Fundamental Constructs in Mathematics

Fundamental Constructs in Mathematics Educationis a unique sourcebook that has been crafted from a collection of classic tasks, extracts, and texts that have been quoted repeatedly in mathematics education literature. Linked together by the editors' narrative, the book provides a fascinating examination of key constructs in mathematics education. Bringing together writing from Balacheff, Brousseau, Bruner, Cobb, Comfrey, Freudenthal, Greeno, Marton, Piaget, Schon, Vygotsky, and many others, this unique examination of constructs in mathematics education will be a valuable resource for anyone reading literature related to learning mathematics be they a teacher, adviser, or a student on a masters or PhD course.

Sources

ix

Introduction

1

(4)

Structure of the book

1

(1)

What is a construct?

2

(3)

SECTION 1 Activating and analysing learning

5

(210)

1 Probing thinking

7

(23)

Introduction

7

(1)

Early years

7

(9)

Middle years

16

(9)

Later years

25

(5)

2 Conditions for learning

30

(49)

Introduction

30

(1)

Assumptions and theories

30

(22)

What is learning?

52

(27)

3 Analysis of learning for informing teaching

79

(20)

Introduction

79

(1)

Theory of didactic situations

79

(5)

Activity theory

84

(8)

Constructivisms

92

(7)

4 Affect in learning mathematics

99

(16)

Introduction

99

(1)

Motivation, intention and desire

99

(16)

5 Learners' powers

115

(28)

Introduction

115

(1)

Natural powers

115

(10)

Discerning similarities and differences

125

(4)

Mental imagery and imagination

129

(3)

Generalising and abstracting

132

(5)

Generalising and specialising

137

(2)

Conjecturing and convincing

139

(4)

6 Learning as action

143

(38)

Introduction

143

(2)

Learner action

145

(16)

Learning phases

161

(4)

Turning actions into objects

165

(8)

Learning from examples

173

(1)

Practice and skills

174

(7)

7 Learning what?

181

(36)

Introduction

181

(1)

Using powers

181

(3)

Mathematical thinking

184

(9)

Mathematical themes

193

(3)

Mathematical techniques and procedures

196

(2)

Mathematical topics

198

(8)

What learners learn

206

(9)

SECTION 2 Guiding and directing learning

215

(96)

8 Teachers' roles

217

(11)

Introduction

217

(1)

Positioning

217

(3)

Teachers, learners and mathematics

220

(3)

Teaching as...

223

(5)

9 Initiating mathematical activity

228

(32)

Introduction

228

(1)

Principles

228

(10)

Tasks

238

(7)

Situations and apparatus

245

(15)

10 Sustaining mathematical activity

260

(20)

Introduction

260

(1)

Integrating frameworks

260

(6)

Teacher intervention

266

(11)

Mathematical discussion

277

(3)

11 Concluding mathematical activity

280

(8)

Introduction

280

(1)

Reflection

280

(8)

12 Having learned... ?

288

(23)

Introduction

288

(1)

Knowing

288

(5)

Understanding

293

(18)

Epilogue

311

(2)

Bibliography

313

(18)

Index

331

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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Fundamental Constructs in Mathematics Education

Summary

Table of Contents

Supplemental Materials