Theories of Mathematics Education: Seeking New Frontiers PDF
Preview Theories of Mathematics Education: Seeking New Frontiers
Advances in Mathematics Education Editors: Prof.Dr.GabrieleKaiser,UniversityofHamburg Prof.Dr.BharathSriraman,TheUniversityofMontana Bharath Sriraman (cid:2) Lyn English Editors Theories of Mathematics Education Seeking New Frontiers Prof.BharathSriraman Prof.LynEnglish DeptofMathematicalSciences CentreforLearningInnovation TheUniversityofMontana QueenslandUniversityofTechnology Missoula,MT59812-0864 VictoriaParkRoad USA KelvinGrove,QLD4059 [email protected] Australia [email protected] ISBN978-3-642-00741-5 e-ISBN978-3-642-00742-2 DOI10.1007/978-3-642-00742-2 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2009938521 ©Springer-VerlagBerlinHeidelberg2010 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. 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Coverdesign:deblik Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Series Preface AdvancesinMathematicsEducationisanewandinnovativebookseriespublished bySpringer thatbuildson the success andtherich history of ZDM—The Interna- tional Journal on Mathematics Education (formerly known as Zentralblatt für Di- daktikderMathematik).OnecharacteristicofZDMsinceitsinceptionin1969has beenthepublicationofthemedissuesthataimtobringthestate-of-the-artoncen- tralsub-domainswithinmathematicseducation.Thepublishedissuesincludearich varietyoftopicsandcontributionsthatcontinuetobeofrelevancetoday.Thenewly establishedmonographseriesaimstointegrate,synthesizeandextendpapersfrom previously published themed issues of importance today, by orienting these issues towardsthefuturestateoftheart.Themainideaistomovethefieldforwardwith abookseriesthatlookstothefuturebybuildingonthepastbycarefullychoosing viableideasthatcanfruitfullymutateandinspirethenextgenerations.Takinginspi- rationfromHenriPoincaré(1854–1912),whosaid“Tocreateconsistspreciselyin notmakinguselesscombinationsandinmakingthosewhichareusefulandwhich are only a small minority. Invention is discernment, choice”, this is our attempt to create something new for the field by making useful combinations of existing ideaswiththosethatareconsideredtobeatthefrontiersofthefieldofmathemat- ics education research today, to carefully select from the past and cross-fertilize ideas across generations with the hope of producing something relevant, forward oriented,syntheticandinnovative.Theseriesissupportedbyaneditorialboardof internationallywell-knownscholars,whobringintheirlongexperienceinthefield aswellastheirexpertisetothisseries.Themembersoftheeditorialboardare:Ubi- ratanD’Ambrosio(Brazil),MiriamAmit(Israel),JinfaCai(USA),HelenForgasz (Australia),andJeremyKilpatrick(USA). We hope that the first book in this series on Theories of Mathematics Educa- tion provides a prototype of the book series. Theories of Mathematics Education carriesforwardandconsolidatestheworkandvoicesoffourgenerationsofmathe- maticseducationresearchers.Thebook’sinspirationliesintheworkofHans-Georg Steiner’s(1928–2004)internationalstudygroupcalledTheoryofMathematicsEdu- cation(TME)whichhadheldfiveinternationalconferencesuntil1992,andoffered v vi SeriesPreface a regular topic study group at the quadrennial International Congress of Mathe- matics Education (ICME) until the turn of the last century at which point activity seemed to cease. The editors of the book (Sriraman and English) revived the ac- tivity of this group at the 2005 Annual meeting of the International Group for the PsychologyofMathematicsEducation(IGPME)inMelbourne,inaresearchforum focussed on theories. Five years later, substantial work on theories has been ac- complishedbynumerousgroupsandresearchersaroundtheworld,inunexpected, surprisingandfruitfuldirectionssuchascomplexitytheoryandtheneurosciences. Thisincludessustainedcollaborativeworkbyparticipantsfromthe2005PMEfo- rumthatresultedintwoZDMissuesontheoriesin2005(issue6)and2006(issue1), inadditiontoworkontheoriesatsubsequentConferencesofEuropeanResearchers