Learning and teaching mathematics: an international perspective
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hove
Psychology Press
1997
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 443 S. Ill., graph. Darst. |
| ISBN: | 0863774547 0863774555 |
Staff View
MARC
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| 300 | |a XIV, 443 S. |b Ill., graph. Darst. | ||
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Record in the Search Index
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|---|---|
| adam_text | Contents
Contributors xi
About this book: A brief overview
T. Nunes and P. Bryant xiii
PART I MATHEMATICS AND INTELLIGENCE 1
1 The nature of mathematical concepts
Gerard Vergnaud 5
Introduction 5
The theory of conceptual fields 9
Elementary algebra and formal calculations 25
Tool concepts and object concepts 26
Conclusion 27
2 Systems of signs and mathematical reasoning
Terezinha Nunes 29
Why do we need the idea of mediated action when
discussing mathematical knowledge? 29
Variations in systems of signs and their impact on
children s reasoning 32
The connection between systems of signs and
different practices in mathematics 40
Lessons from the analysis of mediated activity
for the mathematics classroom 42
V
Vi CONTRIBUTORS
PART n THE DEVELOPMENT OF MATHEMATICAL
UNDERSTANDINGS 45
3 Mathematical understanding in the nursery
school years
Peter Bryant 53
Do children have genuine mathematical experiences
in the pre school period? 53
Counting 54
Sharing and one to one correspondence 60
Sharing and division 63
Adding and subtracting 65
Conclusions 67
4 Word problems: A vehicle for promoting authentic
mathematical understanding and problem solving
in the primary school?
L Verschaffel and E. De Corte 69
Introduction 69
Classifications of word problems 70
Representing arithmetic word problems 76
Selecting and executing the arithmetic actions 83
Interpreting and verifying the answer 93
Conclusions and future perspectives 94
Acknowledgements 97
5 Children s understandings of turn and angle
Sandra Magina and Celia Hoyles 99
General framework of the study 99
Children s conception of angle 100
Introduction to the study 101
Activities with cardboard watches 103
Results from the prediction activities 108
Results from the tasks of comparing times 111
Conclusions 113
6 Knowing about proportions in different contexts
Janice A. Singer, Amy S. Kohn and Lauren B. Resnick 115
Introduction 115
Protoquantitative reasoning 118
First steps to quantification: Protoratios 126
True ratios: Scalar and functional reasoning 128
Concluding discussion 130
Acknowledgements 132
CONTENTS vii
7 Mathematical concepts at the secondary school level:
The learning of algebra and functions
Carolyn Kieran 133
Distinguishing between algebra and functions 133
Algebra 137
Functions 150
Conclusions 156
Acknowledgements 158
PART m SOCIAL AND CULTURAL INFLUENCES ON
MATHEMATICS LEARNING 159
8 Happy birthday to you: Early mathematical thinking
of Asian, South American, and US children
Herbert P. Ginsburg, Y. Elsie Choy, Luz Stella Lopez,
Rebecca Netley and Chi Chao Yuan 163
Introduction 163
The present study 171
Method 171
Results 176
Discussion 196
Conclusions 200
Acknowledgements 201
Appendix: Birthday party game 202
9 Learning arithmetic with an abacus
Giyoo Hatano 209
How an abacus is used and learned 210
Becoming a master in mental abacus operation: A case of
routine expertise 214
The abacus makes a difference in arithmetic 224
Implications for mathematics instruction 229
Acknowledgements 231
10 What children and teachers count as mathematics
Guida de Abreu, Alan J. Bishop and Geraldo Pompeu Jr. 233
Introduction 233
Cognition, beliefs, and attitudes 235
What children count as mathematics 237
Educational approaches to cultural conflict 253
The teachers perspective 255
Concluding remarks 263
Acknowledgements 264
Vtii CONTRIBUTORS
11 Social Interactions and Mathematics Learning
M.L Schubauer Leoni and A. N. Perret Clermont 265
A first study: Piagetian vs. school tasks 265
The meaning attributed to the object in terms of the
questioning context 270
Moving from a bipolar to a bipolar model of knowledge
construction 271
The emergence of the notion of a didactic contract 272
The study of the didactic contract via the teacher 273
The study of the didactic contract via the pupil 275
The didactic contract and the institutional meta contract 276
The organized breaking of the didactic contract 277
A psychosocial theory of social interactions and a
didactic theory of didactic interactions 278
An example of research into didactic interactions 280
Epilogue 282
Acknowledgement 283
PART IV CONSTRUCTING KNOWLEDGE IN THE CLASSROOM 285
12 Meaning mathematically with computers
Richard Noss 289
Introduction 289
Mathematical meaning 290
Formalisation 292
Generalisation 298
Abstraction 303
Towards a theoretical framework 309
Note 314
13 Mediating between concrete and abstract
Koeno Gravemeijer 315
Introduction 315
Long division with manipulatives 316
Realistic mathematics education 320
Key principles of realistic mathematics education 328
Discussion 342
14 Charming fractions or fractions being charmed?
L Streefland 347
Introduction and overview 347
A bird s eye view on fractions 349
Some chocolate bars for some children 351
Where do we go from here? A dilemma 352
Table arrangements 353
Dealing with the course of fair sharing 358
On the way to formal operations 361
Discussion 370
CONTENTS iX
15 Didactic engineering
Regine Douady 373
Introduction 373
A. Mathematical knowledge in the didactic relation 374
B. Examples of didactical engineering 378
Conclusion 400
References 403
Author index 433
Subject index 439
|
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:46:18Z |
| institution | BVB |
| isbn | 0863774547 0863774555 |
| language | English |
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| physical | XIV, 443 S. Ill., graph. Darst. |
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| publisher | Psychology Press |
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| spelling | Learning and teaching mathematics an international perspective ed. by T. Nunes ... Hove Psychology Press 1997 XIV, 443 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Didactiek gtt Leren gtt Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematik (DE-588)4037944-9 gnd rswk-swf Lernen (DE-588)4035408-8 gnd rswk-swf Mathematik (DE-588)4037944-9 s Lernen (DE-588)4035408-8 s DE-604 Nunes, Terezinha edt Bryant, Peter 1937- (DE-588)173325386 edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009188475&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Learning and teaching mathematics an international perspective Didactiek gtt Leren gtt Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematik (DE-588)4037944-9 gnd Lernen (DE-588)4035408-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4035408-8 |
| title | Learning and teaching mathematics an international perspective |
| title_auth | Learning and teaching mathematics an international perspective |
| title_exact_search | Learning and teaching mathematics an international perspective |
| title_full | Learning and teaching mathematics an international perspective ed. by T. Nunes ... |
| title_fullStr | Learning and teaching mathematics an international perspective ed. by T. Nunes ... |
| title_full_unstemmed | Learning and teaching mathematics an international perspective ed. by T. Nunes ... |
| title_short | Learning and teaching mathematics |
| title_sort | learning and teaching mathematics an international perspective |
| title_sub | an international perspective |
| topic | Didactiek gtt Leren gtt Mathématiques - Étude et enseignement Wiskunde gtt Mathematik Mathematics Study and teaching Mathematik (DE-588)4037944-9 gnd Lernen (DE-588)4035408-8 gnd |
| topic_facet | Didactiek Leren Mathématiques - Étude et enseignement Wiskunde Mathematik Mathematics Study and teaching Lernen |
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