Rowland / Ruthven Mathematical Knowledge in Teaching

1. Auflage 2011
ISBN: 978-90-481-9766-8
Verlag: Springer-Verlag
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 304 Seiten

The quality of primary and secondary school mathematics teaching is generally agreed to depend crucially on the subject-related knowledge of the teacher. However, there is increasing recognition that effective teaching calls for distinctive forms of subject-related knowledge and thinking. Thus, established ways of conceptualizing, developing and assessing mathematical knowledge for teaching may be less than adequate. These are important issues for policy and practice because of longstanding difficulties in recruiting teachers who are confident and conventionally well-qualified in mathematics, and because of rising concern that teaching of the subject has not adapted sufficiently. The issues to be examined in Mathematical Knowledge in Teaching are of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing more effective approaches to characterizing, assessing and developing mathematical knowledge for teaching.

Autoren/Hrsg.

Rowland, Tim

Ruthven, Kenneth

Inhaltsverzeichnis

1;Contents;5
2;Contributors;7
3;1 Introduction: Mathematical Knowledge in Teaching;9
3.1; Background: The Topic and the Book;9
3.2; Introduction to Section 1;10
3.3; Introduction to Section 2;11
3.4; Introduction to Section 3;12
3.5; Critical Discussion and Synthesis;13
3.6;References;13
4;Part I Conceptualising Mathematical Knowledge in Teaching;14
5;2 Conceptualising Teachers' Mathematical Knowledge in Teaching;15
5.1; Introduction;15
5.2; Shulman's Conceptualisation;16
5.3; Fennema and Franke's Conceptualisation;19
5.4; The Mathematics Teaching and Learning to Teach Project (MTLT) and the Learning Mathematics for Teaching Project (LMT): A Practice-Based Framework of Teachers' Mathematical Knowledge for Teaching;21
5.5; The Knowledge Quartet;24
5.6; Synthesis;26
5.7; Implications and Limitations;28
5.8;References;30
6;3 Knowing and Identity: A Situated Theory of Mathematics Knowledge in Teaching;32
6.1; The Problem of Mathematics Teacher Knowledge;33
6.2; A Case Study from Primary Mathematics: Alexandra's Knowledge of the Multiplication and Division of Fractions;34
6.3; Is this just an Issue for Primary Teaching?;39
6.4; The Contribution of Situated Theories: What Does This Mean for Teacher Knowledge?;40
6.5; Implications for the Practices of Teaching, Teacher Education and Development;43
6.6;References;45
7;4 Changed Views on Mathematical Knowledge in the Course of Didactical Theory Development: Independent Corpus of Scientific Knowledge or Result of Social Constructions?;48
7.1; Introduction;48
7.2; The 'Stoffdidaktik' Elaboration of Mathematical Knowledge as an Essential Factor Influencing Teaching and Learning Processes;49
7.3; The Synchronization Between the Dynamics of Knowledge Development and the Processes of Teaching and Learning;51
7.4; Mathematics Education Research and Mathematical Teaching-Learning-Practice as Independent Institutional Systems;56
7.5; Mathematical Knowledge in Teaching: A Case Illustrating the Epistemology-based Interaction View on Teaching Learning Processes;60
7.6;References;67
8;5 Teaching Mathematics as the Contextual Application of Mathematical Modes of Enquiry;70
8.1; One of Bill's Experiences;70
8.2; One of Anne's Experiences;70
8.3; Introduction;71
8.4; The Roles of Mathematical Modes of Enquiry in Teaching;71
8.5; Mathematical Modes of Enquiry;73
