)werebasedonthese

learningvignettes,andimbeddedatpointsthroughoutthevideosothatteachers

wereabletodrawonspecificteachingmomentstheyhadjustwatchedwhen

reflectingonanswerstothequestions.Finally,theneuroscience‐basedmodelsof

learningpresentedtoteacherswereconstructedbasedonthesevideocasesin

ordertorelatetothespecificelementsandvariablescentraltoeach.Thesevideo

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vignettesandthecorrespondingneurosciencesupplementswillbediscussedin

furtherdetailintheMaterialsandMethodssectionofthispaper.

CommonLanguage

Thefinaltaskinassemblingtheresearchdesignwastoestablishacommon

languagetoallowformeaningfuldiscussionbetweenresearcherandteachers,and

guidetheincorporationofneurosciencedataintothisdiscussion.

Abasicfamiliaritywithbehavioralandeducationaltermswasassumedfor

subjectsduringconstructionofinterviewprotocolsandpresentationof

neuroscienceinformation.Carewastakentostripawayanypsychologicaljargon,

mathematicalterminology,andneurosciencelanguagethatmaynotbealreadypart

ofsubjects’vocabulary.Throughoutinterviews,closeattentionwaspaidtothe

languageandtermsusedbyanindividualsubject.Anyfollow‐upquestionsor

discussionremainedconsistentwiththisvocabularyandterminology,anddidnot

introducenewlanguage.

Itwasestablishedthatneuroscienceinformationwouldbepresentedto

teachersintwoways.First,aone‐pagesummaryofrecentcognitiveneuroscience

findingsrelevanttothespecificteachingmomenttheywatchedwasgivento

teacherstoread.Thiswrittensummarywasaccompaniedbyasimpleiconic

drawingofthebrain,withkeyareasdiscussedinthewrittensummaryclearly

labeled.Additionalpicturesandsymbolicelementsservedtoillustratethe

neuroscienceinformationinawayconsistentwiththefiguresanddiagramsone

mightfindinpre‐serviceteachereducationmaterials.Inbothofthese

supplementarymaterials,vocabularydidnotexceedthatwhichateachermight

comeintocontactwithincourseworkmaterials.Forexamplebrainareaswere

discussedasbeinginthe“front,”“back”or“side”ofthebrainratherthan“frontal”

“pre‐frontal”“occipital”or“temporal.”Neurosciencesupplementswillbediscussed

infurtherdetailinthematerialsandmethodssectionofthispaper.

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CollectionofPilotData

Thesecondgoalofthisprojectwastotesttheefficacyoftheresearchmodel

bycollectingpilotdata.Interviewswereplannedoverthecourseofthe2010–

2011academicyearwithearlychildhoodmatheducatorsfromvariouseducational

andphilosophicalbackgroundsthathadbeenteachingbetweentwoandfiveyears

inavarietyofpre‐schoolprograms.Itwasestablishedthateachinterviewwouldbe

videorecordedusingaMacintoshMacBookPro.Recordingsofinterviewswouldbe

editedandorganizedusingtheiMovieprogram.Finally,videoswouldbeexported

toQuicktimeandstoredonanexternalharddriveforlaterreviewandanalysis.

MaterialsandMethods

ProjectDesign

Subjectswererandomlyassignedtooneofthreeresearchvignettes:Number

Sense,Arithmetic,orPattern.Eachvignettewascomposedofthreeclinical

interviewsincluding(1)ashort,structuredinterviewaskingteacherstoprovide

informationontheirbackground,pathtoteaching,andphilosophicalapproach(2)a

semi‐structuredinterviewbuiltaroundvideocasesofearlymathteachingmoments

(3)amoreopen‐endedreflectiveinterviewfollowingpresentationofneuroscience

supplements.ResearchvignetteswerepresentedasaPowerPointPresentationona

MacintoshMacBookcomputer.Allclinicalinterviewswerevideorecordedusingthe

iMovieprogramonthesamecomputer.

ResearchVignettes

Thethreemathtopicschosenforthevignettesshareasolidfoundationof

relevantliteraturefromthefieldsofeducation,developmentalpsychology,cognitive

psychologyandmostrecently,cognitiveneuroscience.Thesetopicsarealsocentral

toquestionsguidingcurrentinvestigationintothedevelopmentofmathematical

thinkinginthebrain.

Eachvignetteincludeduniquevideocasesandneurosciencesupplements.

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VideoCases

AllvideoswerechosenfromtheVITAL(VideoInteractionsforTeachingand

Learning)vaultatTeacher’sCollege,ColumbiaUniversity.Eachislessthanthree

minutesinlength,andwasdividedintothreesegmentsshorterthanoneminute.

Eachvideowaschosentopresentateachingmomentthataimedatbuilding

orassessingachild’s/children’sunderstandingofeithernumbersense,arithmetic

orpattern.Belowarebriefdescriptionsofeachvideocase:

NumberSense

• CaseshowedteacherataprivateManhattanpreschoolinherownclassroomwithagroupofpreschoolstudents

• TeacheragreedtobevideorecordedwhileteachinglessonsadaptedfromtheBigMathForLittleKidscurriculum,whichisbasedoncurrentresearchabouthownumbersenseisbuilt

• Activityinvolvedaskingagroupofchildrentofind“fours”ofamongrepresentationsofdifferentnumbersandquantitiesonmulti‐coloredcardsspreadonthefloor:numeralswithandwithoutnumberwords,lines,dots,andpicturesofobjects.

o CLIP1:teacherintroducestasktochildreno CLIP2:veryyoungchildiscalleduptofindafour,usesatrial‐

and‐errorapproachuntilguidedtopickupcorrectcardbycolor

o CLIP3:olderchildcomesforwardandquicklyfindsacorrectcard

Arithmetic

• CaseshowedgraduatestudentatTeachersCollegeconductingateachinginterviewwithapreschoolstudentinaManhattanpreschoolclassroom

• Graduatestudentrecordedinterviewastraininginusingtheclinicalinterviewmethodtoassessandsupportchildren’slearningofarithmetic

• Activityinvolvedaskingchildtocountusingsmallgreenblocks.Usingagameof“addingapples,”childwaspresentedwithtwoadditionproblems

o CLIP1:Childcountstheblocksshehas(six)arrangedintworowsofthree

o CLIP2:Interviewgiveschildsevenmoreblocks,sheincorporatesthemintorowsandcountsthirteencorrectly

16

o CLIP3:Interviewergiveschildonemoreblock,sheincorporatesit,andincorrectlycountsthirteenagain

Pattern

• CaseshowedgraduatestudentatTeachersCollegeandteacher(PrincipalInvestigator)conductingateachinginterviewwithapreschoolstudentinteacher’sownclassroominMontessori‐basedprivateprogressivepreschool

• Graduatestudentrecordedinterviewastraininginusingtheclinicalinterviewmethodtoassessandsupportchildren’slearningofpattern/earlyalgebra

• Activityinvolved(1)askingchildtowatchteacherconstructanABABpatterninvolvingalternatinggroupsofobjectswhichshefirstdescribeswithlanguageand(2)askingchildtobuildasimilarpatternbyherselfwhichtheteacherdescribeswithlanguage

o CLIP1:Childwatchesteacherasshe“thinksofpatterninhermind,”describespatternverbally(“Threecameos,twobluestones…”)andthenconstructsit,placingcameoshorizontallyandstonesvertically

o CLIP2:Teacherdescribesnewpatternforchildto“holdinhermind:”(“Twocameos,threebluestones…)

o CLIP3:Childassemblespattern,preservingcorrectnumberingroupsandABABstructure,butbeginningwithbluestonesandplacingallgroupshorizontally

ClinicalInterviews

ProtocolsforInterviews1and3wereidenticalforallresearchvignettes.

(SeeAppendixAandC).

Thesecondclinicalinterviewprotocol(Interview2)soughttoprobe

teachers’in‐the‐momentreactionstoearlymathteachingmoments.Foreachofthe

threevignettes,numbersense,arithmeticandpattern,videoclipswereeditedinto

threesegmentswhichwereembeddedintoPowerPointslides.Segmentswere

basedonnaturaldivisionsintheteachingmoment,i.e.task‐setup,taskpresentation

bytheteacher,andtaskperformancebythestudent.

Aftereachclip,teacherswereaskedtwoquestions,foratotalofsix(See

AppendixB).Thoughthereisslightvariationintheorderingofthequestionsbased

ondifferencesineachvideo,thequestionsfollowabasiccontinuum:Thefirstsetof

17

questionsinvitesreflectiononstudentbehavior,suchasengagementandinteraction

withmaterials.Thesecondsetaskssubjectstoevaluatetheconceptualteaching

method,i.e.theconcepttheteacherwasattemptingtoteach,andtheapproachused

toteachit.Thelastsetofquestionsaimedatteachers’intuitionsregarding

cognition,includingthechild’sdevelopingmathematicalabilitiesandstrategiesin

solvingthetasks.

