Learning and Teaching Mathematics: An International Perspective

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ISBN: 9780863774553 | 0863774555
Cover: Nonspecific Binding
Copyright: 8/1/1999

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The authors of this volume, which is newly available in paperback, all hold the view that mathematics is a form of intelligent problem solving which plays an important part in children's lives outside the classroom as well as in it.Learning and Teaching Mathematicsprovides an exciting account of recent and radically different research on teaching and learning mathematics which will have a far reaching effect on views about mathematical education.

Contributors

About this book: A brief overview

xiii

T. Nunes

P. Bryant

PART I MATHEMATICS AND INTELLIGENCE

(44)

The nature of mathematical concepts

(24)

Gerard Vergnaud

Introduction

(4)

The theory of conceptual fields

(16)

Elementary algebra and formal calculations

(1)

Tool-concepts and object-concepts

(1)

Conclusion

(2)

Systems of signs and mathematical reasoning

(16)

Terezinha Nunes

Why do we need the idea of mediated action when discussing mathematical knowledge?

(3)

Variations in systems of signs and their impact on children's reasoning

(8)

The connection between systems of signs and different practices in mathematics

(2)

Lessons from the analysis of mediated activity for the mathematics classroom

(3)

PART II THE DEVELOPMENT OF MATHEMATICAL UNDERSTANDINGS

(114)

Mathematical understanding in the nursery school years

(16)

Peter Bryant

Do children have genuine mathematical experiences in the pre-school period?

(1)

Counting

(6)

Sharing and one-to-one correspondence

(3)

Sharing and division

(2)

Adding and subtracting

(2)

Conclusions

(2)

Word problems: A vehicle for promoting authentic mathematical understanding and problem solving in the primary school?

(30)

L. Verschaffel

E. De Corte

Introduction

(1)

Classifications of word problems

(6)

Representing arithmetic word problems

(7)

Selecting and executing the arithmetic actions

(10)

Interpreting and verifying the answer

(1)

Conclusions and future perspectives

(3)

Acknowledgements

(2)

Children's understandings of turn and angle

(16)

Sandra Magina

Celia Hoyles

General framework of the study

(1)

Children's conception of angle

100

(1)

Introduction to the study

101

(2)

Activities with cardboard watches

103

(5)

Results from the prediction activities

108

(3)

Results from the tasks of comparing times

111

(2)

Conclusions

113

(2)

Knowing about proportions in different contexts

115

(18)

Janice A. Singer

Amy S. Kohn

Lauren B. Resnick

Introduction

115

(3)

Protoquantitative reasoning

118

(8)

First steps to quantification: Protoratios

126

(2)

True ratios: Scalar and functional reasoning

128

(2)

Concluding discussion

130

(2)

Acknowledgements

132

(1)

Mathematical concepts at the secondary school level: The learning of algebra and functions

133

(26)

Carolyn Kieran

Distinguishing between algebra and functions

133

(4)

Algebra

137

(13)

Functions

150

(6)

Conclusions

156

(2)

Acknowledgements

158

(1)

PART III SOCIAL AND CULTURAL INFLUENCES ON MATHEMATICS LEARNING

159

(126)

Happy birthday to you: Early mathematical thinking of Asian, South American, and US children

163

(46)

Herbert P. Ginsburg

Y. Elsie Choy

Luz Stella Lopez

Rebecca Netley

Chi Chao-Yuan

Introduction

163

(8)

The present study

171

(1)

Method

171

(5)

Results

176

(20)

Discussion

196

(4)

Conclusions

200

(1)

Acknowledgements

201

(1)

Appendix: Birthday party game

202

(7)

Learning arithmetic with an abacus

209

(24)

Giyoo Hatano

How an abacus is used and learned

210

(4)

Becoming a master in mental abacus operation: A case of routine expertise

214

(10)

The abacus makes a difference in arithmetic

224

(5)

Implications for mathematics instruction

229

(2)

Acknowledgements

231

(2)

What children and teachers count as mathematics

233

(32)

Guida de Abreu

Alan J. Bishop

Geraldo Pompeu Jr.

Introduction

233

(2)

Cognition, beliefs, and attitudes

235

(2)

What children count as mathematics

237

(16)

Educational approaches to cultural conflict

253

(2)

The teachers' perspective

255

(8)

Concluding remarks

263

(1)

Acknowledgements

264

(1)

Social Interactions and Mathematics Learning

265

(20)

M.L Schubauer-Leoni

A.-N. Perret-Clermont

A first study: Piagetian vs. school tasks

265

(5)

The meaning attributed to the object in terms of the questioning context

270

(1)

Moving from a bipolar to a tripolar model of knowledge construction

271

(1)

The emergence of the notion of a ``didactic contract''

272

(1)

The study of the didactic contract via the teacher

273

(2)

The study of the didactic contract via the pupil

275

(1)

The didactic contract and the institutional meta-contract

276

(1)

The organized breaking of the didactic contract

277

(1)

A psychosocial theory of social interactions and a didactic theory of didactic interactions

278

(2)

An example of research into didactic interactions

280

(2)

Epilogue

282

(1)

Acknowledgement

283

(2)

PART IV CONSTRUCTING KNOWLEDGE IN THE CLASSROOM

285

(118)

Meaning mathematically with computers

289

(26)

Richard Noss

Introduction

289

(1)

Mathematical meaning

290

(2)

Formalisation

292

(6)

Generalisation

298

(5)

Abstraction

303

(6)

Towards a theoretical framework

309

(5)

Note

314

(1)

Mediating between concrete and abstract

315

(32)

Koeno Gravemeijer

Introduction

315

(1)

Long division with manipulatives

316

(4)

Realistic mathematics education

320

(8)

Key principles of realistic mathematics education

328

(14)

Discussion

342

(5)

Charming fractions or fractions being charmed?

347

(26)

L. Streefland

Introduction and overview

347

(2)

A bird's-eye view on fractions

349

(2)

Some chocolate bars for some children

351

(1)

Where do we go from here? A dilemma

352

(1)

Table arrangements

353

(5)

Dealing with the course of fair sharing

358

(3)

On the way to formal operations

361

(9)

Discussion

370

(3)

Didactic engineering

373

(30)

Regine Douady

Introduction

373

(27)

Mathematical knowledge in the didactic relation

374

(4)

Examples of didactical engineering

378

(22)

Conclusion

400

(3)

References

403

(30)

Author index

433

(6)

Subject Index

439

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Learning and Teaching Mathematics: An International Perspective

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