8.6; An Artificial Teacher Activity;75
8.7; Stimulus 1: Problems About Inverse Proportion;77
8.8; Stimulus 2: The Day's Newspaper;80
8.9; Discussion;81
8.10; Moving Forward;84
8.11; Conclusion;85
8.12;References;85
8.13; Appendix;87
8.14; Exercise 12;87
9;6 Conceptualising Mathematical Knowledge in Teaching;88
9.1; Subject Knowledge Differentiated;88
9.2; Subject Knowledge Contextualised;91
9.3; Subject Knowledge Interactivated;93
9.4; Subject Knowledge Mathematised;95
9.5; Reconceptualising Subject Knowledge in Teaching;98
9.6;References;100
10;Part II Understanding the Cultural Context of Mathematical Knowledge in Teaching;102
11;7 The Cultural Location of Teachers' Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research?;103
11.1; Introduction;103
11.2; Mathematical Knowledge in Teaching: A Culturally-Located Model;104
11.3; The Project;107
11.4; Pauline;109
11.5; Eva;112
11.6; Discussion;115
11.6.1; Pauline;115
11.6.2; Eva;117
11.7; Conclusion;119
11.8;References;120
12;8 How Educational Systems and Cultures Mediate Teacher Knowledge: `Listening' in English, FrenchINTbreak; and German Classrooms;123
12.1; Introduction;123
12.2; Listening to and 'Hearing' Students;125
12.3; Teacher Knowledge, Pedagogic Practice and Classroom Environments;127
12.4; The Study;128
12.5; Mathematics Classroom Environment;129
12.6; Teacher Knowledge and Listening to Pupils;131
12.6.1; Content Knowledge for Teaching;131
12.6.2; 'Listening Knowledge' in/for Teaching;133
12.7; Discussion and Conclusions;137
12.8;References;138
13;9 Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching;142
13.1; Introduction;142
13.2; Mathematics Teacher Education in Post Apartheid South Africa;143
13.3; Studying Mathematics and Teaching in Mathematics Teacher Education;145
13.3.1; Reading 'What' in the Constitution of Mathematics in and for Teaching;146
13.3.2; Reading 'How' in the Constitution of Mathematics in and for Teaching;152
13.4; Three Cases of Mathematics Teacher Education;152
13.4.1; Case 1: Teaching and Learning Mathematical Reasoning;153
13.4.2; Case 2: Algebra Content and Pedagogy;153
13.4.3; Case 3: Reflecting on Mathematics Teaching;158
13.5; Mathematics for Teaching Across Cases of Mathematics Teacher Education;160
13.6; In Conclusion;161
13.7;References;162
14;10 Audit and Evaluation of Pedagogy: Towards a Cultural-Historical Perspective;164
14.1; Introduction;164
14.2; Accounting for the Dialectic of Audit;165
14.3; What Is the Purpose of Audit and Evaluation of Teachers Knowledge?;170
14.4;What Kinds of Knowledge ‘Should’ (Mathematics) Teachers ‘Have’ for – or ‘Display’ in – Teaching?;171
14.5; How Can We Audit/Assess Teacher Knowledge: What Tools/Technologies Do We Have?;172
14.6; Conclusion;177
14.7; Discussion: Towards a Collective Subject;178
14.8;References;179
15;11 The Cultural Dimension of Teachers' Mathematical Knowledge;182
15.1; A Case for Considering Culture in Research on Teachers' Mathematical Knowledge;182
15.2; The Interplay Between the Cultural Context and Mathematical Knowledge for/in Teaching;185
15.2.1; The Cultural Embedding of Mathematical Knowledge in Teaching in the Context of National Educational Systems;185
15.2.2; The Cultural Embedding of Mathematical Knowledge for Teaching in the Context of Diverse Teacher Education Programmes;187
15.2.3; The Embedding of Mathematical Knowledge for Teaching in a ''Knowledge Economy'' Culture;188
15.3; Implications for Teacher Education;189
15.4;References;192