Inthisway,Interview2wasconsistentwiththecognitiveclinicalinterview

methodofprobingknowledgestructureinacareful,step‐upfashion.Questions

werescaffoldedtodescribeteachers’relativeplaceonacontinuumofknowledge

spanningbehavioral,educational,psychological,developmental,andcognitivelevels

ofanalysisregardingteachingandlearning.

Foreachvignette,Interview2includedadifferentconsiderationnotedafter

thelastsetofquestionsonthestudent’scognitiveprocess:

Fornumbersense,theinterviewerremainedparticularlyopentoexploration

ofwhythesecondchildwasabletoperformthetaskoffindingfoursomuchmore

quicklyandeasilythanthefirstchild.

Forarithmetic,theinterviewerremainedparticularlyopentoexplorationof

theuseofblocksinsolvingtheproblem,includingwhythechildarrangedtheblocks

thewayshedid,andhowthisaffectedherperformance/success.

Forpattern,theinterviewerremainedparticularlyopentoexplorationof

whythechildpreservedtheoverallstructureofthepattern,butdidnotpreserve

theorderdescribedwithlanguageandneglectedspatialdetails.

NeuroscienceSupplements

Theinformationpresentedintheneurosciencesupplementsprovided

teacherswithasimplifiedsummaryofcurrentandsoundcognitiveneuroscience

findingsrelatedtothetopicsofnumbersense,arithmeticandpattern.Ratherthan

givingteachersacompletemodeloraprescriptionforteaching,thesesupplements

insteadaimedtoestablishaproblemspacewithinwhichbothteacherand

researchercouldmeettoaskandanswerquestionsaboutthespecificteaching

momenttheywatched.

18

Neuroscienceinformationwaspresentedintwoways:(1)asaone‐page

printedsummaryofresearchfindingsand(2)asaniconicdiagramofthebrainwith

relevantlabels,picturesandsymbols.

Theprintedsupplementsfirstsummarizewhathascometobegenerally

agreeduponwithinthefieldofimagingresearchregardingthebrainareasactivein

thetypeofmathtaskpresentedinthevideocase.Nextthesupplementsbriefly

outlinehowbrainpathwaysandconnectionsmightsupportperformanceofthese

mathematicaltasksduringthepreschoolyears.Finally,thesupplementspresent

teacherswithasuggestionorthrustoftheresearchtoguidespeculationandopen

thewayforfurtherquestionsanddebate.Thesedescriptionsaresimpleand

strippedofanyneuroscientificlanguagethatmaybeunfamiliartoteachers.For

example,“takingpicturesofadultsandchildren’sbrains”isusedinsteadof“PET”or

“fMRI.”Additionally,byusinglanguagesuchas“researcherswanttoknow,”

“researchersposethat,”“somestudiessuggest,”and“children’sbrains…seemto

have,”thesupplementsaimedatcreatingspaceforthecollaborativeconstruction,

throughactivebi‐directionaldialogue,ofmodelsincorporatingcognitive

neurosciencefindingsintoateacher’sownexperience‐basedintuitivemodelof

mathlearning.

Thepicturesupplementssupportedprintedinformationinavisualformat.

Thesediagramsweresimilartofiguresexplaininglearningprocessesthatteachers

mightencounterinapre‐serviceorgraduateteachereducationtextbook.The

picturesupplementsshowedasimplepicture/picturesofthebrainthatwere

biologicallyaccuratewithwell‐definedgyributwithoutcoloredregionsor

superimposedoutlines.Brainareasdescribedintheprintedsupplementwere

labeledclearlywithwords,i.e.vision,generalreasoning,language,workingmemory.

Simpleandcolorfulimagesweregatheredonlineandlaidoutingeneralproximity

tocorrespondingbrainregions.Forinstance,acardwiththeword“Five”was

placedbesidelabeledlanguageareasinthelefthemisphere,whilealineofrubber

duckswasplacedbesidevisuo‐spatialareasintherighthemisphere.

Itisimportanttonotethattheseneurosciencesupplementswerecarefully

constructedbytheprincipalinvestigator,basedonnearlytwoyearsofstudying

19

peer‐reviewedliteratureandgraduatecourseworkincognitivepsychology,

developmentalpsychology,cognitiveneuroscienceandeducation.Informationwas

drawnfromnumerous,wide‐spreadandqualifiedsources,andpresentedinaway

thatthePrincipalInvestigatorfeltwouldbemeaningfulandeasilyunderstoodby

teachers,basedonfiveyearsofexperienceteachinganddevelopingmathcurricula

inanearlychildhoodclassroom.

Carewasputintopresenting“highqualityknowledgeonthebrainin

digestibleformandinterpretingneurosciencefromtheperspectiveofandinthe

languageofeducators(Goswami,2006).”Thus,theinformationintheneuroscience

supplementsdoesnotinvolvedirectconnectionsbetweenpiecemealfindingsand

recommendationsforteaching.Rather,thestatementsintheneuroscience

supplementsrepresentthecurrentthrustoftheliteratureonmathlearningandthe

brain,builtinturnonafoundationofeducational,developmentalandcognitive

psychology.

Furthermore,themodelsarepresentedintheircurrent‐andincomplete‐

theoreticalstate,withcorrespondingquestions,ambiguitiesandgapsinknowledge.

Thiswasdoneinhopesthatcurrentmodelscouldbeanalyzedandextended

collaborativelybybothteacherandresearcher.Acompletetheoreticalbackground

ofthedevelopingtheoriesonmathlearningpresentedintheneuroscience

supplementsisbeyondthescopeofthispaper.Evenso,afullreferencesection,

includingmanysolidreviews,hasbeenprovidedafterneurosciencesupplementsin

AppendixD.

PilotDataAcquisition

Subjects

SixteacherswererecruitedfromarangeofNewYorkCitypreschools,

includingpublicPre‐K,private,andprogressiveprograms.Allteacherswerefemale,

andhadbeenteachinginearlychildhoodbetweentwoandsevenyears.Subjects

20

wereeithercurrentlyenrolledinorhadcompletedanEarlyChildhoodEducation

degreeprogram.Noteachershadcompletedcourseworkinneuroscience.

Subjectswereassignedrandomlytoonofthethreeresearchvignettes,so

thattwointerviewswerecollectedforNumberSense,twoforArithmetic,andtwo

forPattern.Partlyduetothedesiretokeepinterviewsessionsnaturalandnot

overly“scientific,”verbalconsentwasobtainedpriortointerview.Teacherswere

informedthatpilotdatawasbeinggathered,andthatwrittenconsentwouldbe

obtainedbeforeanyrecordedmaterialwasshownpubliclyoronline,andbeforeany

personalquoteswerepublished.

Methods

Interviewswereconductedatquiet,familiar,yetneutrallocations,including

emptyschoolclassrooms,orroomsinresidencesotherthanthesubjects’home.

Teacherswerecomfortablyseatedwithinterviewerbeforethecomputerandbriefly

toldthattheywouldbewatchingsomevideosofpreschoolchildrenlearningmath,

andreflectingonwhattheysaw.Noise‐blockingheadphoneswereprovidedwhile

watchingvideoclips.

Interview1wasconducted.SubjectsthenwereshownthePowerPoint

Presentation.Slide1informedthesubjectthattheywouldbewatchingapre‐school

agedchild/pre‐schoolchildreninaManhattanpreschool.Slides2–4showedvideo

clips1–3.Betweeneachclip,subjectswererecordedansweringtwoquestionsto

completeInterview2.PowerpointpresentationsaswellastheiMovieprogram

werekeptinseparatewindowsonthedesktoptoallowforeasytransitionbetween

presentationandrecording.

Subjectswerepresentedwithneurosciencesupplementsuponcompletionof

Interview2.Printedmaterialwasinpaperform,andthepicturewasshownasthe

lastPowerPointslide.Subjectsweregivenasmuchtimeasneededtogetageneral

senseofthematerial,andwereassuredthattheydidnotneedtomemorizeor

repeatinformation.Oncesubjectsconfirmedthattheyfeltsufficientlyfamiliarized

withtheneurosciencesupplements,Interview3wasconducted.

21

Aspreviouslymentioned,Interview3wasamoreopen‐endedandreflective

clinicalinterviewthatattemptedtofindmatchesbetweenteachers’intuitionsand

neuroscienceinformation,evidenceofmisconceptionsaboutneuroscience,andany

teacherperspectivesorknowledgeregardingquestionsorholesincurrenttheories

ofmathlearningintheyoungbrain.

