Critical Issues in Mathematics Education · Philip Clarkson Norma Presmeg Editors Critical Issues in Mathematics Education Major Contributions of Alan Bishop 123 Editors PhilipClarkson NormaPresmeg FacultyofEducation IllinoisStateUniversity AustralianCatholicUniversity DepartmentofMathematics FitzroyVIC3065 313StevensonHall Australia NormalIL61790-4520 [email protected] USA [email protected] ISBN:978-0-387-09672-8 e-ISBN:978-0-387-09673-5 LibraryofCongressControlNumber:2008930313 (cid:2)c 2008SpringerScience+BusinessMedia,LLC Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. 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Printedonacid-freepaper springer.com Contents SectionI Introduction 1 DevelopingaFestschriftwithaDifference ........................ 3 PhilipClarksonandNormaPresmeg 2 InConversationwithAlanBishop ............................... 13 PhilipClarkson SectionII TeacherDecisionMaking 3 Decision-Making,theInterveningVariable........................ 29 AlanJ.Bishop 4 Teachers’DecisionMaking:fromAlanJ.BishoptoToday.......... 37 HildaBorko,SarahA.RobertsandRichardShavelson SectionIII SpatialAbilities,Visualization,andGeometry 5 Spatial Abilities and Mathematics Education–AReview .......................................... 71 AlanJ.Bishop 6 Spatial Abilities Research as a Foundation for Visualization in Teaching andLearningMathematics...................................... 83 NormaPresmeg 7 Spatial Abilities, Mathematics, Culture, andthePapuaNewGuineaExperience........................... 97 M.A.(Ken)Clements v vi Contents SectionIV CulturalandSocialAspects 8 VisualisingandMathematicsinaPre-TechnologicalCulture.........109 AlanJ.Bishop 9 Cultural and Social Aspects of Mathematics Education: RespondingtoBishop’sChallenge ...............................121 BillBarton 10 Chinese Culture, Islamic Culture, andMathematicsEducation.....................................135 FrederickLeung SectionV SocialandPoliticalAspects 11 MathematicalPowertothePeople ...............................151 AlanJ.Bishop 12 Mathematical Power as Political Power–ThePoliticsofMathematicsEducation ...................167 ChristineKeitelandRenukaVithal SectionVI TeachersandResearch 13 Research,Effectiveness,andthePractitioners’World ..............191 AlanJ.Bishop 14 PracticingResearchandResearchingPractice ....................205 JeremyKilpatrick 15 Reflexivity, Effectiveness, and the Interaction ofResearcherandPractitionerWorlds ...........................213 KennethRuthven SectionVII Values 16 Mathematics Teaching and Values Education–AnIntersectioninNeedofResearch ..................231 AlanJ.Bishop 17 ValuingValuesinMathematicsEducation ........................239 WeeTiongSeah Index .............................................................253 Contributors BillBarton Dept.ofMathematics,TheUniversityofAuckland,PrivateBag92019,Auckland MailCentre,Auckland1142,NewZealand,[email protected] AlanJ.Bishop Faculty of Education, Monash University, Wellington Road, Clayton, Victoria 3168,Australia,[email protected] HildaBorko School of Education, Stanford University, 485 Lasuen Mall, Stanford, CA 94305-3096,USA,[email protected] PhilipC.Clarkson FacultyofEducation,AustralianCatholicUniversity,FitzroyVIC3065,Australia, [email protected] M.A.(Ken)Clements Department of Mathematics, IllinoisState University, Normal, IL61790-4520, UnitedStatesofAmerica,[email protected] ChristineKeitel FachbereichErziehungswissenschaftundPsychologie,FreieUniversita¨tBerlin, HabelschwerdterAllee45,14195Berlin,Germany,[email protected] JeremyKilpatrick 105AderholdHall,UniversityofGeorgia,Athens,GA30602-7124,UnitedStates ofAmerica,[email protected] FrederickLeung ChairFacultyofEducation,TheUniversityofHongKong,PokfulamRoad,Hong Kong,[email protected] NormaPresmeg IllinoisStateUniversity,DepartmentofMathematics,313StevensonHall,Normal IL61790-4520,USA,[email protected] vii viii Contributors SarahA.Roberts SchoolofEducation,249UCBUniversityofColorado,Boulder,CO80309-0249, USA,[email protected] KennethRuthven FacultyofEducation,UniversityofCambridge,184HillsRoad,CambridgeCB2 8PQ,UnitedKingdom,[email protected] WeeTiongSeah Faculty of Education, Monash University (Peninsula Campus), PO Box 527, Frankston,Vic.3199,Australia,[email protected] RichardShavelson SchoolofEducation,485LasuenMall,StanfordUniversity,CA94305-3096,USA, [email protected] RenukaVithal DeanofEducation,FacultyofEducation,UniversityofKwaZulu-Natal,Edgewood Campus,PrivateBagX03,Ashwood3605,SouthAfrica,[email protected] Section I Introduction