Critical Issues in Mathematics Education: Major Contributions of Alan Bishop

251 Pages·2008·2.95 MB·English

by  Philip Clarkson

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.
Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare
notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjectto
proprietaryrights.
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, Illinois State University, Normal, IL 61790-4520,
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
Chapter1
Developing a Festschrift with a Difference
PhilipClarksonandNormaPresmeg
AFestschriftisnormallyunderstoodtobeavolumepreparedtohonourarespected
academic, reflecting on his or her significant additions to the field of knowledge
to which they have devoted their energies. It is normal for such a volume to be
composedofcontributionsfromthosewhohaveworkedcloselywiththeacademic,
including doctoral students, and others whose work is also known to have made
importantcontributionswithinthesameareasofresearch.
It was the dearth of volumes of this type in the area of mathematics education
research that Philip Clarkson and Michel Lokhorst, then a commissioning editor
withKluwerAcademicPublishers,startedtodiscusssome5yearsago.Thisdiscus-
sionpointwasembeddedinabroaderconversationthatlamentedthefactthatlittle
waspublishedthatkeptatraceofhowideasdevelopedovertimeineducation,and
inmathematicseducationinparticular.Associatedwiththisnotionwashowweasa
communitywerenotverygoodatlinkingthedevelopmentofideaswiththepeople
who had worked on them, and the individual contexts within which their thinking
occurred.Wewonderedwhethersomethingshouldbedonetodrawattentiontothis
issue.OnewaytodothatwastobeginthetaskofcomposingaFestschrift,butwith
adifference.
Inthinkingthroughtheimplicationsofthisproposition,itseemedusefultostruc-
ture the volume in such a way that perhaps more could be achieved than by just
initiating a call for contributions to honour a colleague who had made a long and
importantcontributiontomathematicseducation.Wewonderedwhetherastructure
couldbedevelopedfortheproposedvolumethatemphasisedthefollowing:
(cid:2)
(cid:2) theideasofthehonouredacademicthatsheorhehaddeveloped,
(cid:2) whereandhowtheyweredeveloped,and
whatbecameofthoseideasoncetheywerepublishedandtakenup,ornottaken
up, by the community of scholars that were working in that particular area, in
thiscasemathematicseducation.
P.Clarkson
FacultyofEducation,AustralianCatholicUniversity,FitzroyVIC3065,Australia
e-mail:[email protected]
P.Clarkson,N.Presmeg(eds.),CriticalIssuesinMathematicsEducation, 3
(cid:2)C SpringerScience+BusinessMedia,LLC 2008
4 P.Clarkson,N.Presmeg
Wedecidedthatindeedsuchaprojectshouldbeinitiated.Itwasrelativelyeasy
todecidetofocusonAlanBishop’scontributionstomathematicseducationoverthe
last40years,whicharestillcontinuing.This,thenisthegoalofthisvolume.
The purpose of this volume is twofold, each part of equal weight, although the
secondcomponenthasgiventheimpetusandstructureforthevolume.Thefirstis
toputintoperspectivethecontributionthat(nowEmeritus)ProfessorAlanBishop
has made to mathematics education research beginning in the 1960s. The other is
toreviewsixcriticalissuesthathavebeenimportantintheestablishmentofmathe-
maticseducationresearchoverthelast50years,includingupdatingtosomeextent
current developments in each of these areas. The volume was planned to make a
valuablecontributiontotheongoingreflectionofmathematiceducationresearchers
world wide, but also to address topics relevant to policy makers and teacher edu-
cators who wish to understand some of the key issues with which mathematics
education has been and still is concerned. However all ideas develop within an
historical context. Hence in various places within this volume comment is made
with regard to the contexts within which Bishop’s contributions to these research
issuesweremade.
Bishop’s contributions can be conveniently outlined through a consideration of
thefollowingsixissuesastheyrelatetomathematicseducationresearch:
(cid:2)
(cid:2) Teacherdecision-making
(cid:2) Spatialabilities,visualizationandgeometry
(cid:2) Culturalandsocialaspectsofmathematicseducation
(cid:2) Sociopoliticalissuesformathematicseducation
(cid:2) Teachersandresearch
Valuesandteachingmathematics.
The structure of the volume has been developed around these six issues, each
issuebeingthefocusofasectionofthevolume.Eachsectionhasthreeorfourcom-
ponents. The first component of each section is a brief introduction that positions
andgivesacontextfortheBishoparticlereprintedinthesection.
Thesecondcomponentofeachsectionisareprintofaparticular“key”journal
articleorbookchapterthatBishoppublished.Eachkeyarticlehasbeenchosento
typify his contribution to the ongoing research on that issue. These articles were
selectedinconversationwithBishop.
Thefinalcomponentofeachsectionconsistsofoneortwoinvitedchaptersfrom
selectedauthors.WechoseauthorswhohadeitherworkeddirectlywithBishop,or
hadworkedwiththeideascanvassedintheirsection.
AuthorswereaskedtousetheBishopkeyarticlefortheirsectionasafocusfora
commentaryonthatissueinmathematicseducation.Weanticipatedthattheauthors
wouldusethekeyarticlesindifferentways:perhapsasastartingpointtodevelopa
dialogwiththearticleinsomeway,ortotakethekeyarticleandmapouthowthe
ideashave orhave notbeen takenupinsucceeding years,ortolookbacktowhat
precededthepublicationofthearticleandplaceitinanhistoricalcontext,ortostart
in a completely different place and come back to the notions discussed in the key