Inordertoexploretheseconnections,follow‐upquestionswereaskedto

furtherexposeteachers’thoughtsandbeliefs.Specificconsiderationsforeach

researchvignetteareoutlinedbelow.

NumberSense

• Howdoteacher’sintuitionsabouttheimportanceofbuildingastrongnumbersenseinpreschoolchildrenmatcheducationalresearch?

• Whatintuitionsdoesteacherhaveregardingdifferentkindsofmathematicalinformationrepresenteddifferentwaysinthebrain?

• Whatevidencedoesteacher’sreflectionrevealofbrainmythsaboutdifferentkindsoflearners(i.e.visualorverbal)or“exercisingthewholebrain?”

• Particularopennesswasgiventoanyintuitionsabouthowtobestsupportthebuildingofnumbersenseasaconcept

• Considerationwasgiventothefactthatteachershadwatchedimplementationofaresearch‐basedcurriculum:BigMathForLittleKids(Greenes,Ginsburg&Balfanz,2004).

Arithmetic

• Howdoteacher’sintuitionsabouthowandwhentosupportarithmeticskillsmatcheducationalresearch?

• Whatintuitionsdoesteacherhaveregardingthedevelopmentofarithmetic,andhowthisinteractswiththeneedforconcreteobjectsandtheuseofsymbols?

• Whatevidencedoesteacher’sreflectionrevealofbrainmythsaboutpurelyconstructivistenrichmentmodelsorabuiltin“mathcenter”inthebrain?

• Particularopennesswasgiventoanyintuitionsabouthowandwhentheshifttolanguage‐basedmathfactshappensorshouldhappentobestsupportmathematicaldevelopment.

• Considerationwasgiventothefactthatteachershadwatchedateachingmomentbuiltontheclinicalinterviewmethod,whichallowedfreeuseofconcretematerialsforproblemsolving,butwasalsoteacherdirected.

22

Pattern

• Howdoteacher’sintuitionsabouttheteachingpatternsupportcurrentfindingineducationalresearchaboutchildren’suseofvisuo‐spatialskillsinmathtasks?

• Whatintuitionsdoesteacherhaveregardinghowsuchtasksdrawonlanguage,mathfactsandvisuo‐spatialreasoning?

• Whatevidencedoesteacher’sreflectionrevealofbrainmythsaboutright/leftbrainlearners?

• Particularopennesswasgiventoanyintuitionsabouttheroleofvisuo‐spatialabilitiesinbuildingthedeepmathematicalunderstandingneededforhigher‐levelmathskillssuchasalgebraicthinking.

• Considerationwasgiventothefactthatteachershadwatchedateachingmomentthatwasbasedonaprogressivevisuo‐spatialmethodofmathinstruction(theMontessorimethod).

AftercompletionofInterview3,teacherswerethankedfortheirparticipationanddismissed.

PilotDataAnalysis

Theresearchdesignyieldedasmallandcohesivesetofpilotdata,whilestill

allowingforatleastonedegreeofcomparisonbothacrossandwithinvignettes.The

sixinterviewsubjectswerecurrentlyteachinginavarietyofpre‐schoolclassrooms,

includingpublicPre‐K,privateandprogressiveprograms.Theyhadvaried

backgroundexperiences,rangingfromdaycarecenterstoprivateandlabpreschools.

Theyalsohadvariededucation,spanningpartiallycompletedcourseworkforaBAin

EarlyChildhoodwithpendingcertification,toanMAinEarlyChildhoodwith

certification.Subjectswererandomlyassignedtooneofthreeresearchvignettes.

Thus,sixinterviewswereanalyzed,twoforeachresearchvignette:NumberSense,

ArithmeticandPattern.

Thegoalofpreliminarydataanalysiswasto(1)determinetheefficacyofthe

researchdesigninengaging/changingteacher’smodelsofstudents’thinking(2)

identifyimportantvariablesandobservationcategoriesforfurtherresearch.

Interviewswereconsideredasindividualcases.Recordedinterviewswerewatched

repeatedlyinordertoorganizeanswerstointerviewquestions.

23

Inordertoaddresstheoverallefficacyoftheresearchdesigninengaging

teacher’smentalmodels,answerstoInterview2weretranscribedandcompared

acrossallsubjects.AspreviouslydiscussedinMaterialsandMethods,Interview2

questionsproceededonacontinuum,callingonteachers’independentabilitiesto

utilizebehavioralobservation,educationalandmathematicslanguage,

developmentalpsychology,andfinallycognitivepsychologyintheiranswers.Three

observationcategoriesweresetup,basedontheoverarchinglevelofanalysisthat

questionsinvitedteacherstouseintheirreflectiononthevideocasesegments.

(1) Areteachersabletocomfortablyanswerquestionsbasedonobservationsof

children’sbehaviorinagiventeachingmoment?

(2) Areteachersabletoeasilyidentifytheconceptbeingtaughtanddiscusswhy

theywoulduseasimilar/differentapproach?

(3) Willteacher’sdiscussionofstudents’developingmathabilitiesandstrategies

revealanexplanatorymodelofchildren’scognitiveprocessesduringthe

teachingmoment?

Forthefinalquestion,answerswerereviewedtodetermineifateacher’s

intuitivemodelwasabletoprovideanadequateexplanationregardingspecific

considerationsforeachmathtopic.ForNumberSense,whywasthesecondchild

wasabletoperformthetasksomuchmorequicklyandeasily?ForArithmetic,what

wasthesignificanceofthechild’suseofblocks?ForPattern,whydidthechild

preservethestructureofthepattern,butnottheorderprescribedinlanguage,or

thespatialorientationofthematerials?

Inordertoassesshowtheneuroscienceinformationpresentedinthe

supplementsengagedteachers’currentmodels,answers1‐3ofInterview3were

transcribedandcomparedacrossallsubjects,includinganswerstofollow‐up

questions.Answerswereorganizedaccordingtothelevelatwhichthedeveloping

modelsofmathematicalthinkinginpreschoolstudents,presentedineducational

neuroscience,matchedteachers’ownintuitivemodelsasdescribedinInterview2.

Threeobservationcategoriesweresetup,basedonthespecificconsiderations

24

guidingtheinterview,whichareoutlinedinMaterialsandMethods.These

considerationsaimedtoidentify:

(1) Howteachers’intuitivemodelsmatchthefoundationaldevelopmentalor

educationalpsychologytheoriesonthemathtopic.

(2) Howteachers’intuitivemodelsmatchthemodelsofmathematicalthinking

presentedbycognitivepsychology,onwhichcognitiveneurosciencemodels

arebased.

(3) Evidenceofbrainmythsspecificallyrelevanttothemathtopic.

Inordertoidentifyhowneuroscienceinformationmightimpactorchangea

teacher’scurrentmodelofmathematicalthinking,answerstoInterview3,including

question4,werereviewedinordertogathercasedescriptivesonhowthe

neuroscienceinformation(1)resolvedquestionsorambiguitiesregardinga

student’sthoughtprocess,(2)changedateachers’opinionsorbeliefsabout

children’smathematicalthinking,or(3)gaveateachernewinsightintostudents’

thinking.

Toassesstheabilityoftheresearchdesigninestablishingacommon

languagebetweenresearchersandteachers,interviewswerethoroughlycombed

for(1)termsthatwerenoteasilyunderstoodbyteachers,(2)instanceswhere

teacherswereabletosubstitutetheirowndefinitionsofforgottenorunfarmiliar

terms,(3)phrasesthatexemplifymeaningfulcommunication,includingteachers’

descriptionsofexperience‐basedintuitionsandactivesense‐makingof

neuroscienceinformation.

Finally,allinterviewsweresearchedforanyinstanceswhereteacher’s

intuitionscouldbeseenasguidingcurrentquestionsineducationalneuroscience

research.

25

PreliminaryResultsandDiscussion

Forthepurposeofdiscussion,subjectsarelabeledTeacher1–Teacher6.

Teachers1and2participatedintheNumberSensevignette.Teachers3and4

participatedintheArithmeticvignette.Teachers5and6participatedinthePattern

Vignette.

Interview2:TeacherMentalModels

Behavior

Basedonthesixinterviewsconductedforthisproject,mostteacherswere

comfortablereflectingonstudent’sbehavior,andallbutonewereabletoassess

studentengagementandthesignificanceofspecificbehaviorstothemathtask

beingtaught.Teacher1explainedthatshedidnotknowifstudentswatchingthe

lessonwereengagedfromtheirbehavior.Allotherteachersdescribedstudents’

being“quiet,”or“fixated,”“orienting,”“listening,”andansweringquestions“right

away.”Allteacherswereabletoexplainwhyastudentpickedupa“red”/”orange”

card,identifytheskillastudentwasdemonstratingbycountingblocks,andrelate

thesignificanceinachild’sassemblyofapattern.

