视觉空间表征的类型和数学问题解决毕业论文外文翻译.docx
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视觉空间表征的类型和数学问题解决毕业论文外文翻译.docx
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视觉空间表征的类型和数学问题解决毕业论文外文翻译
外文文献资料
JournalofEducationalPsychology,1999,91,4,684-689.
TypesofVisual-SpatialRepresentationsandMathematicalProblemSolving
MaryHegartyandMariaKozhevnikov
UniversityofCalifornia,SantaBarbara
Althoughvisual-spatialrepresentationsareusedextensivelyinmathematicsandspatialabilityishighlycorrelatedwithsuccessinmathematicseducation,researchtodatehasnotdemonstratedaclearrelationshipbetweenuseofvisual-spatialrepresentationsandsuccessinmathematicalproblemsolving.Theauthorsdistinguished2typesofvisual-spatialrepresentations:
schematicrepresentationsthatencodethespatialrelationsdescribedinaproblemandpictorialrepresentationsthatencodethevisualappearanceoftheobjectsdescribedintheproblem.Participantssolvedmathematicalproblemsandreportedontheirsolutionstrategies.Theauthorswereabletoreliablyclassifytheirvisual-spatialrepresentationsasprimarilyschematicorprimarilypictorial.Useofschematicspatialrepresentationswasassociatedwithsuccessinmathematicalproblemsolving,whereasuseofpictorialrepresentationswasnegativelycorrelatedwithsuccess.Useofschematicrepresentationswasalsosignificantlycorrelatedwithonemeasureofspatialability.Theresearchthereforehelpsclarifytherelationshipbetweenvisualimagery,spatialability,andmathematicalproblemsolving.
Visualimageryreferstotheabilitytoformmentalrepresentationsoftheappearanceofobjectsandtomanipulatetheserepresentationsinthemind(Kosslyn,1995).Mostresearchersagreethatsuchvisualrepresentationsareimportantinmathematicseducationbecausetheyenhanceanintuitiveviewandanunderstandinginmanyareasofmathematics(e.g.,Krutetskii,1976;Usiskin,1987).Thereisasignificantrelationshipbetweenspatialabilityandachievementinmathematics(e.g.,Battista,1990).However,thewideuseofvisualimagesbystudentsisnotalwayseffectiveinproblemsolvingandcanleadtoerroneoussolutions(e.g.,Lean&Clements,1981;Presmeg,1992).Inthisstudy,weclarifytherelationshipbetweenvisualimagery,spatialability,andmathematicalproblemsolvingbyidentifyingtwodifferenttypesofvisual-spatialrepresentationsusedinsolvingmathematicalproblems—schematicandpictorialrepresentations—andbyshowingthattheyaredifferentiallyrelatedtosuccessinmathematicalproblemsolving.
Visual-SpatialRepresentationsinMathematicalProblemSolving
Thereisextensiveresearchinmathematicsshowingacorrelationbetweenspatialabilityandmathematicalperformance(e.g.,Battista,1990;McGee,1979;Sherman,1979;Smith,1964).Forexample,Sherman(1979)reportedthatthespatialabilityfactorwasoneofthemainfactorssignificantlyaffectingmathematicalperformance.Thiscorrelationincreaseswiththecomplexityofmathematicaltasks(seeKaufmann,1990,forareview).
Otherinvestigationshavefocusedonthementalprocessesusedinsolvingmathematicalproblems,particularlytheroleofdiagramsandvisual-spatialimagesinmathematicalproblemsolving.Inthesestudies,studentsreportedtheirsolutionprocessesaftersolvingproblemsorwhilesolvingproblems.Onthebasisofsuchstudies,Krutetskii(1976)concludedthatindividualscanbeclassifiedintothreegroupsaccordingtohowtheyprocessmathematicalinformation.Thefirstgroupconsistsofverbalizers,whopreferverballogicalratherthanimagerymodeswhenattemptingtosolveproblems;thesecondgroup,visualizers,involvesthosewhoprefertousevisualimagery;andthethirdgroup,mixers,containsindividualswhohavenotendencyonewayortheother.
FollowingtheKrutetskiimodel,Moses(1980),Suwarsono(ascitedinLean&Clements,1981),andPresmeg(1986a,1986b,1992)recognizedthatindividualscouldbeplacedonacontinuumwithregardtotheirpreferenceforusingvisualimagerywhilesolvingmathematicalproblems.Theauthorsofthesestudiesdefinedmathematicalvisualityastheextenttowhichapersonpreferstousevisualimageryordiagramswhenattemptingmathematicalproblems.Suwarsonodevelopedaninstrumenttomeasureanindividual'slevelofvisuality—theMathematicalProcessingInstrument(MPI),whichhasbeenusedextensivelyinfurtherresearchonthistopic.Asurprisingresultfromthisliteratureisthatthewideuseofvisualimagesisnotalwayseffectiveandcansometimesleadtoerroneoussolutionsofmathematicalproblems.Findinganegativecorrelationbetweenmathematicalvisualityandbothspatialabilityandmathematicalperformance,LeanandClements(1981)concludedthatverbalizersoutperformvisualizersonbothmathematicalandspatialabilitytests.Onthispoint,Presmeg(1986a,1986b)identifiedfivekindsofimageryusedbyhighschoolstudentsinsolvingmathematicalproblems:
(a)concretepictorialimagery(picturesinthemind);(b)patternimagery(purerelationshipsdepictedinavisual-spatialscheme);(c)kinestheticimagery,whichinvolveshandmovementandothergestures;(d)dynamicimagery,whichinvolvesdynamictransformationsofgeometricfigures;and(e)memoryofformulas,whereinvisualizerstypicallyimagineaformulawrittenonablackboardorintheirnotebooks.
