Thinking as Communicating: Human Development, the Growth of Discourses, and Mathematizing

by Anna Sfard

• ISBN13: 9780521161541
• ISBN10: 0521161541
• Edition: 1st
• Format: Paperback
• Copyright: 2010-02-22
• Publisher: Cambridge University Press

Summary

This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.

Author Biography

Anna Sfard's research focuses on the development of mathematical discourses in individual lives and in the course of history. In a series of studies in Israel, Canada, and the United States, she has been investigating the development of mathematical thinking in both history and individual learning. Results of these studies, both theoretical and empirical, have been published in more than 100 articles and edited volumes, many of which have been widely cited. The recipient of the 2007 Freudhental Medal for research in mathematics education, she is a Professor of Mathematics Education at the University of Haifa, the first holder of the Lappan-Phillips-Fitzgerald endowed chair at Michigan State University, and a Visiting Professor at the Institute of Education in London.

Table of Contents

Series Foreword	p. xi
Introduction	p. xiii
Acknowledgments	p. xxi
Discourse on Thinking
Puzzling about (Mathematical) Thinking	p. 3
The Quandary of Number	p. 4
The Quandary of Abstraction (and Transfer)	p. 9
The Quandary of Misconceptions	p. 16
The Quandary of Learning Disability	p. 22
The Quandary of Understanding	p. 27
Puzzling about Thinking - in a Nutshell	p. 32
Objectification	p. 34
What Is Research and What Makes It Ineffective?	p. 35
Metaphors as Generators of New Discourses	p. 39
The Metaphor of Object	p. 42
The Gains of Objectification	p. 51
The Traps of Objectification - the Case of the Discourse on Thinking	p. 56
Objectification - in a Nutshell	p. 63
Commognition: Thinking as Communicating	p. 65
Monological and Dialogical Discourses on Thinking	p. 65
Disobjectification of Discourses on Thinking - Brief History	p. 68
We Are Almost There: Participationism	p. 76
Finally: Thinking as Communicating	p. 80
Thinking as Communicating - in a Nutshell	p. 91
Thinking in Language	p. 94
The Dilemma of Relation between Thinking and Speaking	p. 95
Commognizing in Language	p. 101
What Are the Properties of Commognition That Recursivity Makes Possible?	p. 109
Human Development as the Development of Discourses	p. 115
Thinking in Language - in a Nutshell	p. 123
Mathematics as Discourse
Mathematics as a Form of Communication	p. 127
What Makes Mathematical Discourse Distinct	p. 129
Challenges to Mathematical Communication	p. 135
Visual Mediation in Mathematical Communication	p. 146
Visual Realizations of Mathematical Signifiers	p. 154
Mathematics as a Form of Communication - in a Nutshell	p. 160
Objects of Mathematical Discourse: What Mathematizing Is All About	p. 163
Mathematical Objects	p. 164
Historical Development of Mathematical Objects	p. 174
Individualization of Mathematical Objects	p. 177
Challenges of Object Construction	p. 182
Objects of Mathematical Discourse - in a Nutshell	p. 192
Routines: How We Mathematize	p. 195
Meaningfulness from Repetition	p. 195
Rules of Discourse	p. 200
Routines	p. 208
Routines and Creativity	p. 216
Routines - in a Nutshell	p. 220
Explorations, Deeds, and Rituals: What We Mathematize For	p. 222
Explorations	p. 223
Deeds	p. 236
Rituals	p. 241
Development of Routines	p. 245
Explorations, Deeds, and Rituals: What We Mathematize For - in a Nutshell	p. 259
Looking Back and Ahead: Solving Old Quandaries and Facing New Ones	p. 261
Looking Back: What Has Been Done	p. 262
What Happened to the Old Quandaries	p. 263
What Happened to Research on Thinking and Human Development	p. 275
Some Implications for the Practice of Teaching and Learning	p. 280
Looking Ahead: Facing New Question (and New Quandaries?)	p. 289
Looking Back and Ahead - in a Nutshell	p. 292
Glossary of Commognition	p. 295
References	p. 303
Name Index	p. 319
Subject Index	p. 322
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