视觉-空间表征的类型和数学问题解决 毕业论文外文翻译

视觉-空间表征的类型和数学问题解决毕业论文外文翻译TypesofVisual-SpatialRepresentationsandTheirMathematicalProblemSolvingAbstract:Visual-spatialrepresentationhasreceivedsignificantattentioninrecentyearsinthecontextofcognitivepsychologyandmathematicseducation.Thepurposeofthispaperistoprovideanoverviewofthedifferenttypesofvisual-spatialrepresentationsandtheirroleinmathematicalproblemsolving.Thepaperalsobrieflydiscussesthecognitiveprocessesinvolvedincreatingandusingvisual-spatialrepresentationsinmathematicalproblemsolving.Thereviewsuggeststhatvisual-spatialrepresentationscanbecategorizedintofourmaintypes:pictorial,diagrammatic,graphical,andtactile.Eachtypehasitsstrengthsandlimitationsintermsofthecognitivedemandsandmathematicalproblemsthattheycanaddress.Moreover,thecreationanduseofvisual-spatialrepresentationsinmathematicalproblemsolvingrequiresdifferentcognitiveprocesses,suchasselectiveattention,spatialreasoning,andmentalimagery.Implicationsformathematicseducationarediscussed.1.Introduction:Visual-spatialrepresentationhasbeenatopicofdiscussionincognitivepsychologyandmathematicseducationformanyyears.Theuseofvisual-spatialrepresentationsinmathematicalproblemsolvinghasbeenfoundtobebeneficialinenhancingproblem-solvingskillsandmathematicalunderstanding(Hegarty&Kozhevnikov,1999;Lesh&Zawojewski,2007).Accordingtothecognitiveloadtheory(Sweller,Ayres,&Kalyuga,2011),visual-spatialrepresentationscanreducecognitiveloadbyprovidinganexternalmeansfororganizingandprocessinginformation.Inthispaper,weprovideanoverviewofthedifferenttypesofvisual-spatialrepresentationsandtheirroleinmathematicalproblemsolving.Wealsobrieflydiscussthecognitiveprocessesinvolvedincreatingandusingvisual-spatialrepresentationsinmathematicalproblemsolving.2.TypesofVisual-SpatialRepresentation:Visual-spatialrepresentationscanbeclassifiedintodifferenttypesbasedontheirmodeofrepresentationandformat.AccordingtoLeshandZawojewski(2007),therearefourmaintypesofvisual-spatialrepresentations:pictorial,diagrammatic,graphical,andtactile.2.1PictorialRepresentation:Pictorialrepresentationreferstotheuseofpicturesorphotographstorepresentmathematicalconceptsorproblems.Pictorialrepresentationsareoftenusedinelementaryschoolmathematicstorepresentandsolveproblemsinvolvingfractions,geometry,andmeasurement.Forexample,theuseofpicturestorepresentfractionscanhelpstudentsunderstandtheconceptofafractionasapartofawhole.Theuseofpicturescanalsohelpstudentsvisualizeandsolvegeometryproblems.2.2DiagrammaticRepresentation:Diagrammaticrepresentationreferstotheuseofdiagramsordrawingstorepresentmathematicalconceptsorproblems.Diagrammaticrepresentationsareoftenusedinmiddleandhighschoolmathematicstorepresentandsolveproblemsinvolvingalgebra,trigonometry,andcalculus.Forexample,theuseofacoordinateplanetographlinearequationscanhelpstudentsunderstandtherelationshipbetweentheequationanditsgraph.Theuseofdiagramscanalsohelpstudentsvisualizeandsolveproblemsinvolvinggeometricfigures.2.3GraphicalRepresentation:Graphicalrepresentationreferstotheuseofgraphsorchartstorepresentmathematicalconceptsorproblems.Graphicalrepresentationsareoftenusedinhighschoolandcollegemathematicstorepresentandsolveproblemsinvolvingdataanalysis,calculus,anddifferentialequations.Forexample,theuseofalinegraphtorepresentdatacanhelpstudentsunderstandtherelationshipbetweenvariables.Theuseofgraphscanalsohelpstudentsvisualizeandsolveproblemsinvolvingfunctions.2.4TactileRepresentation:Tactilerepresentationreferstotheuseofphysicalobjectsormanipulativestorepresentmathematicalconceptsorproblems.Tactilerepresentationsareoftenusedinelementaryschoolmathematicstorepresentandsolveproblemsinvolvingcounting,operations,andmeasurement.Forexample,theuseofblocksorcubestorepresentnumberscanhelpstudentsunderstandtheconceptofadditionandsubtraction.Theuseofmanipulativescanalsohelpstudentsvisualizeandsolveproblemsinvolvinggeometricfigures.3.CognitiveProcessesinVisual-SpatialRepresentation:Creatingandusingvisual-spatialrepresentationsinmathematicalproblemsolvingrequiresdifferentcognitiveprocesses,suchasselectiveattention,spatialreasoning,andmentalimagery.3.1SelectiveAttention:Selectiveattentionreferstotheabilitytofocusonrelevantinformationwhileignoringirrelevantinformation.Inmathematicalproblemsolving,selectiveattentionisimportantinidentifyingandinterpretingtherelevantinformationinaproblem,andselectingtheappropriatevisual-spatialrepresentationtorepresenttheproblem.3.2SpatialReasoning:Spatialreasoningreferstotheabilitytothinkandreasonaboutobjectsandtheirspatialrelationships.Inmathematicalproblemsolving,spatialreasoningisimportantincreatingandinterpretingvisual-spatialrepresentations,andinapplyinggeometricconceptsandprinciplestosolveproblems.3.3MentalImagery:Mentalimageryreferstotheabilitytocreatementalimagesofobjectsoreventsinthemind.Inmathematicalproblemsolving,mentalimageryisimportantinvisualizingandmanipulatingvisual-spatialrepresentations,andinconstructingmentalmodelsofmathematicalconceptsandprinciples.4.ImplicationsforMathematicsEducation:Visual-spatialreprese