Theories of Mathematics Education: Seeking New Frontiers

650 Pages·2010·5.725 MB·English

by  Jeremy Kilpatrick (auth.), Bharath Sriraman, Lyn English (eds.)

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
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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
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wah:LawrenceErlbaum&Associates.
Introduction xi
Campbell,J.(Ed.)(2005).HandbookofMathematicalCognition.Routledge:PsychologyPress:
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InternationalResearchinMathematicsEducation(2nded.).Routledge:TaylorandFrancis.
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