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

• Raymond Duval
Book

1. Front Matter
Pages i-xxiv
2. Raymond Duval
Pages 1-19
3. Raymond Duval
Pages 21-43
4. Raymond Duval
Pages 73-111
5. Back Matter
Pages 113-117

### Introduction

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.

### Keywords

Mathematics education Semiotics in mathematics education Teaching methods in mathematics education New ways of teaching mathematics Registers of semiotic representations Mathematical thinking Psychology of mathematics education Cognitive processes in mathematics education Educational research and planning Teacher education Teaching-learning processes

#### Authors and affiliations

• Raymond Duval
• 1
1. 1.Université du Littoral Côte d’OpaleDunkerqueFrance

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-319-56910-9
• Copyright Information Springer International Publishing AG 2017
• Publisher Name Springer, Cham
• eBook Packages Education
• Print ISBN 978-3-319-56909-3
• Online ISBN 978-3-319-56910-9