Table Of ContentMathematical Knowledge
in Teaching
Mathematics Education Library
VOLUME 50
ManagingEditor
A.J.Bishop,MonashUniversity,Melbourne,Australia
EditorialBoard
M.G.BartoliniBussi,Modena,Italy
J.P.Becker,Illinois,U.S.A.
M.Borba,RioClaro,Brazil
B.Kaur,Singapore
C.Keitel,Berlin,Germany
G.Leder,Melbourne,Australia
F.Leung,HongKong,China
D.Pimm,Edmonton,Canada
K.Ruthven,Cambridge,UnitedKingdom
A.Sfard,Haifa,Israel
Y.Shimizu,Tennodai,Japan
O.Skovsmose,Aalborg,Denmark
Forfurthervolumes:
http://www.springer.com/series/6276
·
Tim Rowland Kenneth Ruthven
Editors
Mathematical Knowledge
in Teaching
123
Editors
TimRowland KennethRuthven
UniversityofCambridge UniversityofCambridge
FacultyofEducation FacultyofEducation
184HillsRoad 184HillsRoad
CB28PQCambridge CB28PQCambridge
UnitedKingdom UnitedKingdom
[email protected] [email protected]
SeriesEditor:
AlanJ.Bishop
MonashUniversity
Melbourne3800
Australia
[email protected]
ISBN978-90-481-9765-1 e-ISBN978-90-481-9766-8
DOI10.1007/978-90-481-9766-8
SpringerDordrechtHeidelbergLondonNewYork
©SpringerScience+BusinessMediaB.V.2011
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Contents
1 Introduction:MathematicalKnowledgeinTeaching . . . . . . . . 1
TimRowlandandKennethRuthven
PartI ConceptualisingMathematicalKnowledgeinTeaching
2 ConceptualisingTeachers’MathematicalKnowledgeinTeaching . 9
MarilenaPetrouandMariaGoulding
3 KnowingandIdentity:ASituatedTheoryofMathematics
KnowledgeinTeaching. . . . . . . . . . . . . . . . . . . . . . . . . 27
JeremyHodgen
4 ChangedViewsonMathematicalKnowledgeintheCourse
ofDidacticalTheoryDevelopment:IndependentCorpus
ofScientificKnowledgeorResultofSocialConstructions? . . . . . 43
HeinzSteinbring
5 Teaching Mathematics as the Contextual Application
ofMathematicalModesofEnquiry . . . . . . . . . . . . . . . . . . 65
AnneWatsonandBillBarton
6 ConceptualisingMathematicalKnowledgeinTeaching . . . . . . . 83
KennethRuthven
PartII UnderstandingtheCulturalContextofMathematical
KnowledgeinTeaching
7 The Cultural Location of Teachers’ Mathematical
Knowledge: Another Hidden Variable in Mathematics
EducationResearch? . . . . . . . . . . . . . . . . . . . . . . . . . . 99
PaulAndrews
8 How Educational Systems and Cultures Mediate
Teacher Knowledge: ‘Listening’ in English, French
andGermanClassrooms . . . . . . . . . . . . . . . . . . . . . . . . 119
BirgitPepin
v
vi Contents
9 ModellingTeachinginMathematicsTeacherEducation
andtheConstitutionofMathematicsforTeaching . . . . . . . . . 139
JillAdlerandZainDavis
10 Audit and Evaluation of Pedagogy: Towards
aCultural-HistoricalPerspective . . . . . . . . . . . . . . . . . . . 161
JulianWilliams
11 TheCulturalDimensionofTeachers’MathematicalKnowledge . . 179
AndreasJ.StylianidesandSeánDelaney
PartIII Building Mathematical Knowledge in Teaching
byMeansofTheorisedTools
12 TheKnowledgeQuartetasanOrganisingFrameworkfor
DevelopingandDeepeningTeachers’MathematicsKnowledge . . 195
FayTurnerandTimRowland
13 LearningtoTeachMathematicsUsingLessonStudy . . . . . . . . 213
DoloresCorcoranandSandyPepperell
14 Using Theories to Build Kindergarten
Teachers’MathematicalKnowledgeforTeaching . . . . . . . . . . 231
DinaTirosh,PessiaTsamir,andEstherLevenson
15 Teachers’StoriesofMathematicalSubjectKnowledge:
AccountingfortheUnexpected . . . . . . . . . . . . . . . . . . . . 251
JulieRyanandJulianWilliams
16 BuildingMathematicalKnowledgeinTeachingbyMeans
ofTheorisedTools . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
JoséCarrillo
17 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
KennethRuthvenandTimRowland
AuthorIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
SubjectIndex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
Contributors
JillAdlerUniversityoftheWitwatersrand,Parktown,Johannesburg2196,
SouthAfrica;andKing’sCollegeLondon,UK.,[email protected]
PaulAndrewsFacultyofEducation,UniversityofCambridge,Cambridge
CB28PQ,UK,[email protected]
BillBartonDepartmentofMathematics,UniversityofAuckland,Auckland1142,
NewZealand,[email protected]
JoséCarrilloFacultyofEducationalSciences,UniversityofHuelva,Huelva
E21007,Spain,[email protected]
DoloresCorcoranSt.Patrick’sCollege,DublinCityUniversity,Dublin9,Ireland,
