# Semiotics as a Tool for Learning Mathematics

## How to Describe the Construction, Visualisation, and Communication of Mathematical Concepts

Book

1. Front Matter
Pages i-vi
Pages 1-21
2. ### Communication

1. Front Matter
Pages 23-23
Pages 25-42
Pages 43-66
3. ### Visualisation

1. Front Matter
Pages 67-67
2. Caroline Yoon
Pages 69-87
3. Caroline Yoon, Tessa Miskell
Pages 89-109
Pages 111-126
5. Patricia Perry, Leonor Camargo, Carmen Samper, Óscar Molina, Adalira Sáenz-Ludlow
Pages 127-153
Pages 155-179
4. ### Problem Solving

1. Front Matter
Pages 181-181
2. Christof Schreiber
Pages 183-208
3. Victor V. Cifarelli
Pages 209-225

### Introduction

Semiotics as a Tool for Learning Mathematics is a collection of ten theoretical and empirical chapters, from researchers all over the world, who are interested in semiotic notions and their practical uses in mathematics classrooms. Collectively, they present a semiotic contribution to enhance pedagogical aspects both for the teaching of school mathematics and for the preparation of pre-service teachers. This enhancement involves the use of diagrams to visualize implicit or explicit mathematical relations and the use of mathematical discourse to facilitate the emergence of inferential reasoning in the process of argumentation. It will also facilitate the construction of proofs and solutions of mathematical problems as well as the progressive construction of mathematical conceptions that, eventually, will approximate the concept(s) encoded in mathematical symbols. These symbols hinge not only of mental operations but also on indexical and iconic aspects; aspects which often are not taken into account when working on the meaning of mathematical symbols. For such an enhancement to happen, it is necessary to transform basic notions of semiotic theories to make them usable for mathematics education. In addition, it is also necessary to back theoretical claims with empirical data. This anthology attempts to deal with such a conjunction. Overall, this book can be used as a theoretical basis for further semiotic considerations as well as for the design of different ways of teaching mathematical concepts.

### Keywords

Diagrams Visualization Argumentation Communication Inferential Thinking

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