Mathematical Discourse: Language, Symbolism And Visual Images

Kay L. O'Halloran

Continuum International Publishing Group | 2005 | 226 páginas | PDF | 7,8 Mb

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This book develops a theory of mathematics as a multi-semiotic discourse from the perspective of M. A. K. Halliday's systemic functional linguistics. From this perspective mathematical discourse is seen to involve the use of the three semiotic resources of language, visual images and mathematical symbolism. These semiotic resources are considered as functional sign systems which are organised grammatically. O'Halloran suggests that mathematical texts represent specific semiotic choices from the available grammatical systems. From this she articulates the ways in which a social semiotic perspective can inform mathematics teaching and learning.

Índice

Contents
Acknowledgements
Copyright Permission Acknowledgements
1 Mathematics as a Multisemiotic Discourse
1.1 The Creation of Order
1.2 Halliday's Social Semiotic Approach
1.3 Mathematics as Multisemiotic
1.4 Implications of a Multisemiotic View
1.5 Tracing the Semiotics of Mathematics
1.6 Systemic Functional Research in Multimodality
2 Evolution of the Semiotics of Mathematics
2.1 Historical Development of Mathematical Discourse
2.2 Early Printed Mathematics Books
2.3 Mathematics in the Early Renaissance
2.4 Beginnings of Modern Mathematics: Descartes and Newton
2.5 Descartes' Philosophy and Semiotic Representations
2.6 A New World Order
3 Systemic Functional Linguistics (SFL) and Mathematical Language
3.1 The Systemic Functional Model of Language
3.2 Interpersonal Meaning in Mathematics
3.3 Mathematics and the Language of Experience
3.4 The Construction of Logical Meaning
3.5 The Textual Organization of Language

3.6 Grammatical Metaphor and Mathematical Language
3.7 Language, Context and Ideology
4 The Grammar of Mathematical Symbolism
4.1 Mathematical Symbolism
4.2 Language-Based Approach to Mathematical Symbolism
4.3 SF Framework for Mathematical Symbolism
4.4 Contraction and Expansion of Experiential Meaning
4.5 Contraction of Interpersonal Meaning
4.6 A Resource for Logical Reasoning
4.7 Specification of Textual Meaning
4.8 Discourse, Grammar and Display
4.9 Concluding Comments
5 The Grammar of Mathematical Visual Images
5.1 The Role of Visualization in Mathematics
5.2 SF Framework for Mathematical Visual Images
5.3 Interpersonally Orientating the Viewer
5.4 Visual Construction of Experiential Meaning
5.5 Reasoning through Mathematical Visual Images
5.6 Compositional Meaning and Conventionalized Styles of Organization
5.7 Computer Graphics and the New Image of Mathematics
6 Intersemiosis: Meaning Across Language, Visual Images and Symbolism
6.1 The Semantic Circuit in Mathematics
6.2 Intersemiosis: Mechanisms, Systems and Semantics
6.3 Analysing Intersemiosis in Mathematical Texts
6.4 Intersemiotic Re-Contexualization in Newton's Writings
6.5 Semiotic Metaphor and Metaphorical Expansions of Meaning
6.6 Reconceptualizing Grammatical Metaphor
7 Mathematical Constructions of Reality
7.1 Multisemiotic Analysis of a Contemporary Mathematics Problem
7.2 Educational Implications of a Multisemiotic Approach to Mathematics
7.3 Pedagogical Discourse in Mathematics Classrooms
7.4 The Nature and Use of Mathematical Constructions
References
Index