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Mathematical Knowledge in Teaching.

By: Contributor(s): Material type: TextSeries: Publisher: Dordrecht : Springer Netherlands, 2010Copyright date: ©2011Edition: 1st edDescription: 1 online resource (299 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9789048197668
Subject(s): Genre/Form: DDC classification:
  • 510.71
Online resources:
Contents:
Intro -- Contents -- Contributors -- 1 Introduction: Mathematical Knowledge in Teaching -- Background: The Topic and the Book -- Introduction to Section 1 -- Introduction to Section 2 -- Introduction to Section 3 -- Critical Discussion and Synthesis -- References -- Part I Conceptualising Mathematical Knowledge in Teaching -- 2 Conceptualising Teachers' Mathematical Knowledge in Teaching -- Introduction -- Shulman's Conceptualisation -- Fennema and Franke's Conceptualisation -- 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 -- The Knowledge Quartet -- Synthesis -- Implications and Limitations -- References -- 3 Knowing and Identity: A Situated Theory of Mathematics Knowledge in Teaching -- The Problem of Mathematics Teacher Knowledge -- A Case Study from Primary Mathematics: Alexandra's Knowledge of the Multiplication and Division of Fractions -- Is this just an Issue for Primary Teaching? -- The Contribution of Situated Theories: What Does This Mean for Teacher Knowledge? -- Implications for the Practices of Teaching, Teacher Education and Development -- References -- 4 Changed Views on Mathematical Knowledge in the Course of Didactical Theory Development: Independent Corpus of Scientific Knowledge or Result of Social Constructions? -- Introduction -- The 'Stoffdidaktik' Elaboration of Mathematical Knowledge as an Essential Factor Influencing Teaching and Learning Processes -- The Synchronization Between the Dynamics of Knowledge Development and the Processes of Teaching and Learning -- Mathematics Education Research and Mathematical Teaching-Learning-Practice as Independent Institutional Systems.
Mathematical Knowledge in Teaching: A Case Illustrating the Epistemology-based Interaction View on Teaching Learning Processes -- References -- 5 Teaching Mathematics as the Contextual Application of Mathematical Modes of Enquiry -- One of Bill's Experiences -- One of Anne's Experiences -- Introduction -- The Roles of Mathematical Modes of Enquiry in Teaching -- Mathematical Modes of Enquiry -- An Artificial Teacher Activity -- Stimulus 1: Problems About Inverse Proportion -- Stimulus 2: The Day's Newspaper -- Discussion -- Moving Forward -- Conclusion -- References -- Appendix -- Exercise 12 -- 6 Conceptualising Mathematical Knowledge in Teaching -- Subject Knowledge Differentiated -- Subject Knowledge Contextualised -- Subject Knowledge Interactivated -- Subject Knowledge Mathematised -- Reconceptualising Subject Knowledge in Teaching -- References -- Part II Understanding the Cultural Context of Mathematical Knowledge in Teaching -- 7 The Cultural Location of Teachers' Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research? -- Introduction -- Mathematical Knowledge in Teaching: A Culturally-Located Model -- The Project -- Pauline -- Eva -- Discussion -- Pauline -- Eva -- Conclusion -- References -- 8 How Educational Systems and Cultures Mediate Teacher Knowledge: L̀istening' in English, FrenchINTbreak -- and German Classrooms -- Introduction -- Listening to and 'Hearing' Students -- Teacher Knowledge, Pedagogic Practice and Classroom Environments -- The Study -- Mathematics Classroom Environment -- Teacher Knowledge and Listening to Pupils -- Content Knowledge for Teaching -- 'Listening Knowledge' in/for Teaching -- Discussion and Conclusions -- References -- 9 Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching -- Introduction.
Mathematics Teacher Education in Post Apartheid South Africa -- Studying Mathematics and Teaching in Mathematics Teacher Education -- Reading 'What' in the Constitution of Mathematics in and for Teaching -- Reading 'How' in the Constitution of Mathematics in and for Teaching -- Three Cases of Mathematics Teacher Education -- Case 1: Teaching and Learning Mathematical Reasoning -- Case 2: Algebra Content and Pedagogy -- Case 3: Reflecting on Mathematics Teaching -- Mathematics for Teaching Across Cases of Mathematics Teacher Education -- In Conclusion -- References -- 10 Audit and Evaluation of Pedagogy: Towards a Cultural-Historical Perspective -- Introduction -- Accounting for the Dialectic of Audit -- What Is the Purpose of Audit and Evaluation of Teachers Knowledge? -- What Kinds of Knowledge 'Should' (Mathematics) Teachers 'Have' for - or 'Display' in - Teaching? -- How Can We Audit/Assess Teacher Knowledge: What Tools/Technologies Do We Have? -- Conclusion -- Discussion: Towards a Collective Subject -- References -- 11 The Cultural Dimension of Teachers' Mathematical Knowledge -- A Case for Considering Culture in Research on Teachers' Mathematical Knowledge -- The Interplay Between the Cultural Context and Mathematical Knowledge for/in Teaching -- The Cultural Embedding of Mathematical Knowledge in Teaching in the Context of National Educational Systems -- The Cultural Embedding of Mathematical Knowledge for Teaching in the Context of Diverse Teacher Education Programmes -- The Embedding of Mathematical Knowledge for Teaching in a ''Knowledge Economy'' Culture -- Implications for Teacher Education -- References -- Part III Building Mathematical Knowledge in Teaching by Means of Theorised Tools -- 12 The Knowledge Quartet as an Organising Framework for Developing and Deepening Teachers' Mathematics Knowledge -- Introduction -- Rationale.