inMathematicsEducation(CERME),prominentamongwhichistheworkon“net- working strategies” that produced a substantial ZDM issue in 2008 (issue 3). The “networking”approachaimstoconnectdifferenttheoreticalapproachesusingsev- eralstrategies.Itrejectsisolationistictendenciesofseparatingdifferenttheoretical approachesandbasesitsworkontheassumptionthatthevarietyofdifferenttheo- reticalapproachesandperspectivesin mathematicseducationresearchserved as a richresourceuponwhichthescientificcommunityshouldbuildvialayeredconnec- tions between different theories. The intention is not to develop one grand unified theory, but to network local theories that deal with background theories, and use divergingconceptualsystemsfordescribingthesamephenomena. Anotherdistinctfeatureofthisbookseriesistheusageoftheancientscholarly Chinese and Indian traditions of commentaries. As the Taoist scholar Guo Xiang (252–312C.E)andtheIndianadvaitistShankara(788–820C.E)demonstrated,the purposeofacommentaryisnotonlytoelucidateideaspresentinanoriginaltext,but alsotophilosophizeandprovidedeepermeaningtoolderideas,andweaddtotake themforwardinwaysnotconceivedoforiginally.Thisseriesandthepresentbook strivetodosobysolicitingcommentariesfromexpertsandnovices.Wefinditpar- ticularlyimportanttointegratenewervoices,includingthosethathavejustentered thefield,inordertopreventanorthodoxyseepingintotherealmofideas.Inaddi- tionprefacestochapterssetthestageforthemotivation,purpose,andbackground ofagivenwork. We hope this new series will inspire readers in the present and the future to continuedevelopingfruitfulideasofrelevanceforourscholarlycommunitiesacross theworld. GabrieleKaiser BharathSriraman To Sabine,Sarah, JacobandMiriamfortheirunwaveringsupport & RichardLeshforbeinganever-ending source offuture-orientedideas Introduction A Synthesized and Forward-Oriented Case for Mathematics Education We take this opportunity to offer a few remarks on the background and motiva- tionforthiseditedcollectionofchaptersthataimtoseeknewfrontiersfortheories of mathematics education. This book grew out of the 29th meeting of the Interna- tional Group of the Psychology of Mathematics Education (PME) in Melbourne, 2005, where we co-organized a research forum on theories of mathematics edu- cation (see English and Sriraman 2005). This led to our production of two ZDM issuesontheoriesofmathematicseducation,whichconsistedofextendedversions ofthepaperspresentedattheresearchforuminadditiontocomplementarytheoret- icalperspectivesthatwerenotpresentintheforum(seeSriramanandEnglish2005, 2006). Numerous handbooks have been published since 2005 that have provided grist for the theoretical foundations of our field (e.g., Alexander and Winne2006; Campbell 2005; English et al. 2008; Lester 2007), and suggest that the identity of ourfieldiscontinuallydeveloping(Sriraman2009).Therearenewerdevelopments innumerousareaswithinmathematicseducationsuchascomplexitytheory,neuro- sciences,criticaltheory,feministtheory,socialjusticetheory,networkingtheories, andsemiotics.ThisfirstbookinthenewSpringerseriesAdvancesinMathematics Educationistheidealplatformtotakeanavantgardelookattheoriesofmathemat- ics education, using the two ZDM issues on theories as a point of departure. The booksynthesizesthepastandorientstowardsnewerfrontiersbysynergizingareas thathavebeendevelopingrapidlyinthelastfiveyears. After13monthsofveryintenseactivitywiththecastof50+contributingauthors, we have finally succeeded in bringing together a substantial book on theories of mathematics education. The task was by no means easy given the extremely tight deadline; indeed the book would not have been possible without the excellent co- operation of each and every author. The book comprises of 19 parts consisting of 59 prefaces, chapters and commentaries,with ∼30% of the chapters comingfrom thetwopreviousZDMissuesontheories(SriramanandEnglish2005,2006).The chapterbyJudithJacobsonfeministpedagogycomesfroma1994issueofZDM, andthechapterbyGeraldGoldinonproblemsolvingheuristics,affect,anddiscrete