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Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations

Authors: Duval, Raymond

  • Presents a new way to teach and learn mathematics 
  • Provides a method for teachers to use the registers of semiotic representations theory in their everyday work at the classroom
  • Explains how to develop the cognitive processes required to the acquisition of mathematical knowledge
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eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-56910-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA
  • ISBN 978-3-319-56909-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

In this book, Raymond Duval shows how his theory of registers of semiotic representation can be used as a tool to analyze the cognitive processes through which students develop mathematical thinking. To Duval, the analysis of mathematical knowledge is in its essence the analysis of the cognitive synergy between different kinds of semiotic representation registers, because the mathematical way of thinking and working is based on transformations of semiotic representations into others. Based on this assumption, he proposes the use of semiotics to identify and develop the specific cognitive processes required to the acquisition of mathematical knowledge. In this volume he presents a method to do so, addressing the following questions:

• How to situate the registers of representation regarding the other semiotic “theories”

• Why use a semio-cognitive analysis of the mathematical activity to teach mathematics

• How to distinguish the different types of registers

• How to organize learning tasks and activities which take into account the registers of representation

• How to make an analysis of the students’ production in terms of registers

Building upon the contributions he first presented in his classic book Sémiosis et pensée humaine, in this volume Duval focuses less on theoretical issues and more on how his theory can be used both as a tool for analysis and a working method to help mathematics teachers apply semiotics to their everyday work. He also dedicates a complete chapter to show how his theory can be applied as a new strategy to teach geometry.

“Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations is an essential work for mathematics educators and mathematics teachers who look for an introduction to Raymond Duval’s cognitive theory of semiotic registers of representation, making it possible for them to see and teach mathematics with fresh eyes.

Professor Tânia M. M. Campos, PHD.

About the authors

Raymond Duval is a philosopher and psychologist, devoted to researching mathematics education since the 1970s. He has worked at the Research Institute on Mathematical Education (IREM) in Strasbourg, France, from 1970 to 1995, where he developed an important research in cognitive psychology. Today, he is honorarius professor of the University du Litoral Côte d'Opale, France. His book Sémiosis et pensée humaine (1995) is a milestone in the theory of registers of semiotic representations, and his research papers over the years have greatly influenced research in mathematics education. 

Table of contents (4 chapters)

  • Representation and Knowledge: The Semiotic Revolution

    Duval, Raymond

    Pages 1-19

  • Mathematical Activity and the Transformations of Semiotic Representations

    Duval, Raymond

    Pages 21-43

  • Registers of Semiotic Representations and Analysis of the Cognitive Functioning of Mathematical Thinking

    Duval, Raymond

    Pages 45-71

  • The Registers: Method of Analysis and Identification of Cognitive Variables

    Duval, Raymond

    Pages 73-111

Buy this book

eBook $79.99
price for USA (gross)
  • ISBN 978-3-319-56910-9
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.99
price for USA
  • ISBN 978-3-319-56909-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Understanding the Mathematical Way of Thinking – The Registers of Semiotic Representations
Authors
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-56910-9
DOI
10.1007/978-3-319-56910-9
Hardcover ISBN
978-3-319-56909-3
Edition Number
1
Number of Pages
XXIV, 117
Number of Illustrations and Tables
41 b/w illustrations, 9 illustrations in colour
Additional Information
Jointly published with Proem Editora, São Paulo. Original Portuguese edition published by Proem Editora, São Paulo, Brazil, 2011
Topics