Developing the Knowledge Quartet -- Context and Purpose of the Research -- Method -- Conceptualising the Knowledge Quartet -- Foundation -- Transformation -- Connection -- Contingency -- The Knowledge Quartet and Mathematics Teaching Development -- Development in Conceptions of Mathematics Teaching -- Development of Content Knowledge -- Conclusion -- References -- 13 Learning to Teach Mathematics Using Lesson Study -- Introduction -- Enhancement of Teaching Through Lesson Study -- Lesson Study Appraised -- The Role of Knowledgeable Other(s) -- The Dublin Study -- Overview of the Lesson Study Elective Course -- Data Analysis -- 'Doing' Lesson Study -- Preparing the Lessons: Cycle One -- Research Lessons: Cycle Two -- Learning Takes Time -- 'Doing' Lesson Study: Cycle Three -- 'Doing' Mathematics -- 'Being' in the Lesson Study Elective Community of Practice -- Discussion -- Identity in Terms of Learning to Teach Mathematics -- The Case of Brd -- Descriptive Synopsis of Bríd's Lesson -- Learning from Teaching -- Mathematics Teaching and Matters of Interpretation -- Findings -- Lesson Study as a Tool for Developing Mathematical Knowledge in Teaching -- References -- 14 Using Theories to Build Kindergarten Teachers' Mathematical Knowledge for Teaching -- Introduction -- Combining Theories of Teacher Knowledge with Theories of Mathematics Knowledge -- Dimensions of Knowledge for Teaching -- Concept Image-Concept Definition (CICD) -- The Combined Framework -- Setting -- Research Segments -- Building Kindergarten Teachers' SCK Regarding Concept Images and Concept Definitions of Triangles -- Differentiating Between SCK and KCT -- Building Kindergarten Teachers' KCT Regarding Concept Definitions and Concept Images of Triangles -- Kindergarten Children's Knowledge of Pentagons -- Summing Up and Looking Ahead -- References.
15 Teachers' Stories of Mathematical Subject Knowledge: Accounting for the Unexpected -- Introduction -- Teachers' Mathematical Knowledge -- Testing Subject Knowledge -- Personalised Diagnostic Maps of Subject Knowledge -- Narrative Accounts -- The Impetus of 'Troubles' -- Lorna -- Charlene -- Comparison, Contrast and Limitations -- Conclusion and Discussion -- References -- 16 Building Mathematical Knowledge in Teaching by Means of Theorised Tools -- Introduction -- Theorised Tools from Teachers Knowledge: KQ, SMK &amp -- PCK, MKT -- The CICD -- A Theorised Tool from Mathematics Knowledge -- The Role of the Researcher/Instructor/Teacher Educator in Building Mathematical Knowledge in Teaching -- The Role of the Mathsmaps in Building Mathematical Knowledge and PCK -- Final Remarks -- References -- 17 Conclusion -- Author Index -- Subject Index.
Summary: This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.
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Intro -- Contents -- Contributors -- 1 Introduction: Mathematical Knowledge in Teaching -- Background: The Topic and the Book -- Introduction to Section 1 -- Introduction to Section 2 -- Introduction to Section 3 -- Critical Discussion and Synthesis -- References -- Part I Conceptualising Mathematical Knowledge in Teaching -- 2 Conceptualising Teachers' Mathematical Knowledge in Teaching -- Introduction -- Shulman's Conceptualisation -- Fennema and Franke's Conceptualisation -- 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 -- The Knowledge Quartet -- Synthesis -- Implications and Limitations -- References -- 3 Knowing and Identity: A Situated Theory of Mathematics Knowledge in Teaching -- The Problem of Mathematics Teacher Knowledge -- A Case Study from Primary Mathematics: Alexandra's Knowledge of the Multiplication and Division of Fractions -- Is this just an Issue for Primary Teaching? -- The Contribution of Situated Theories: What Does This Mean for Teacher Knowledge? -- Implications for the Practices of Teaching, Teacher Education and Development -- References -- 4 Changed Views on Mathematical Knowledge in the Course of Didactical Theory Development: Independent Corpus of Scientific Knowledge or Result of Social Constructions? -- Introduction -- The 'Stoffdidaktik' Elaboration of Mathematical Knowledge as an Essential Factor Influencing Teaching and Learning Processes -- The Synchronization Between the Dynamics of Knowledge Development and the Processes of Teaching and Learning -- Mathematics Education Research and Mathematical Teaching-Learning-Practice as Independent Institutional Systems.