mathematicscomesfroma2004issueofZDM. ix x Introduction However,manyofthesechaptershavebeenreworkedbytheauthorsand/orin- cludenewprefacesandcommentaries.Inmanycasestheseolderchaptersalsoin- clude two or more commentaries that critically examine the ideas presented, ana- lyzetheirrelevanceforthefieldtoday,andsuggestawayforward.Forinstancethe chapterbyJacobshasanewprefaceandthreecommentariesthatexaminethesignif- icanceofJacobs’ideasoffeministpedagogy,inlightofresearchfindingsongender andmathematicsadecadeandahalflaterfromAustralia,Turkey,andIceland.Sim- ilarly the chapter by Goldin includes a contemporary commentary from Jinfa Cai and the Lesh and Sriraman chapter on mathematics education as a design science receivescriticalcommentariesfromauthorsinIsrael,Denmark,andtheU.S. The cynical reader might ask, what is so special about this particular book in comparisontothenumerousotherbooksthatarepublished.Thestyleofprefaceand commentariesisbothanalytic(analysisofideaspresented)andsynthetic(makingit cohereinthelargerschemeofthings).Thisallowsfortheoreticalideaspresentedto bediscussedfullyandtakenindirectionsdifferentfromtheauthors.Thebookalso containsthevoicesofmultigenerationsofmathematicseducators,includingthose that have been around since the major research journals were founded in the late 1960’s, the numerous movers and shakers of paradigms, researchers coming from very different theoretical backgrounds, and newer voices in the fledgling areas of complexity,neuroscience,aestheticsandnetworkingtheories.Thisbookconsisting of 19 parts, 17 prefaces and 23 commentaries synergizes the efforts of numerous groups across the globe in the ongoing debates on theory development in mathe- maticseducation.Thebookpresentsagoodcasethattheorydevelopmentisindeed progressingondifferentgeographicalandtrans-disciplinaryfronts,andourfieldhas indeedconsolidatedandsynthesizedpreviousworkandmovedforwardinunimag- inedandproductiveways. Wewouldliketothanktheeditorialboardforitsinputonvariousmanuscripts, and the very large cast of ad-hoc reviewers that include most of the book authors. Last but not least we acknowledge the unwavering support of Heine Clemens at Springer Berlin/Heidelberg with developing the larger concept and scope of this book and all matters related to publishing logistics, as well as Gabriele Kaiser for herfaithandsolidarityinthisendeavor. Acknowledgements Thefirsteditor(Sriraman)wouldliketothanktheSabbaticalandFaculty ExchangeProgramofTheUniversityofMontanaforprovidingthetimeandsupportnecessaryfor completingthismonumentalendeavor.Inaddition,awholeheartedthankyoutoLynEnglishfor hermentorshipandexpertiseintheartofediting.Thisbookwouldnothavematerializedwithout hersuperbtalentandguidance. BharathSriraman LynEnglish References Alexander,P.,&Winne,P.(Eds.)(2006).HandbookofEducationalPsychology(2nded.).Mah- wah:LawrenceErlbaum&Associates. Introduction xi Campbell,J.(Ed.)(2005).HandbookofMathematicalCognition.Routledge:PsychologyPress: ImprintofTaylorandFrancis. English,L.,Bussi,M.,Jones,G.,Lesh,R.,Sriraman,B.,&Tirosh,D.(Eds.)(2008).Handbookof InternationalResearchinMathematicsEducation(2nded.).Routledge:TaylorandFrancis. English, L., & Sriraman, B. (Eds.) (2005). Theories of mathematics education. In H. Chick & J.L. Vincent (Eds.), Proceedings of the 29th Annual meeting of the International Group of PsychologyofMathematicsEducation(Vol.1,pp.170–172).Melbourne,Australia. Lester,F.(Ed.)(2007).SecondHandbookofResearchonMathematicsTeachingandLearning. Charlotte,NC:InformationAgePublishing. Sriraman,B.(2009).Ontheidentitiesofmathematicseducation.Interchange:AQuarterlyReview ofEducation,40(1),119–135. Sriraman,B.,&English,L.(Eds.)(2005).Theoriesofmathematicseducation(partA).ZDM—The InternationalJournalonMathematicsEducation,37(6). Sriraman,B.,&English,L.(Eds.)(2006).Theoriesofmathematicseducation(partA).ZDM—The InternationalJournalonMathematicsEducation,38(1).
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