16;Part III Building Mathematical Knowledge in Teaching by Means of Theorised Tools;195
17;12 The Knowledge Quartet as an Organising Framework for Developing and Deepening Teachers' Mathematics Knowledge;196
17.1; Introduction;196
17.1.1; Rationale;196
17.2; Developing the Knowledge Quartet;197
17.2.1; Context and Purpose of the Research;197
17.2.2; Method;198
17.2.3; Conceptualising the Knowledge Quartet;200
17.2.3.1; Foundation;201
17.2.3.2; Transformation;201
17.2.3.3; Connection;202
17.2.3.4; Contingency;202
17.3; The Knowledge Quartet and Mathematics Teaching Development;203
17.3.1; Development in Conceptions of Mathematics Teaching;204
17.3.2; Development of Content Knowledge;207
17.4; Conclusion;210
17.5;References;212
18;13 Learning to Teach Mathematics Using Lesson Study;214
18.1; Introduction;214
18.2; Enhancement of Teaching Through Lesson Study;214
18.3; Lesson Study Appraised;216
18.4; The Role of Knowledgeable Other(s);217
18.5; The Dublin Study;218
18.6; Overview of the Lesson Study Elective Course;219
18.6.1; Data Analysis;220
18.6.2; 'Doing' Lesson Study;221
18.6.2.1;Preparing the Lessons: Cycle One;221
18.6.2.2; Research Lessons: Cycle Two;222
18.6.2.3; Learning Takes Time;222
18.6.3; 'Doing' Lesson Study: Cycle Three;222
18.6.4; 'Doing' Mathematics;223
18.6.5; 'Being' in the Lesson Study Elective Community of Practice;224
18.7; Discussion;225
18.7.1; Identity in Terms of Learning to Teach Mathematics;225
18.8; The Case of Brd;225
18.8.1;Descriptive Synopsis of Bríd’s Lesson;226
18.8.2; Learning from Teaching;226
18.9; Mathematics Teaching and Matters of Interpretation;228
18.10; Findings;228
18.10.1; Lesson Study as a Tool for Developing Mathematical Knowledge in Teaching;229
18.11;References;230
19;14 Using Theories to Build Kindergarten Teachers' Mathematical Knowledge for Teaching;232
19.1; Introduction;232
19.2; Combining Theories of Teacher Knowledge with Theories of Mathematics Knowledge;233
19.2.1; Dimensions of Knowledge for Teaching;233
19.2.2; Concept Image-Concept Definition (CICD);234
19.2.3; The Combined Framework;236
19.3; Setting;237
19.4; Research Segments;238
19.4.1; Building Kindergarten Teachers' SCK Regarding Concept Images and Concept Definitions of Triangles;238
19.4.2; Differentiating Between SCK and KCT;240
19.4.3; Building Kindergarten Teachers' KCT Regarding Concept Definitions and Concept Images of Triangles;242
19.5; Kindergarten Children's Knowledge of Pentagons;245
19.6; Summing Up and Looking Ahead;247
19.7;References;249
20;15 Teachers' Stories of Mathematical Subject Knowledge: Accounting for the Unexpected;252
20.1; Introduction;252
20.2; Teachers' Mathematical Knowledge;253
20.3; Testing Subject Knowledge;256
20.4; Personalised Diagnostic Maps of Subject Knowledge;258
20.5; Narrative Accounts -- The Impetus of 'Troubles';261
20.6; Lorna;262
20.7; Charlene;265
20.8; Comparison, Contrast and Limitations;268
20.9; Conclusion and Discussion;269
20.10;References;271
21;16 Building Mathematical Knowledge in Teaching by Means of Theorised Tools;273
21.1; Introduction;273
21.2; Theorised Tools from Teachers Knowledge: KQ, SMK & PCK, MKT;274
21.3; The CICD -- A Theorised Tool from Mathematics Knowledge;278
21.4; The Role of the Researcher/Instructor/Teacher Educator in Building Mathematical Knowledge in Teaching;280
21.5; The Role of the Mathsmaps in Building Mathematical Knowledge and PCK;282
21.6; Final Remarks;283
21.7;References;285
22;17 Conclusion;288
23;Author Index;291
24;Subject Index;296