Mathematical Knowledge in Teaching: A Case Illustrating the Epistemology-based Interaction View on Teaching Learning Processes -- References -- 5 Teaching Mathematics as the Contextual Application of Mathematical Modes of Enquiry -- One of Bill's Experiences -- One of Anne's Experiences -- Introduction -- The Roles of Mathematical Modes of Enquiry in Teaching -- Mathematical Modes of Enquiry -- An Artificial Teacher Activity -- Stimulus 1: Problems About Inverse Proportion -- Stimulus 2: The Day's Newspaper -- Discussion -- Moving Forward -- Conclusion -- References -- Appendix -- Exercise 12 -- 6 Conceptualising Mathematical Knowledge in Teaching -- Subject Knowledge Differentiated -- Subject Knowledge Contextualised -- Subject Knowledge Interactivated -- Subject Knowledge Mathematised -- Reconceptualising Subject Knowledge in Teaching -- References -- Part II Understanding the Cultural Context of Mathematical Knowledge in Teaching -- 7 The Cultural Location of Teachers' Mathematical Knowledge: Another Hidden Variable in Mathematics Education Research? -- Introduction -- Mathematical Knowledge in Teaching: A Culturally-Located Model -- The Project -- Pauline -- Eva -- Discussion -- Pauline -- Eva -- Conclusion -- References -- 8 How Educational Systems and Cultures Mediate Teacher Knowledge: L̀istening' in English, FrenchINTbreak -- and German Classrooms -- Introduction -- Listening to and 'Hearing' Students -- Teacher Knowledge, Pedagogic Practice and Classroom Environments -- The Study -- Mathematics Classroom Environment -- Teacher Knowledge and Listening to Pupils -- Content Knowledge for Teaching -- 'Listening Knowledge' in/for Teaching -- Discussion and Conclusions -- References -- 9 Modelling Teaching in Mathematics Teacher Education and the Constitution of Mathematics for Teaching -- Introduction.

