Learning and Teaching Mathematics: An International Perspective

Front Cover......Page 1
Title Page......Page 4
Copyright......Page 5
Contents......Page 6
Contributors\0......Page 12
About this book A hrief overview\0......Page 14
PART I MATHEMATICS AND INTELLIGENCE\0......Page 16
Introduction\0......Page 20
The theory of conceptual fields\0......Page 24
Elementary algebra and formal calculations\0......Page 40
Tool-concepts and object-concepts\0......Page 41
Cnnciucion\0......Page 42
Why do we need the idea of mediated action when discussing mathematical knowledge?\0......Page 44
Variations in systems of signs and their impact on children\'s reasoning\0......Page 47
The connection between systems of signs and different practices in mathematics\0......Page 55
Lessons from the analysis of mediated activity for the mathematics classroom\0......Page 57
PART II THE DEVELOPMENT OF MATHEMATICA UNDERSTANDINGS\0......Page 60
Do children have genuine mathematical experiences in the pre-school period?\0......Page 68
Counting\0......Page 69
Sharing and one-to-one correspondence\0......Page 75
Sharing and division\0......Page 78
Adding and subtracting\0......Page 80
Conc icinns\0......Page 82
Introduction\0......Page 84
Classifications of word problems\0......Page 85
Representing arithmetic word problems\0......Page 91
Selecting and executing the arithmetic actions\0......Page 98
Interpreting and verifying the answer\0......Page 108
Conclusions and future perspectives\0......Page 109
Acknowledgements\0......Page 112
General framework of the study\0......Page 114
Children\'s conception of angle\0......Page 115
Introduction to the study\0......Page 116
Activities with cardboard watches\0......Page 118
Results from the prediction activities\0......Page 123
Results f r o m the tasks of comparing times\0......Page 126
Conclusions\0......Page 128
Intmductinn\0......Page 130
Protoguantitative reasoning\0......Page 133
First steps to quantification: Protoratios\0......Page 141
True ratios: Scalar and functional reasoning\0......Page 143
Concluding discussion\0......Page 145
Acknowledgements\0......Page 147
Distinguishing between algebra and functions\0......Page 148
Algebra\0......Page 152
Functions\0......Page 165
Conclusions\0......Page 171
Acknowledgements\0......Page 173
PART III SOCIAL AND CULTURAL INFLUENCES ON MATHEMATICS LEARNING\0......Page 174
Intrnduction\0......Page 178
Method\0......Page 186
Results\0......Page 191
Discussion\0......Page 211
A psychosocial theory of social interactions and a\0......Page 0
Acknowledgements\0......Page 216
Appendix: Birthday party game\0......Page 217
9 Learning arithmetic with an abacus\0......Page 224
How an abacus is used and learned\0......Page 225
Becoming a master in mental abacus operation: A case of routine expertise\0......Page 229
The abacus makes a difference in arithmetic\0......Page 239
Implications for mathematics instruction\0......Page 244
Acknowledgements\0......Page 246
Introduction\0......Page 248
Cognition, beliefs, and attitudes\0......Page 250
What children count as mathematics\0......Page 252
Educational approaches to cultural conflict\0......Page 268
The teachers\' perspective\0......Page 270
Concluding remarks\0......Page 278
Acknowledgements\0......Page 279
A first study: Piagetian vs. school tasks\0......Page 280
The meaning attributed to the object in terms of the questioning context\0......Page 285
Moving from a bipolar to a tripolar model of knowledge construction\0......Page 286
The emergence of the notion of a \"didactic contract\"\0......Page 287
The study of the didactic contract via the teacher\0......Page 288
The study of the didactic contract via the pupil\0......Page 290
The didactic contract and the institutional meta-contract\0......Page 291
The organized breaking of the didactic contract\0......Page 292
didactic theory of didactic interactions\0......Page 293
An example of research into didactic interactions\0......Page 295
Epilogue\0......Page 297
Acknowledgement\0......Page 298
PART IV CONSTRUCTING KNOWLEDGE IN THE CLASSROOM\0......Page 300
12 Meaning mathematically with computers\0......Page 304
Introduction\0......Page 274
Mathematical meaning\0......Page 305
Formalisation\0......Page 307
Generalisation\0......Page 314
Abstraction 3O\0......Page 18
Towards a theoretical framework\0......Page 324
Note\0......Page 329
Introduction\0......Page 330
Long division with manipulatives\0......Page 331
Realistic mathematics education\0......Page 335
Key principles of realistic mathematics education\0......Page 343
Introduction and overview\0......Page 362
A bird\'s-eye view on fractions\0......Page 364
Some chocolate bars for some children\0......Page 366
Where do we go from here? A dilemma\0......Page 367
Table arrangements\0......Page 368
Dealing with the course of fair sharing\0......Page 373
On the way to formal operations\0......Page 376
Discussion\0......Page 385
Introduction\0......Page 388
A. Mathematical knowledge in the didactic relation\0......Page 389
B. Examples of didactical engineering\0......Page 393
Conclusion\0......Page 415
References\0......Page 418
Author index\0......Page 448
Subject index\0......Page 454
Back Cover......Page 459