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1、APOS:AConstructivistTheoryofLearninginUndergraduateMathematicsEducationResearchEdDubinsky,GeorgiaStateUniversity,USAandMichaelA.McDonald,OccidentalCollege,USATheworkreportedinthispaperisbasedontheprinciplethatresearchinmathematicseducationisstrengthenedins
2、everalwayswhenbasedonatheoreticalperspective.Developmentofatheoryormodelinmathematicseducationshouldbe,inourview,partofanattempttounderstandhowmathematicscanbelearnedandwhataneducationalprogramcandotohelpinthislearning.Wedonotthinkthatatheoryoflearningisas
3、tatementoftruthandalthoughitmayormaynotbeanapproximationtowhatisreallyhappeningwhenanindividualtriestolearnoneoranotherconceptinmathematics,thisisnotourfocus.Ratherweconcentrateonhowatheoryoflearningmathematicscanhelpusunderstandthelearningprocessbyprovidi
4、ngexplanationsofphenomenathatwecanobserveinstudentswhoaretryingtoconstructtheirunderstandingsofmathematicalconceptsandbysuggestingdirectionsforpedagogythatcanhelpinthislearningprocess.Modelsandtheoriesinmathematicseducationcan??????supportprediction,haveex
5、planatorypower,beapplicabletoabroadrangeofphenomena,helporganizeone’sthinkingaboutcomplex,interrelatedphenomena,serveasatoolforanalyzingdata,andprovidealanguageforcommunicationofideasaboutlearningthatgobeyondsuperficialdescriptions.Wewouldliketooffertheses
6、ixfeatures,thefirstthreeofwhicharegivenbyAlanSchoenfeldin“Towardatheoryofteaching-in-context,”IssuesinEducation,bothaswaysinwhichatheorycancontributetoresearchandascriteriaforevaluatingatheory.1Inthispaper,wedescribeonesuchperspective,APOSTheory,intheconte
7、xtofundergraduatemathematicseducation.Weexplaintheextenttowhichithastheabovecharacteristics,discusstherolethatthistheoryplaysinaresearchandcurriculumdevelopmentprogramandhowsuchaprogramcancontributetothedevelopmentofthetheory,describebrieflyhowworkingwitht
8、hisparticulartheoryhasprovidedavehicleforbuildingacommunityofresearchersinundergraduatemathematicseducation,andindicatetheuseofAPOSTheoryinspecificresearchstudies,bothbyresearcherswhoaredevelopingitaswellasot
