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

$124.99

Part of Learning in Doing: Social, Cognitive and Computational Perspectives

  • Date Published: January 2008
  • availability: Available
  • format: Hardback
  • isbn: 9780521867375

$124.99
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About the Authors
  • 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.

    • Divided into two independent parts: those interested mainly in theorising about human thinking may satisfy themselves with Part I, where references to mathematics are scarce; those who reach for this book because of their interest in mathematical thinking can head directly toward Part II
    • The glossary of the basic commognitive terms appended at the end of the book, and the summarising ('nutshell') section at the end of every chapter support various, non-linear ('random access') forms of reading
    • A combination of theoretical analyses and empirical studies; the reader is provided with the opportunity to learn and practise the distinctive commognitive methods of discourse analysis using many data samples
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    Reviews & endorsements

    "[...] In her new book, Sfard describes, in detail, her views on thinking and learning. [...] The book also includes a glossary. Because some of the terms have been coined by the author, the glossary is, indeed, helpful. Overall, the book will likely please those already familiar with Sfard's views on learning. The book will be a must-have for those who are already convinced that her unique characterization of thinking is on the right track in helping to explain why students have difficulty learning mathematics. [...] Sfard's discussion of mathematical objects and routines is compelling and may be informative to others attempting to conduct research on how we carry out mathematical processing."
    --Shelia M. Kennison, PsycCRITIQUES, Volume 53, Issue 45

    "...a truly impressive accomplishment,...more surprising in its systematic unity and comprehensive claims....A centerpiece of Sfard’s theory is the definition of a math object as the recursive tree of its manifold visual realizations....presented with all the grace, simplicity, insight and rigor of an elegant mathematical proof....built up from quasi-axiomatic principles, through intermediate theorems, illustrated with persuasive minimalist examples....Sfard’s analysis helps us see the various emergent roles the students’ participations play in their discourse—without requiring us to reduce the complexity of the social and semantic interrelationships....Sfard’s theory resolves many quandaries that have bothered people about participationist and group cognitive theories....Sfard has done us the great service of bringing the “linguistic turn” of twentieth century philosophy (notably Wittgenstein) into 21st C. learning science, elaborating its perspective on the challenging example of math ed. She shows how to see math concepts and student learning as discourse phenomena rather than mental objects....Sfard has provided us with one of the most impressive unified, homogenous theories of learning...."
    --Gerry Stahl, International Journal of Computer-Supported Collaborative Learning (2008)

    "Why should readers of JCEP be interested in Anna Sfard’s book? The main reason is that Sfard poses the same fundamental questions about thinking, talking, learning, and teaching that each one of us has certainly asked him or herself but rarely had the time and tenacity to explore systematically....this is fascinating reading because you not only follow the logic of the material, but simultaneously peek into the mental laboratory of the author..."
    --Alex Kozulin, International Center for the Enhancement of Learning Potential, Journal of Cognitive Education and Psychology

    "If this reviewer's experience is any guide, the constant stream of insights that Sfard provides through to the final pages of the last chapter are more than ample reward for the reader's persistence."
    --Paul Cobb, Vanderbilt University, Human Development Journal

    "Anna Sfard’s impressive Thinking as Communicating presents us with a series of detailed arguments for a communicational paradigm in the study of learning and development...I am grateful to Sfard for providing this very carefully reasoned approach to understanding the development of mathematical thinking as discursive activity. She gives us a very well-specified example of a "practice theory,"..."
    --Jay Lemke, University of Michigan, Mind, Culture, and Activity, 16: 281–284, 2009

    "...masterfully done...well worth one's time and efforts...I highly recommend the book."
    --Bharath Sriraman, the University of Montana: TMME [vol 6, no.3, p. 541]

    "...a comprehensive, coherent and scientific framework for thinking about thinking... In this ambitious book, Sfard sets forth a meticulously-developed framework for thinking about thinking that she labels the commognitive framework...There are two clear audiences for this book. One is philosophers and researchers interested in issues of thinking, in general. The second is those interested in mathematical thinking, in particular, including mathematicians, mathematics education researchers and those interested primarily in advancing mathematical learning..."
    --Erna Yackel, Purdue University, Research in Mathematics Education

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    Product details

    • Date Published: January 2008
    • format: Hardback
    • isbn: 9780521867375
    • length: 352 pages
    • dimensions: 229 x 152 x 24 mm
    • weight: 0.69kg
    • contains: 21 b/w illus. 12 tables
    • availability: Available
  • Table of Contents

    Introduction
    Part I. Discourse on Thinking:
    1. Puzzling about (mathematical) thinking
    2. Objectification
    3. Commognition: thinking as communicating
    4. Thinking in language
    Part II. Mathematics as Discourse:
    5. Mathematics as a form of communication
    6. Objects of mathematical discourse: what mathematizing is all about
    7. Routines: how we mathematize
    8. Explorations, deeds, and rituals: what we mathematize for
    9. Looking back and ahead: solving old quandaries and facing new ones.

  • Author

    Anna Sfard, University of Haifa, Israel and Michigan State University
    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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