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

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Cambridge University Press, Jan 21, 2008 - Psychology
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.
 

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Contents

1 Puzzling about Mathematical Thinking
3
2 Objectification
34
3 Commognition
65
4 Thinking in Language
94
5 Mathematics as a Form of Communication
127
6
163
5x + 8 7x + 4 x
165
Endorsed narratives on
175
Figure 66 Fourstage model of the development of word use
182
7 Routines
195
8 Explorations Deeds and Rituals
222
9 Looking Back and Ahead
261

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About the author (2008)

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 in Michigan State University, and a Visiting Professor at the Institute of Education in London.

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