[email protected]
ZainDavisSchoolofEducation,UniversityofCapeTown,Rondebosch7701,
CapeTown,SouthAfrica,[email protected]
SeánDelaneyMarinoInstituteofEducation,ColáisteMhuire,Dublin9,Ireland,
[email protected]
MariaGouldingInstituteofEducationalTechnology,TheOpenUniversity,
MiltonKeynesMK76AA,UK,[email protected]
JeremyHodgenDepartmentofEducationandProfessionalStudies,King’s
CollegeLondon,Franklin-WilkinsBuilding(WaterlooBridgeWing),London
SE19NH,UK,[email protected]
EstherLevensonSchoolofEducation,TelAvivUniversity,Tel-Aviv69978,
Israel,[email protected]
BirgitPepinFacultyofTeacherEducation,Sør-TrøndelagUniversityCollege,
Trondheim7004,Norway,[email protected]
SandyPepperellDepartmentofEducation,FroebelCollege,Roehampton
University,LondonSW155PJ,UK,[email protected]
vii
viii Contributors
MarilenaPetrouInstituteofEducationalTechnology,TheOpenUniversity,
MiltonKeynesMK76AA,UK,[email protected]
TimRowlandFacultyofEducation,UniversityofCambridge,Cambridge
CB28PQ,UK,[email protected]
KennethRuthvenFacultyofEducation,UniversityofCambridge,Cambridge
CB28PQ,UK,[email protected]
JulieRyanInstituteofEducation,ManchesterMetropolitanUniversity,
ManchesterM202RR,UK,[email protected]
HeinzSteinbringFakultätfürMathematik,UniversitätDuisburg-Essen,Essen
D-45117,Germany,[email protected]
AndreasJ.StylianidesFacultyofEducation,UniversityofCambridge,
CambridgeCB28PQ,UK,[email protected]
DinaTiroshSchoolofEducation,TelAvivUniversity,Tel-Aviv69978,Israel,
[email protected]
PessiaTsamirSchoolofEducation,TelAvivUniversity,Tel-Aviv69978,Israel,
[email protected]
FayTurnerFacultyofEducation,UniversityofCambridge,CambridgeCB28PQ,
UK,[email protected]
AnneWatsonDepartmentofEducation,UniversityofOxford,OxfordOX26PY,
UK,[email protected]
JulianWilliamsSchoolofEducation,UniversityofManchester,Manchester
M139PL,UK,[email protected]
Chapter 1
Introduction:
Mathematical Knowledge in Teaching
TimRowlandandKennethRuthven
Background:TheTopicandtheBook
This book examines the issue of mathematical subject knowledge in teaching.
There is now widespread agreement that the quality of primary and secondary
school mathematics teaching depends crucially on the subject-related knowledge
that teachers are able to bring to bear on their work. However, when discussion
startstofocusinonthespecificformsandfunctionsofmathematicalknowledgefor
teaching,thereismuchlessconcurrence.Thereisnow,however,aprevalentsugges-
tionthateffectiveteachingcallsfordistinctiveformsofsubject-relatedknowledge
and thinking. These are particularly live issues for policy and practice because of
the longstanding difficulties in recruiting teachers who are confident and conven-
tionallywellqualifiedinmathematics,andbecauseofrisingconcernthatteaching
ofthesubjecthasnotadaptedsufficientlytothechangingcircumstancesofschools
andtheirstudents.Theissuestobeexaminedinthisbookare,then,ofconsiderable
significanceinaddressingworld-wideaspirationstoraisestandardsofteachingand
learning in mathematics through developing more effective approaches to charac-
terising,assessinganddevelopingmathematicalknowledgeforteachingwithinthe
professionalworkforce.
Public discussion often proceeds on the basis either that teachers need only
have such mathematical competence as they are expected to develop in their stu-
dents,orthatitmayalsobebeneficialforthemtohavesomewhat‘moreadvanced’
knowledgeofmathematicsthanthesubjectmattertheyareteaching.However,itis
now clear that such perspectives fail to do justice to the situation. Rather, a num-
ber of Anglo-American, Continental-European and East-Asian traditions point to
particular forms of subject-related knowledge that underpin effective teaching of
mathematics and to distinctive mechanisms for developing such knowledge. An
important objective of this book, then, is to develop a critical synthesis of differ-
ent perspectives on mathematical knowledge for and in teaching and to establish
B
T.Rowland( )
FacultyofEducation,UniversityofCambridge,Cambridge CB28PQ,UK
e-mail:[email protected]
T.Rowland,K.Ruthven(eds.),MathematicalKnowledgeinTeaching,Mathematics 1
EducationLibrary50,DOI10.1007/978-90-481-9766-8_1,
(cid:2)C SpringerScience+BusinessMediaB.V.2011