ConceptualTeachingApproach

Allteacherswereabletodiscussthemathconceptbeingtaught,aswellas

theiralignmentwiththeteachingmethod.Differencesdidemergebetween

vignettesonteachers’abilitytonamethemathconceptanduseeducationalor

mathematicallanguage.Forinstance,bothteachersstruggledtonametheconcept

ofNumberSense.Teacher1said,“Whatfourlookslike…aconceptualunderstanding

thatnumbersarerepresentedindifferentways.”Sheadmittedthattheirwasaterm

forthisconcept,andwasembarrassedthatshecouldnotrememberit.Teacher2

answered,“Differentnumbers,differentwaystheyarerepresented...waysyoucan

showfour.”TeachershadnoproblemintheArithmeticvignette,bothreplying

“addition,”rightaway.TherewassomeuncertaintyinthePatternvignette,duein

bothcasestothedifferentelementsincorporatedinthepatterntask(counting,

ordering,spatiallayout),thoughbothteachersidentifiedthatthetaskinvolved

26

“patterns.”Teacher5described“unitsofnumber,patterns,grouping,visual

patterning,”whileTeacher6describeda“numericalrepeatingpattern–groupsof

numbers.”

BothsubjectsintheNumberSensevignetteclaimedthattheywouldteach

thisconceptdifferently.Teacher1statedthatthelessoncouldbetterbetaughtin

smallergroups,withalongerandmoreflexibletimecourseforeachstudentto

answerquestions.Thiswouldallowtheteachertobetterassessstudent

understanding.Shealsoclaimedthatmoresensory/tactilesupportwasneeded.

Teacher2claimedthatratherthanleadingchildrentotheanswerwithclues(the

teacherguidedthechildtopickupanorangecard),theteachershouldhavelether

pickupawrongcard,andthendiscusswhyitdidnotshowfour.Bothteachersin

theArithmeticvignetteclaimedthattheywouldteachthisconceptinasimilarway,

usingmanipulatives,thoughTeacher2statedshewouldstartwithasmaller

numberofblocksfirsttoseewherecountingabilitiesbrokedown.Bothteachersin

thePatternvignetteclaimedtheywouldusethesameteachingmethodofmodeling

thepatternwithlanguagebeforeaskingthechildtolayitout.Teacher5addedthat

shewouldneedtofirstassesswhatindividualpatternabilitiesthestudenthad

beforepresentingalltheelementstogetherinonetask.

Cognition

TeachersanswerstothefinalquestionsinInterview2revealedmixed

abilitiesindiscussingstudents’cognitiveprocesses,includingthemathabilitiesand

mentalstrategiesusedtosolvemathtasks.ForNumberSense,thequestions

probedteachers’intuitionsaboutwhythesecondchildwasabletosolvethetask

morequicklyandeasilythanthefirst.Teacher1claimedthatthetaskdrewon“rote

counting”and“onetoonecorrespondence,”andposedthatthesecondchildhadhad

previousexposuretosymbolsandmoreexposuretosimilaractivities,andthuswas

abletopickupthecardwithlessscaffolding.Teacher2claimedthatthechild

neededtoknow“whatthenumberfouris,”havea”literacyofhowtoshowfour,”and

neededtobeabletocounttofour.Sheposedthatthesecondchildwaspaying

closerattentiontotheactivityandhadalreadyscannedthecard.Sheoutlinedhis

27

strategyaslooking,counting,matchingdotstonumbers....”seeingfour,countingfour

andrecognizingthesymbol.”

ForArithmetic,thequestionsprobedteachers’intuitionsregardingthe

child’suseofblocksinsolvingthetask.Teacher3claimedthattheadditiontask

requiredthechildtousecountingskills,and“remember”theamount13,thoughshe

admittedshedidnotknowthecorrectterminologyforthisskill.Teacher3claimed

thatthechild’sstrategyinvolvedaddingtheblocksintoherowngroupto“make

themhers”andthencounting.Sheclaimedthatthechildsimplymessedupinher

counting,butthatherstrategywassound.Teacher4claimedthatthechilddrewon

onetoonecorrespondence,aswellasvisuo‐spatialskillsinarrangingtheblocksin

rows.Sheconcludedthatthechild’sstrategyledhertosolvethetaskincorrectly,

guessingthatperhapsshe“gotstuck”onthenumber13.

ForPattern,thequestionsprobedteachers’intuitionsregardingwhythe

childpreservedtheoverallstructureofthepattern,butdidnotfollowtheorderas

prescribedintheteacher’slanguage,northespatialorientationofthematerials.

Teacher5claimedthatthechildneededtobeabletocounttothree,understand

whattwoandthreemean,andhavesomefamiliaritywithpattern.Sheposedthat

thechildlistenedandrememberedthepatterninherheadandthenstartedfrom

thebeginninginassemblingthepattern.Teacher5admittedthatshedidnotknow

whythechilddidnotreproducetheexactorderandspatiallayout,guessingthatshe

“focusedmore”onthepattern.Teacher6alsoclaimedthatthechildneededto

understandnumbers,haveaconceptofpattern,andbeabletocount.Sheguessed

thatthechildsimply“associatedtwowithcameosandthreewithstones,”and“let

thatbewhatwasfloatinginhermind…Shewasn’tthinkingaboutorder.”

Interview3:ImpactofNeuroscienceInformation

AnswerstoInterview3revealeddifferencesbetweensubjectsregardinghow

individuals’intuitionsmatchededucational,developmentalandcognitive

psychologytheoriesregardingspecificmathconcepts.Whileexaminationofeach

interviewisbeyondthescopeofthisdiscussion,theinterviewsconductedinthe

NumberSensevignetteserveasanexampleofthesedifferences.

28

Teacher1feltthattheneuroscienceinformationpresentedwasaboutinitial

developmentofmathconcepts,anddemonstratedtheimportanceofmaking

connectionsbetweendifferentkindsofmathinformation.Shewentontodescribe

howdifferentpartsofthebrainare“active,”andmathinformationneedstobe

“dispersed”and“connected”throughoutthebrain.Teacher1statedthattheidea

that“mathconceptsarestoredindifferentareasofthebrainwouldsuggesttomethat

youwanttoexposeorconnectthosemathconceptstoasmanyareasasyoucan.”

Ultimately,shefeltthatthissupportedherintuitionthatmoresensoryandtactile

informationshouldbeincorporatedintotheteachingofthisconcept.Inlightofthis,

shefeltthatthelessonshehadreliedmostlyonlanguage,butlackedinboth

adequatetime,andsensoryinteractionwithconcretematerials.

Incontrast,Teacher2feltthattheneuroscienceinformationsupportedher

intuitionthatthroughoutmathematicaldevelopment,“allchildrenaredevelopingin

brainfunctionsdifferently.”Thereforesomeareasarestrongerthanothers.Teacher

2feltthissupportedherintuitionthatchildrenlearnindifferentwaysand“ifone

wayisn’tworking”ateachercan“gowiththeother.”Ratherthanseeingan

importanceinteachersguidingstudentstobuildconnections,shefeltthatmath

learningshouldbelessteacher‐directed.Aslongasinformationisprovidedasboth

“numbersandtallies”thechildrenwill“figureouttheconnectionfromthere.”

Researchonthetopicofnumbersenseconfirmsthattheconceptunderlies

latermathematicalabilities(Baroody,2010;Dehaene,1997;Dehaene,Piazza,Pinel

&Cohen,2003).Cognitivepsychologyandneuroscienceliteratureshowsthat

mathematicalinformationisrepresentedindifferentareasofthebrain(Delazer&

Benke,1997;Eger,Sterzer,Russ,Giraud,&Kleinschmidt,2003;Lemer,Dehaene,

Spelke&Cohen,2003)andthatsymbolicinformationismappedontomoreabstract

numericalknowledgethroughexperiences,instructionandpractice(Gilmore,

Indefrey,Steinmetz&Kleinshmidt,2001;Lipton&Spelke,2005;Piazza,Pinel,

LeBihan&Dehaene,2007;Strauss,2003).