Mathematics Teacher Education in Post Apartheid South Africa -- Studying Mathematics and Teaching in Mathematics Teacher Education -- Reading 'What' in the Constitution of Mathematics in and for Teaching -- Reading 'How' in the Constitution of Mathematics in and for Teaching -- Three Cases of Mathematics Teacher Education -- Case 1: Teaching and Learning Mathematical Reasoning -- Case 2: Algebra Content and Pedagogy -- Case 3: Reflecting on Mathematics Teaching -- Mathematics for Teaching Across Cases of Mathematics Teacher Education -- In Conclusion -- References -- 10 Audit and Evaluation of Pedagogy: Towards a Cultural-Historical Perspective -- Introduction -- Accounting for the Dialectic of Audit -- What Is the Purpose of Audit and Evaluation of Teachers Knowledge? -- What Kinds of Knowledge 'Should' (Mathematics) Teachers 'Have' for - or 'Display' in - Teaching? -- How Can We Audit/Assess Teacher Knowledge: What Tools/Technologies Do We Have? -- Conclusion -- Discussion: Towards a Collective Subject -- References -- 11 The Cultural Dimension of Teachers' Mathematical Knowledge -- A Case for Considering Culture in Research on Teachers' Mathematical Knowledge -- The Interplay Between the Cultural Context and Mathematical Knowledge for/in Teaching -- The Cultural Embedding of Mathematical Knowledge in Teaching in the Context of National Educational Systems -- The Cultural Embedding of Mathematical Knowledge for Teaching in the Context of Diverse Teacher Education Programmes -- The Embedding of Mathematical Knowledge for Teaching in a ''Knowledge Economy'' Culture -- Implications for Teacher Education -- References -- Part III Building Mathematical Knowledge in Teaching by Means of Theorised Tools -- 12 The Knowledge Quartet as an Organising Framework for Developing and Deepening Teachers' Mathematics Knowledge -- Introduction -- Rationale.

Developing the Knowledge Quartet -- Context and Purpose of the Research -- Method -- Conceptualising the Knowledge Quartet -- Foundation -- Transformation -- Connection -- Contingency -- The Knowledge Quartet and Mathematics Teaching Development -- Development in Conceptions of Mathematics Teaching -- Development of Content Knowledge -- Conclusion -- References -- 13 Learning to Teach Mathematics Using Lesson Study -- Introduction -- Enhancement of Teaching Through Lesson Study -- Lesson Study Appraised -- The Role of Knowledgeable Other(s) -- The Dublin Study -- Overview of the Lesson Study Elective Course -- Data Analysis -- 'Doing' Lesson Study -- Preparing the Lessons: Cycle One -- Research Lessons: Cycle Two -- Learning Takes Time -- 'Doing' Lesson Study: Cycle Three -- 'Doing' Mathematics -- 'Being' in the Lesson Study Elective Community of Practice -- Discussion -- Identity in Terms of Learning to Teach Mathematics -- The Case of Brd -- Descriptive Synopsis of Bríd's Lesson -- Learning from Teaching -- Mathematics Teaching and Matters of Interpretation -- Findings -- Lesson Study as a Tool for Developing Mathematical Knowledge in Teaching -- References -- 14 Using Theories to Build Kindergarten Teachers' Mathematical Knowledge for Teaching -- Introduction -- Combining Theories of Teacher Knowledge with Theories of Mathematics Knowledge -- Dimensions of Knowledge for Teaching -- Concept Image-Concept Definition (CICD) -- The Combined Framework -- Setting -- Research Segments -- Building Kindergarten Teachers' SCK Regarding Concept Images and Concept Definitions of Triangles -- Differentiating Between SCK and KCT -- Building Kindergarten Teachers' KCT Regarding Concept Definitions and Concept Images of Triangles -- Kindergarten Children's Knowledge of Pentagons -- Summing Up and Looking Ahead -- References.

15 Teachers' Stories of Mathematical Subject Knowledge: Accounting for the Unexpected -- Introduction -- Teachers' Mathematical Knowledge -- Testing Subject Knowledge -- Personalised Diagnostic Maps of Subject Knowledge -- Narrative Accounts -- The Impetus of 'Troubles' -- Lorna -- Charlene -- Comparison, Contrast and Limitations -- Conclusion and Discussion -- References -- 16 Building Mathematical Knowledge in Teaching by Means of Theorised Tools -- Introduction -- Theorised Tools from Teachers Knowledge: KQ, SMK &amp -- PCK, MKT -- The CICD -- A Theorised Tool from Mathematics Knowledge -- The Role of the Researcher/Instructor/Teacher Educator in Building Mathematical Knowledge in Teaching -- The Role of the Mathsmaps in Building Mathematical Knowledge and PCK -- Final Remarks -- References -- 17 Conclusion -- Author Index -- Subject Index.

This book examines issues of considerable significance in addressing global aspirations to raise standards of teaching and learning in mathematics by developing approaches to characterizing, assessing and developing mathematical knowledge for teaching.

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