Presmeg(1986a,1986b,1992)arguedthattheuseofconcretepictorialimagerymayfocusthereasoningonirrelevantdetailsthattaketheproblemsolver'sattentionfromthemainelementsintheoriginalproblemrepresentation,whereasotherkindsofimagerymayplayamorepositiverole.Presmegascribedthemostessentialroleinmathematicalproblemsolvingtopatternimagery,inwhichconcretedetailsaredisregardedandpurerelationshipsaredepicted.Thiskindofimagerywasalsoidentifiedbyotherresearchers(Johnson,1987;Krutetskii,1976).However,noneoftheseresearchersexaminedthequantitativerelationshipsbetweenuseofdifferenttypesofimageryandmathematicalproblemsolving,norhavetheyexaminedtherelationshipbetweenspatialabilityanduseofdifferenttypesofimagery.
Insummary,althoughspatialabilitycorrelatespositivelywithmathematicsachievement,preferencetoprocessinformationvisuallycorrelateswithneithermathematicalperformancenorspatialabilitytests.Theseresultshavecastdoubtontheusefulnessofclassifyingstudentsasvisualizersorverbalizers,andasaconsequence,thenumberofeducationalstudiesrelatedtothevisualizer-verbalizercognitivestylehasdeclinedrapidlyoverthepastdecade.
TypesofVisualImageryAbility
Thecurrentresearchdifferentiatesbetweentwodifferentvisualimageryabilitiesidentifiedincognitivepsychologyandneuroscienceresearch.Thisresearchsuggeststhatvisualimageryisnotgeneralandundifferentiatedbutcomposedofdifferent,relativelyindependentvisualandspatialcomponents(e.g.,Farah,Hammond,Levine,&Calvanio,1988;Kosslyn,1995;Logie,1995).Visualimageryreferstoarepresentationofthevisualappearanceofanobject,suchasitsshape,color,orbrightness.Spatialimageryreferstoarepresentationofthespatialrelationshipsbetweenpartsofanobjectandthelocationofobjectsinspaceortheirmovement;further,spatialimageryisnotlimitedtothevisualmodality(i.e.,onecouldhaveanauditoryorhapticspatialimage).Cognitivestudieshaveprovidedevidenceforadissociationbetweenthesetwoaspectsofimagery.First,dual-taskstudieshaveshownthatvisualimagerytasksareimpairedbyconcurrentlyviewingirrelevantpicturesbutnotbymovingone'sarm,whereasspatialimagerytasksareimpairedbyarmmovementsbutnotbyviewingirrelevantpictures(Logie,1995).Furthermore,cognitiveneurosciencestudies(e.g.,Farahetal.,1988)havedemonstratedthatfollowingbrainlesions,patientscanbeextremelyimpairedintaskstappingvisualaspectsofimagerywhileshowingnormalperformanceintestsofspatialimagery.
Wearguethatadissociationbetweenvisualandspatialimageryalsoexistsinindividualdifferencesinimagery—someindividualsareespeciallygoodatpictorialimagery(i.e.,constructingvividanddetailedvisualimages),whereasothersaregoodatschematicimagery(i.e.,representingthespatialrelationshipsbetweenobjectsandimaginingspatialtransformations).Weconsiderspatialabilityasasubsetofimageryabilities,relatedtoschematicimageryandnotrelatedtopictorialimagery(Poltrock&Agnoli,1986).
Thefocusofthisresearchistoidentifyhowspatialandvisualimageryabilitiesaffectproblemsolvinginmathematics.Wefirsthypothesizethatuseofschematicspatialimageryinsolvingmathematicalproblemsisassociatedwithbetterperformance,whereasuseofpictorialimageryisassociatedwithpoorerperformanceinproblemsolvingbecauseittakestheproblemsolver'sattentionfromthemainrelationshipsintheproblemstatement.Second,wehypothesizethatspatialabilityispositivelyassociatedwithuseofschematicimagerybutnotwithuseofpictorialimagery.Finally,totestthealternativehypothesisthatuseofschematicimageryisrelatedtogeneralintelligence,ratherthanspatialabilityspecifically,weincludemeasuresofverbalandnonverbalgeneralintelligence.
Method
Participants
Thirty-threeboysinsixthclass(sixthgrade)inanall-boysprimaryschoolinDublin,Ireland,tookpartinthisstudy.Themeanageoftheparticipantswas12years,1month(range=11years,6months-13years,1month).
Materials
Thefollowingmeasureswereadministeredtothestudents:
1.TheMPIconsistsof15problems,eithertakenfrompreviousstudies(Krutetskii,1976;Lean&Clements,1981)orcomposedspecificallyforthestudy.Apilotstudyhaddeterminedthattheseproblemswereofappropriatedifficultylevelforthestudentsandthatstudentsusedava
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