StudiessuchasthatofBaroody,EilandandThompson(2009)have

investigatedthesuccessofvariousmethodsofinstruction(structuredorsemi‐

structureddiscovery,directinstructionandunstructuredpractice)forfostering

29

preschooler’snumbersense.InlinewiththeintuitionsofTeacher1,recent

researchisshowingthatthebrainlearnscomplexconceptsbestwhentheyare

taughtandexperiencedthroughvarioussensorystimuli(Rains,Kelly,&Durham,

2008;Tokuhama‐Espinosa,2008b;TokuhamaEspinosa,2010).

TheintuitionsofTeacher2showedsomepossibleinterferencefrom

misconceptionsaboutthesignificanceofmathematicalinformationbeing

representedindifferentareasofthebrain.Heranswersseemtoshowsome

evidenceofbrainmythsregardingvisualversusverballearners,andisolatedparts

ofthebrainbeing“stronger”thanotherslikemuscles.Workingfromherown

model,whichlikelywasimpactedbyherbackgroundinSpecialEducation,she

interpretsthefindingstomeanthat“stronger”partsofthebraincanbeusedif

othersaren’t“working.”

Educationalresearchdoeslendsomesupporttotheideathatdifferentiated

instruction(allowingstudentstolearnattheirownlevelandpace)makessense

givenstudents’differentintelligencesandcognitivepreferences(Tomlinson,1999,

Tomlinson&McTighe,2006).However,theeducationalneuroscienceliterature

cautionsthatdespiteitssuccessinclassrooms,moreresearchneedstobe

conductedinordertoestablishwhydifferentiatedinstructionappearstowork

basedonbrainresearch.Differentiationbasedondifferentintelligencesand

cognitivepreferencesremainsintelligentspeculation(Tokuhama‐Espinosa,2010).

Furthermore,thinkingaboutthewaysdifferentchildrenmighttakeinand

learnnewinformationisaseparateconsiderationfromhowconceptual

understandingisfosteredandachieved.Inotherwords,thoughchildrenmight

showstrengthsorweaknessesforvariouskindsofmathematicalinformation,this

doesnotmeanthatbuildingstrongknowledgeofandconnectionsbetweenallof

thesetypesofinformationisnotstillvitalforconceptualdevelopment.

ReviewinganswersforInterview3yieldedsubstantialevidenceof

neuroscienceinformationhavingimpactedorchangedteachers’currentmodels.

ThereflectionsofTeacher6provideanexampleofhowtheneuroscience

informationresolvedambiguitiesinherentinthevideocase.Atfirst,thesubject

couldnotfigureouthowthevideodemonstratedthestudentfavoringorrelyingon

30

visuo‐spatialabilitiesovermathfactsandlanguageinsolvingthepatterntask;

ratherthetwoseemedtobeworkingintandem.

Throughconsiderationofwhatshehasseeninherownclassroom,Teacher6

wasabletoconstructanewmodelofhowvisuo‐spatialabilitiesinteractwithmath

factsandlanguagetoyieldadeeperunderstandingofnumericalpatterns.She

describeshowachangeoccurredinherstudent’sunderstandingofonehundredas

theycountedthedaysofschoolandhungnumbersinrowsoftenonthewall.As

soonastheywereableto“see”theremainingnumberstoonehundredontheir

hands,theirguessesabouthowmanydayswereleftbecamemuchmoreaccurate.It

wasasifthephysicalandvisualconnectiontotheideahelpedtheminternalizeit.

SheconcludedthataboutninetypercentofthemathworkinherMontessori‐based

classroomisindeedbuiltontheideathatmathematicalunderstandingmustinvolve

visualrepresentationsofmathematicalpatterns,suchasatriangleofcoloredbarsof

beadsthatrepresentnumbersonethroughten.Asthesebeadsaremanipulated,

arranged,andphysicallymatchedtonumberedtiles,solidmathematical

understandingisbuilt.

ThereflectionsofTeacher3provideanexampleofhowtheneuroscience

informationchangedteachers’opinionsorbeliefsregardingthemathtopic.She

relatedhow,inherownclassroom,shehadalwaysusedbothsymbolsandconcrete

objectsforchildrenofanyagewhenteachingbeginningaddition,aslongasthey

knownumbersandamounts.Afterconsideringthedevelopmentalshiftthatoccurs

fromreasoningandworkingmemorytosymbolsandmathematicallanguage,the

subjectmused,“Nowthatwe’retalkingaboutit,Ineverthoughtofthereasonofwhy

wewereusingthem…that’sjustwhatyoudowhenyou’reteaching.Ididn’tthink

aboutthewaychildren’smindsworktothatextent…Wow,childrenmaybethreeand

underareworkingonjustwhattheycanholdintheirminds.”

ThereflectionsofTeacher2provideanexampleofhowtheneuroscience

informationgaveteachersnewinsightintostudent’sthinking.Atfirst,sheclaimed

thatnumbersenseasaconceptwasnotsomethingthatwasexplicitlytaughtinher

emergent,child‐centeredclassroom.Afterconsideringhowmathematical

informationisrepresentedinthebrainandconnectedintotheconceptofnumber

31

sense,sherealizedthatherstudents’discoveriesduringblockplaydemonstrated

how“differentareasprocessdifferentrepresentationsofnumbers.”Theyseeand

handlequantities,uselanguagetocount,comparemoreorless,andusemathto

“figurethingsout.”Inthiswaythereis“numbersenseallovertheplace.”Teacher2

saidtheneuroscienceinformationremindedherthat“sometimesyouarenot

understandingwhatkidsareunderstanding…,”that“[neuroscience]isanotherwayof

observingthechild.”

CommonLanguage

Inthesixinterviewsconductedtherewerefewinstanceswhereteachers

werenotabletounderstandterms.Theflexibilityoftheclinicalinterviewallowed

theresearchertorepeatandre‐wordphrasesslightlysothatteacherswereableto

succeedinunderstandingandansweringallquestions.Onecuriousfindingwasthat

allsixteacherspausedforsomelengthwhileansweringquestion5ofInterview2,

whichaskedthemtolistthemathabilitiesthatthechildneededtohavetosolvethe

task.Atsomepointduringtheiranswer,allsixteachersalsorepeatedtheterm

“mathabilities”tothemselves,whichaidedtheminthinkingofafewmore.

Therewereseveralinstancesofteachersnotbeingabletorememberor

accessthecorrecteducationalormathematicaltermforanabilityorconcept,but

thisdidnotdetertheminsubstitutingadequatedefinitionsintheirownwords.As

examples,Teacher2used“whatnumberfouris…aliteracyofhowtoshowfour,”in

theplaceofnumbersense.Teacher1used“whatfourlookslike,”whenshecannot

recalltheproperterm,likelyinplaceofthetermsubitize.Teacher3admittedshe

wasnotsureof“terminology”formathabilitiesinvolvedinaddition,butwasableto

identify“countingskills”and“rememberingtheamountof13,”whichservesasa

fairdefinitionforcardinality.

Mostimportantly,reviewoftheinterviewsyieldedmanyphrasesthat

exemplifymeaningfulcommunicationbetweeneducatorandresearcherregarding

students’mathematicalthinkingasitrelatestocognitiveneurosciencefindings.As

Teacher1stated,knowingthatmathconceptscanbestoredindifferentareasofthe

brain“[suggests]tomethatyouwanttoexpose–orconnect–thosemathconceptsto

32

asmanyareasasyoucan.”Asteacher3articulated,theneuroscienceperspectiveis

“veryexciting,eventhoughit’sscientific…teachingissuchanintuitive

science…youngerchildrenrespondmoretoobjectsbecausetheyusetheirworking

memory,reasoning,whattheyknow…ItjustconfirmsthattheywaythatIapproach

teachingmathisawaythatworksforchildrenofthisage.”AsTeacher5stated,“I’m

interestedtoknowmore…it’snotenoughtohelpmebeabetterteacher.Someofitis

whatIalreadyknow…so,youknowthesethingsareindifferentpartsofthebrain,

and…soIshoulddowhatbetter?”

Foreachofthethreemathtopicsexploredintheseinterviews,important

questionsemergedduringteacherinterviewsthatcanbeseenasparticularly

relevantinthattheytouchuponareasattheforefrontofthebodyofresearchon

whichtheneurosciencesupplementsdrew(FullReferencesinAppendixD).For

NumberSense,thesequestionsconcerntheteacher’sroleinbuildingstrongnumber

senseinstudents.Whatistheimportanceofadequatetimeforstudentstoexplore

materialsandsolvetasks?Howimportantissensoryortactileinformationin

buildingthisconcept?Whataspectsofnumbersensedochildrenbuildontheir

own,andwhichrequiredirectinstructionforconnectionstobemadebetween

differentkindsofmathematicalinformationasitisstoredinthebrain?

ForArithmetic,thesequestionsconcernwhenandhowtheshiftfrom

relianceonconcreteobjectstovisualandlanguageabilitiesoccursorshouldoccur.

