This book contributes to the current debate about how to think and talk about human thinking so as to resolve or bypass such time-honored quandaries as the controversy of nature vs. nurture, the body and mind problem, the question of learning transfer, and the conundrum of human consciousness. The author responds to the challenge by introducing her own "commognitive" conceptualization of human thinking. She argues for this special approach with the help of examples of mathematical thinking. Except for its contribution to theorizing on human development, the book is relevant to researchers looking for methodological innovations, and to mathematics educators seeking pedagogical insights and improvements.
Author(s): Anna Sfard
Edition: 1
Year: 2008
Language: English
Pages: 352
Cover......Page 1
Half-title......Page 3
Series-title......Page 5
Dedication......Page 6
Title......Page 7
Copyright......Page 8
Contents......Page 9
Series Foreword......Page 13
Introduction......Page 15
Acknowledgments......Page 23
Part I: Discourse on Thinking......Page 27
1 Puzzling about (Mathematical) Thinking......Page 29
1 The Quandary of Number......Page 30
2. The Quandary of Abstraction (and Transfer)......Page 35
3. The Quandary of Misconceptions......Page 42
4. The Quandary of Learning Disability......Page 48
5. The Quandary of Understanding......Page 53
6. Puzzling about Thinking – in a Nutshell......Page 58
2 Objectification......Page 60
1 What Is Research and What Makes It Ineffective?......Page 61
2 Metaphors as Generators of New Discourses......Page 65
3 The Metaphor of Object......Page 68
3.1 Reification......Page 70
3.2 Alienation......Page 76
4 The Gains of Objectification......Page 77
5 The Traps of Objectification – the Case of the Discourse on Thinking......Page 82
6 Objectification – in a Nutshell......Page 89
1. Monological and Dialogical Discourse as on Thinking......Page 91
2.1 Objectification in Monological Discourse on Thinking......Page 94
2.2 Dialogical Attempts at Disobjectification......Page 97
3. We Are Almost There: Participationism......Page 102
4.1 Defining Thinking......Page 106
4.2 Defining Communication......Page 110
5. Thinking as Communicating – in a Nutshell......Page 117
4 Thinking in Language......Page 120
1 The Dilemma of Relation between Thinking and Speaking......Page 121
2 Commognizing in Language......Page 127
3 What Are the Properties of Commognition That Recursivity Makes Possible?......Page 135
3.1 Reasoning......Page 136
3.2 Abstracting......Page 137
3.3 Objectifiying......Page 138
3.4 Subjectifying......Page 139
3.5 Consciousness......Page 140
4 Human Development as the Development of Discourses......Page 141
4.1 Why Do Discourses Change?......Page 142
4.2 How Do Discourses Change?......Page 144
5 Thinking in Language – in a Nutshell......Page 149
Part II: Mathematics as Discourse......Page 151
5 Mathematics as a Form of Communication......Page 153
1 What Makes Mathematical Discourse Distinct......Page 155
2 Challenges to Mathematical Communication......Page 161
3 Which is more?......Page 163
4 The same......Page 164
6 Objects of Mathematical Discourse......Page 189
1.1 Discursive Objects......Page 190
1.2 How Discursive Objects Come into Being......Page 193
1.3 Mathematical Objects as Abstract d-Objects......Page 198
2 Historical Development of Mathematical Objects......Page 200
3 Individualization of Mathematical Objects......Page 203
4.1 The Challenge of Reification and the Anxiety of Unrealized Signifiers......Page 208
4.2 Challenges of Saming......Page 211
4.3 Challenges of Encapsulation......Page 215
4.4 Pedagogical Remark......Page 217
5. Objects of Mathematical Discourse – in a Nutshell......Page 218
1. Meaningfulness from Repetition......Page 221
2. Rules of Discourse......Page 226
Variability......Page 228
Tacitness (Interpretive Nature)......Page 229
Value-Ladedness (Normativeness)......Page 230
Flexibility......Page 231
Contingency......Page 232
3. Routines......Page 234
4. Routines and Creativity......Page 242
Example 1: Add One Out......Page 243
Example 2: Measuring Height with a Barometer......Page 244
5. Routines – in a Nutshell......Page 246
8 Explorations, Deeds, and Rituals: What We Mathematize For......Page 248
1. Explorations......Page 249
1.1 More about Endorsed Narratives......Page 250
1.2 Construction of Narratives......Page 251
1.3 Substantiation of Narratives......Page 257
1.4 Recalling......Page 260
2. Deeds......Page 262
3. Rituals......Page 267
4.1 The Road to Exploration Must Sometimes Lead through Ritual......Page 271
4.2 Thoughtful Imitation and the Ritualized Beginnings......Page 275
4.3 Transforming Ritual into Exploration......Page 277
4.4 Spurring and Cultivating Learning: The Principles of the Continuity of Discourse and of the Commognitive Conflict......Page 280
5. Explorations, Deeds, and Rituals: What We Mathematize For – in a Nutshell......Page 285
9 Looking Back and Ahead: Solving Old Quandaries and Facing New Ones......Page 287
1. Looking Back: What Has Been Done......Page 288
2.1 The Quandary of Number......Page 289
2.2 The Quandary of Abstraction (Situatedness)......Page 291
2.3 The Quandary of Misconceptions......Page 293
2.4 The Quandary of Learning (Dis)abilities......Page 295
2.5 The Quandary of Understanding......Page 297
3. What Happened to Research on Thinking and Human Development......Page 301
4. Some Implications for the Practice of Teaching and Learning......Page 306
4.1 Learning-Teaching Agreement as a Condition for Learning......Page 308
4.2 Factors That Shape Learning......Page 313
5. Looking Ahead: Facing New Questions (and New Quandaries?)......Page 315
6. Looking Back and Ahead – in a Nutshell......Page 318
Glossary of Commognition......Page 321
References......Page 329
Name Index......Page 345
Subject Index......Page 348