Atwhatageindevelopment(somewherebetweenthreeandfiveaccordingto

teachersinterviewed)dochildrennaturallymakethisshift?Howdoeslanguage

learninginteractwiththisshift,ie(asTeacher4observedinherownmulti‐lingual

classroom),whydoEnglishlanguagelearnersseemtohaveanadvancedabilityto

solveadditionproblemsusinglanguage?

ForPattern,thesequestionsconcerntheroleofvisuo‐spatialabilitiesin

understandingofpattern.Howshouldteachingofpatternincorporateandbuild

differentelementsofpattern(language,counting,numbersense,sensory,visuo‐

spatial)intoinstruction?Whatevidenceistherethatstudentsneedthevisuo‐

spatialelementinordertorecognizeandunderstandmathematicalpatterns,a

33

valuablecomponentofalgebraicandabstractmathematicalthinking,ina

meaningfulway?

Discussion

Accordingtothepreliminarydata,thisresearchdesignachievedtheaimof

establishingcommonmodelsandlanguageinordertoengendermeaningful

discussionbetweenresearcherandteachers.Videocasesservedasafunctional

problemspacewithinwhichinterviewerandintervieweecouldmeettoexplore

varioustopicsinearlychildhoodmathematics.Theclinicalinterviewtechnique

servedit’spurposeingatheringteacher’sintuitivementalmodelsatthelevelof

theirownthoughtsandbeliefs,andprovidedarichsourceofdescriptivedataon

howneuroscienceinformationengaged/impactedteachers’currentmodels.Finally,

analysisofthisdatarevealedobservationcategoriesthatcanbeusedforuseofthe

researchmodelinfurtherstudy.Interestinginteractionsbetweenteachers’

intuitionsandgapsinneuroscientificknowledgepointthewaybacktothebrainlab.

Whilethisstudywasdesignedasagenerativemethod,theresultsopenthe

wayforapplicationofmoreconvergentmethods.Theusetheobservation

categoriesandvariablesdiscussedabovecancontinuetorefineongoinggenerative

research,viabothinductiveanddeductivemethods(Clement,2000).

Infurtherstudies,answerstoInterview2maybeassignedvaluesaccording

toTeacherEfficacyandTeacherBeliefscodingschemessimilartothoseemployed

incurrenteducationalresearchusingvideocasestoassessteacherknowledge(see

Rosenfeld,2010forareview).

Arubriccouldalsobedesignedtoratetheimpactofneuroscience

informationonteacher’scurrentbeliefs.Commonelements,elementsthatappear

inmorethanfiftypercentofinterviews,couldbecollectedforteachers’modelsand

language.Inthisway,alargersetofdatacouldbeanalyzedwithincreased

reliability.

Ultimately,thisprojectdemonstratedthattheteachersinterviewedhave

stronginstinctsthatmatch,question,andchallengecurrenteducational

neurosciencefindings,andtheycanbevaluablecontributorsinidentifying

34

importantavenuesforfurtherresearch.AsTokuhama‐Espinosa(2010)states:

“Greatteachershavealwayssensewhatmethodsworked;thankstobrain‐imaging

technologyandbetterresearchtechniques,itisnowpossibletosubstantiatemany

ofthesebeliefswithempiricalscientificresearch.”

ProjectSignificance

Thisprojectapproachestheriftbetweenneuroscienceandeducationfroma

trulyneuroeducationalperspective.AccordingtoKurtFischer,headoftheMind

BrainandEducationinitiativeatHarvard,whateducationneedsisnota“quickfix”

fromneuroscience,butratherthecreationofanewfieldthatintegrates

neuroscienceandothercognitivescienceswitheducation.(FischerandImmordino‐

Yang,2008).Intermsofitsresearchgoals,mechanismsandmethodology,this

projectcanbeseenasatruecollaborationbetweendevelopmentalandcognitive

psychology,educationandneuroscience.

Theprojectdesignrepresentsanewresearchmethod,assembledfromtime‐

honoredmethodsthatsharetheconvictionthatcloseandcarefulobservationofthe

childorstudentiswhatallowsustoenterhismind.(Piaget,1975,Ginsburg,1997,

Kilbane,2008).Thesemethodscannotbeconductedincontrolledlaboratories

wheresubjectsspendafewhourssigningformsandbeingmeasuredwithmachines.

Whilesuchstudiescertainlyhavetheirplaceinscientificstudy,thesuccessful

educationalneuroscienceresearchermustspendtimewithteachers,innatural

settings,havinghonest,respectfulandmeaningfuldiscourse(Goswami,2006).True

andequalcollaborationneedsasharedlanguageandwaysofthinking,andthese

taketime.

ThePrincipalInvestigatorofthecurrentprojecthascompletedboth

undergraduateandgraduatedegreesincognitiveandeducationalneuroscience,and

hasovertwoyearsoftrainingusingthecognitiveclinicalinterviewmethodto

assessbothchildren’smathematicalthinking,andteacher’sknowledgeofstudent

thinking.Shehasalsoco‐developedtheprogramandcurriculaataprogressive

preschool,andhasbeenteachinginthisprogramforfiveyears.Inthissense,the

35

designofthisprojectcanbeseenasanexampleofinnovativeworkbyanew

generationofmulti‐disciplinaryresearcherwhoisdedicatingcombinedexpertisein

bothneuroscienceandeducation“topresentinghighqualityknowledgeonthe

brainindigestibleformandinterpretingneurosciencefromtheperspectiveofandin

thelanguageofeducators,”inorderto“fostersuccessfulexchangeofrelevantdata

betweendisciplines(Goswami,2006).”

Theoverarchinggoaloftheproposedresearchistobeginbuildinga

foundationforcollaborativeexperimentdesignbetweeneducatorsand

neuroscientistsinordertoanswer“bigpicture”questionsthatmattertoteachers.

Mayer(1998)claimsthatdrawingonteachers’experienceandintuitionsabout

students’learningpresentsnewhopeforcollaborativedesignofcognitive

neuroscienceresearchthatwillbetrulymeaningfultoeducators.Withinhisgeneral

skepticismforbuildingabridgebetweenneuroscienceandeducation,Bruer(2006)

holdsouttentativehopefortherareimagingstudythatgoesbeyondsimply

establishinglocalizationclaimsandinsteadexemplifiesbothasufficient

appreciationforthecomplexityandsubtletyofcompetingcognitivemodelsandan

abilityonthepartofresearcherstointerpretimagingdatainlightofalltherelevant

behavioralandneuropsychologicaldataavailable.

Implicationsforfutureresearch

Thisprojectoffersimportantconsiderationsandquestionsforthe

developingfieldofeducationalneuroscience.First,findingawaytoestablisha

commonlanguagebetweeneducatorsandneuroscienceresearchersmayallow

accesstoawealthofintuitiveknowledgeaboutthelearningbrainthatcanresolve

ambiguities,answerquestions,andfine‐tuneinvestigationsforresearchers.What

matcheswillberevealedbetweenteachers’intuitionsaboutstudents’brainsand

neurosciencefindingsoncethebarrierofdifferentlanguageisremoved?

Ontheotherhand,misconceptionsandgapsinteacher’sknowledgewillbe

exposed,allowingforinsightintowhycertainteachingstrategiesandapproaches

maynotbeoptimalforstudentlearning,understandingandachievement,and

36

offeringideasforbetterteaching.Asteacher5expressed,theneuroscience

informationpresentedinthisprojectwas“notenoughtohelpmebeabetter

teacher…“Shefeltthattheinformationshowedherthatsheneededtoknowmore

aboutmathlearninginthebrainordertoguideapplicationtotheclassroom.What

holesinteachers’knowledgeaboutthebrainwillberevealed(independentfrom

unfamiliar/unknownneurosciencevocabularyorterminology)?

AsTeacher3remarked,“Teachingisanintuitivescience.”Insuccessful

classrooms,teachersareconstantlyatwork,applyingapproachesandassessing

theirstudents’behavior,memoryfornewinformationandsubsequent

understanding.Allalongteacher’smodelsmustbeflexibleenoughtoadaptand

changebasedon“whatworks”intheclassroom.Theissuesthataroseinthese

interviews,includingappropriatedegreeoftime,scaffoldingandsensorysupport

foractivities,theinterplayofconcreteandabstractinsupportingconceptual

understanding,andtherolesoflanguage,workingmemoryandspatialskillsin

mathematicalproblemsolving,areissueswithwhichteachersareexperientially

familiar,evenwhentheymaynotbeabletoremembertheterminology.

Manyteachersspendtheircareerstryingandassessingvariousstrategiesin

theirownclassrooms,aswellascommunicatinganddebatingwithotherteachers

abouttheseissues.Sincethe“DecadeoftheBrain,”neurosciencehasbeenhumbled

bytherealization,evenasknowledgehasadvancedmorerapidlythanever,ofhow

verylittleweactuallyknowaboutthethinkingbrain.Thereisadequatereasonto

supposethatteacher’schoicestoredesignorrejectpriorstrategiesthroughouttheir

teachingcareersmayreflectexperienced‐basedintuitionsabouthowchildren’s

brainsatvariousagescanbeengaged,supportedtoprocessandremembernew

information,andtobuildconceptualunderstanding.Howdoteacher’schoicesto

redesignorrejectpriorstrategiesbasedon“whatworks”intheirclassroomreflectan

intuitiveunderstandingofneuroscience­basedrecommendations?

Teachers’intuitionscanalsobeseenasameansofestablishinganotherlevel

ofvaliditybeyondreplicatedfindingsinthebrainlab.Brainresearchistime‐

consuming,expensiveandtedious.TheobstaclespreventingUSstudentsfromthe

37

achievingdeepmathematicalunderstandingneededforacademicsuccessneedto

beremediednow.

Thisethicofcareandrespectforteachers’intuitionsisinitsownrighta

significantaspectoftheproject.Ultimately,theworkoftheeducationalpsychology

researcherandtheteacher,thecognitiveneuroscientistandtheneuroeducatorall

mergewithinthechild'sbrain.Ifneurosciencehopestocrossthebridgeintothe

classroom,itneedstoconsiderthatteachershave,inessence,beenpeeringinto

children'sbrainslongbeforethefirstbrainimagingtechniquesemerged.

Overarchingteachingapproachessuchasstandards‐basedpublicPre‐K

curricula,research‐basedmathcurricula,theMontessorimethod,andvarious

aspectsofprogressivecurriculasuchasconstructivistandemergentapproaches

preserveandpassonteachingmethodsthatshare,tovaryingdegrees,the

convictionthey“work.”TheEarlyChildhoodEducationresearchcommunityhas

cometorealizethatbuildinganunderstandingofwhycertainapproacheswork

whereothersfailisacomplexbutnecessaryendeavorifeducationisgoingto

institutesuccessfulandlonglastingchangesinthequality–andequality–thatwe

provideouryoungeststudents(Clements,2007).

Matheducationisasomberexampleofthecrisisthatoccurswhenmanyof

theacceptedteachingmethodsusedinclassroomsaren’tworkingtobuildsufficient

understandinginstudents.Therearebigquestionsleftunansweredinboththe

educationalandeducationalneuroscienceresearch.Drawingontheanalysisand

comparisonoftwoteacher’sreflectionsonnumbersense(inPreliminaryResults

andDiscussionabove)revealedhowteachers’intuitionscanbebroughttobearon

thesequestions.Forinstance:Howisdevelopingnumbersensebestsupportedinthe

pre­primaryyears,andwhatimplicationsaretherefortheclassroomenvironment?

Whatneuroscientificsupportistherefortheimportanceofadequatetimespent

exploringmaterialsinasensorywayandaskingquestions?Whatsupportistherefor

theimportanceofovertinstructionversusactiveconstructionofknowledgeforthe

developmentofthisconcept?

Fromtheothersideoftheclassroomwall,educationalneuroscienceoffersa

setofscientificallysoundrecommendationsforteachingthathavebeencarefully

38

teasedapartfromintelligentspeculation,misinterpretedfindings,andneuromyths.

Forexample,MindBrainandEducationScienceliteratureadvocatesactive

constructionofknowledge,situatedlearningexperiences,andakeyroleofmotor

andsensoryexperiencesinlearning(Hardiman&Denkla,2009;Tokuhama‐

Espinosa,2010).Inwhatwayareteachers’variousphilosophies/approaches

regardingbestpracticesupportedbycurrentneurosciencerecommendationssuchas

thoseprovidedbyMindBrainandEducationScience?Howdothese

philosophies/approachescorrelatewithateacher’shavingintuitivemodelsoflearning

thatalignwithneuroscience?

Inthefaceofthesequestions,thisprojectrepresentsapromisingstart.The

designoffersavaluabletoolforcontinuedinvestigationthroughbi‐directional

collaboration.Themodelisinfinitelyportable,isnotrestrictedbytimeorlocation,

andisinexpensive.Thecollectionandcodingoffurtherdatacanbeginrightawayto

addressthequestionsaboveastheypertaintoallteachersaswellasspecificsub‐

groupsofteachers.Forexample,asthisprojectisbeingsubmitted,upcoming

interviewshavebeenscheduledwithgroupsofearlychildhoodteachersusinga

standarduniversalPre‐Kmathcurriculumatapublicschoolinalow‐incomeareaof

Brooklyn,aswellasatasuccessfulcharterschool,alsoinalow‐income

neighborhoodinHarlem,whereteachersaretrainedinimplementingresearch‐

basedmathcurricula.Newquestions,variablesandobservationcategorieswill

continuetofurtherimproveandrefinetheresearchmethodastheynaturallyarise.

Inconclusion,weareleftwithasenseofonesharedresearchproject

betweenteachersandresearchers.Thelinesdividingknowledgeintotheseparate

spheresofeducation,developmentalandcognitivepsychology,cognitiveand

educationalneurosciencehavecrossedenoughthattheyhaveblurred.Or,asPiaget

putsit,theschemata,orbuildingblocksofknowledge,havebeensufficiently

diversifiedsothatnewinformation,ratherthanproducingannoyanceandcausing

avoidance,“becomesaproblemandinvitessearching(Piaget,1955).“Inthis

picture,thegoalliesnotinwhatcanbeaccomplishedoncethebridgebetween

neuroscienceandeducationhasbeenconstructed,butratherinthedeep

39

connectionsthatarenaturallyformedthroughthesharedprojectofcreative

problemsolving.

PrincipleInvestigator

JuliaNiego

JuliaNiegoreceivedaBAinBehavioralNeurosciencefromColgateUniversity,

whereshedesignedandimplementedERPstudiesexaminingchangesinbrain

activityassociatedwithananti‐stereotypetrainingtask,andco‐authoredanarticle

forDevelopmentalNeuropsychology(Kellyetal,2002)hypothesizingarolefor

gestureinco‐definingspeechduringdevelopment.Beginningin2004shehas

collaborativelydevelopedaprogressiveMontessori‐basedprogramataprivate

preschoolinBrooklyn,NY,wheresheiscurrentlyteaching,researchingand

supportingstaffunderstandingoflearninganddevelopmentthroughregular

meetingsandworkshops.SherecentlyacceptedapositionforFall2011toco‐

developanearlychildhoodcomponentcurriculumforaneuropsychology‐based

tutoringprogramrunbyDr.AnnaWarren‐Levy.JuliaiscurrentlyaMSstudentin

NeuroscienceandEducationatTeacher’sCollege,ColumbiaUniversity,whereshe

hasspenttwoyearslearningtheclinicalinterviewmethodinadditiontocompleting

extensivecourseworkincognitiveneuroscienceandeducation.Sheisgraduatingin

May2011withaMastersofScienceinNeuroscienceandEducation.

ProjectAdvisors

PeterGordon,PhD.Psychology,MassachusettsInstituteofTechnology

PeterGordonistheProgramCoordinatorfortheNeuroscienceandEducation

ProgramatTeacher’sCollege,ColumbiaUniversity.Hisresearchfocusesonthe

developmentalneuroscienceoflanguageandcognition.Hecurrentlyteaches

SpeechandLanguagePathologyandNeuroscienceandEducationatthegraduate

levelatTeacher’sCollegeColumbiaUniversityandadvisesmulti‐disciplinary

doctoralresearch.

40

HerbertGinsburg,PhD.DevelopmentalPsychology,UniversityofNorthCarolina

HerbertGinsburgistheJacobASchiffFoundationprofessorofPsychologyand

HumanDevelopmentatTeacher’sCollege,ColumbiaUniversity.Hehasmade

significantcontributionstoanunderstandingofmentalprocessesinvolvedinthe

developmentofchildren’smathematicalthinkingusingtheclinicalinterview

method.Hecurrentlyteachestheclinicalinterviewmethodasaresearchtoolatthe

graduatelevelatTeacher’sCollegeandadvisesdoctoralresearchintheCognitive

Sciences.

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Appendix A

Clinical Interview Protocol 1: Teacher background

Pre­Video

TeacherInformation

Canyoutellyourname?

Howmanyyearshaveyoubeenteachinginearlychildhood?

Canyoudescribeyourgeneralpathtoteaching?

Can you briefly describe your general philosophy or approach, something that possibly sets you apart from other teachers?

Appendix B

Clinical Interview 2 Protocols: Teacher mental models

(ScaffoldedInterview)

Number sense

Canyoureflectontheteachingexampleyoujustsaw:

1)Didthechildrenseemengagedduringlesson?Howcouldyoutell?

2)Whatmathconceptdoyouthinktheteacherwasattemptingtoteachtothegroup?

3)Wouldyouhavetaughtthisconceptdifferently?Why/whynot?

4)Didthischildperformthetaskcorrectly/incorrectly?Why/whynot?

5)Whatmathabilitieswouldyousaychildrenhadtohaveinordertoperformthistask?

6)Whatwasthischild’sstrategyinperformingthetasksoquickly?

Walksubjectthroughchild’smentalprocess.

(Exploreanymentionofdifferentrepresentationsofmathinformation/connectionsbetweenmathematicalinformation)

Arithmetic

Canyoureflectontheteachingexampleyoujustsaw:

1)Doesthechildseemengagedinthetask?Howcanyoutell?

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2)Whydoestheteacherchoosetobeginthelessonthisway?

3)Whatmathconceptdoyouthinktheteacherisattemptingtoteach?

Wouldyouhavetaughtthisconceptdifferently?Why/whynot?

4)Whatmathabilitieswouldyousaythechildhadtohaveinordertosolve

thistask?

5)Didthechildsolvethefirsttaskcorrectly/incorrectly?Why/whynot?

Thesecond?Why/whynot?

6))Whatdoyouthinkwasthechild’sstrategyinsolvingtheproblem?

Walksubjectthroughchild’smentalprocess.

(Exploreanymentionofhandlingblocks)

Pattern

Canyoureflectontheteachingexampleyoujustsaw:

1)Didthechildseemengagedduringlesson?Howcouldyoutell?

2)Whatmathconceptdoyouthinktheteacherwasattemptingtoteach?

3)Wouldyouhavetaughtthisconceptdifferently?Why/whynot?

4)Didshesolvethetaskcorrectly/incorrectly?Why/whynot?

5)Whatmathabilitieswouldyousaythechildhadtohaveinordertosolvethistask?

6)Whatdoyouthinkwasthechild’sstrategyinsolvingtheproblem?

Walksubjectthroughchild’smentalprocess.

(Exploreanymentionofchild’sactualconstructionofthepattern,i.e.notfollowingtheexactlanguage)

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Appendix C

Clinical interview protocol 3: Neuroscience follow-up

Protocol2:Follow­up

(Moreopen‐endedinterview)

Doesthisinformationrelatetotheteachingmomentyoujustsaw?How?/Inwhatways?

Doesthisinformationrelateinanywaytowhatyouobserveinyourownclassroom/students?

Doesthisinformationmatchinanywayswithyourpersonalphilosophy/approachasanearlychildhoodteacher?

Canyouthinkofanywaysthatthisinformationmightimpactyourideas/thoughts/beliefsaboutteachingmath,specificallynumbersense/arithmetic/pattern,toyoungchildren?

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AppendixD

NeuroscienceSupplements

PrintedSupplements

Supplement1:NumberSense

Cognitiveneuroscienceresearcherswanttoknowhowachild’sbraindevelopstoachieveunderstandingofamathematicalconceptsuchas“numbersense.”

Takingpicturesofstudents’brainswhileperformingmathtaskshasrevealedthat:

Theareasinthebrainwheredifferentkindsofmathematicalinformationarerepresentedarelargelyinplacebyage3.

Languageareasatthefrontleftsideofthebrainareinvolvedwithprocessingverbalmathinformationsuchasnumberwords(“five”)andalgorithms(“plus”)

Visionareasattheverybackofthebrainareinvolvedwithprocessingwritten/drawnmathinformationsuchaswrittennumerals(5)orsymbols(+).

Associationareasatthetopbackofthebrainareinvolvedwithprocessingquantitativeinformation(“Howmuch”/”Howmany?”).

Visuo‐spatialareasatthetopbackandfrontofthebrainontherightsideareinvolvedwithprocessingvisualandspatialinformation(shape,structureandspace).

Theseareascanbeactiveornotdependingonthemathtaskapersonisdoing.

Aperson’sbrainlooksdifferentwhenlisteningtonumberwords,orrecognizingawrittennumeral,orcountingdots,orestimatingthenumberofobjectsinagroup.

Aspecificconceptthatachilddevelopsaboutmath,suchasnumbersense,involvesconnectionsbetweenthesedifferentareas

Theseconnectionshappenthroughmathematicalexperienceswheremore thanonekindofmathinformationiscalleduponatthesametime.

Studiessuggestthatthewaymathinformationislearneddirectlyinfluenceshowandwhereitisrepresentedinthebrain.Furthermore,thewaystudentsareguidedtousethismathematicalinformationinfluencesthewayitisintegratedandbuiltintomathematicalconcepts.

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Supplement2:Addition

Cognitiveneuroscienceresearcherswanttoknowhowachild’sbraindevelopstobeabletocompleteatasksuchastheadditiontaskpresentedinthislesson.

Researchonmathlearninghasshownthatchildrenbecomemuchfasteratsolvingarithmetictasksastheygetolder.Takingpicturesofstudents’brainswhileperformingmathtaskshasrevealedthat:

Theareasinthebrainthathandlearithmetictasksarelargelyinplacebyage3

Areasoneithersideofthefrontofthebrainhandlegeneralreasoning

Areasjustbehindthefrontofthebrainserveasamentalworkspacefortemporarilyholdingandmanipulatingfactsandinformationthatachildneedstosolveagivenmathproblem

Areasatthefrontleftsideofthebrain(behindtheleftear)handlemathlanguage(numberwords)

Areasatthebackofthebrainhandlevisualinformation(writtennumerals)

Youngerbrainslookdifferentthanolderbrainswhensolvingarithmetictasks

Youngerchildrenshowmostactivityingeneralreasoningandworkingmemoryareas,whileolderchildrenshowmoreactivityinlanguageandvisualareas

Thisshiftcorrespondswithachangeinchildren’sstrategiesforsolvingarithmeticproblems

Youngchildrenrelyonmanipulationofconcreteobjectstosolveadditionandsubtractionproblems,whereaslaterontheyareabletoperformmath“intheirheads,”usingabstractrepresentationsofnumbersvialanguageandvisualsymbols

Studiessuggestthatthewayachild’sbrainprocessesmathinformationatacertainstageindevelopmentdirectlyinfluencesthestrategytheyusewhensolvinganarithmetictask.Ontheotherhand,recentresearchsuggeststhatteachingchildrennewstrategiesmayactuallyinfluencelanguageandvisualareasto“takeover”duringarithmetictaskssothatgeneralreasoningandworkingmemoryarefreeduptohandlemorecomplexinformation,setgoals,andmonitorprogress.

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Supplement3:Pattern

Cognitiveneuroscienceresearcherswanttoknowhowachild’sbraindevelopstobeabletocompleteatasksuchasthepatterntaskthatthischildjustdid.Bytakingpicturesofchildandadultbrainsintheprocessofsolvingmathproblems,researchesposethat:

Theareasinthebrainthathandlevariousmathematicaljobsarelargelyinplacebyage3

Areasattheupperbackofthebrainstoreconceptsof“howmuch”

Areasatthefrontleftsideofthebrainhandlelanguage(numberwords)

Areasatthefrontofthebrainholdfactsandinformationthatachildneedstosolveagivenmathproblem

Ontherightsidethisareaholdsneededvisualandspatialinformationlikea“sketchpad”

Children’sbrains,likeadultbrains,seemtohavetwomain“pathways”orconnectionsbetweentheseareas

Theleftsidehandlesquantitativemathinformationlearnedthroughlanguage,likenumbersandcounting

Therightsidehandlesvisuospatialmathinformationlearnedthroughsensoryexperience,likeshape,structureandpattern

BUTchildren’sbrainsdonothandleamathproblemthesamewaythatadults’brainsdo

Bylookingatpicturesofbrainsdoingmath,researcherscanseethatthesemathareasandtheconnectionsbetweenthemlookdifferentinadultsandchildrenwhentheyaresolvingthesamekindsofproblems

Somestudiessuggestthatpreschoolandkindergartenagedchildrenmayrelymoreonvisuo­spatialknowledgetograspmathconcepts,andthengraduallyshifttoincorporatemorequantitativeknowledgeastheirbrainsdevelopmathematically.

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PictureSupplements

SupplementA:Numbersense

51

Supplement B: Arithmetic

52

Supplement C: Pattern

53

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