This book examines mathematical discourse from the perspective of Michael Halliday's social semiotic theory. In this approach, mathematics is conceptualized as a multisemiotic discourse involving language, visual images and symbolism. The book discusses the evolution of the semiotics of mathematical discourse, and then, proceeds to examine the grammar of mathematical symbolism, the grammar of mathematical visual images, intersemiosis between language, visual images and symbolism and the subsequent ways in which mathematics orders reality. The focus of this investigation is written mathematical texts. The aims of the book are to understand the semantic realm of mathematics and to appreciate the metaphorical expansions and simultaneous limitations of meaning in mathematical discourse. The book is intended for linguists, semioticians, social scientists and those interested in mathematics and science education. In addition, the close study of the multisemiotic mature of mathematics has implications for other studies adopting a social semiotic approach to multimodality.
Author(s): Kay O'Halloran
Edition: First Edition
Publisher: Continuum
Year: 2004
Language: English
Pages: 240
Contents......Page 6
Acknowledgements......Page 9
Copyright Permission Acknowledgements......Page 10
1.1 The Creation of Order......Page 14
1.2 Halliday's Social Semiotic Approach......Page 19
1.3 Mathematics as Multisemiotic......Page 23
1.4 Implications of a Multisemiotic View......Page 26
1.5 Tracing the Semiotics of Mathematics......Page 30
1.6 Systemic Functional Research in Multimodality......Page 32
2.1 Historical Development of Mathematical Discourse......Page 35
2.2 Early Printed Mathematics Books......Page 37
2.3 Mathematics in the Early Renaissance......Page 46
2.4 Beginnings of Modern Mathematics: Descartes and Newton......Page 51
2.5 Descartes' Philosophy and Semiotic Representations......Page 59
2.6 A New World Order......Page 70
3.1 The Systemic Functional Model of Language......Page 73
3.2 Interpersonal Meaning in Mathematics......Page 80
3.3 Mathematics and the Language of Experience......Page 88
3.4 The Construction of Logical Meaning......Page 91
3.5 The Textual Organization of Language......Page 94
3.6 Grammatical Metaphor and Mathematical Language......Page 96
3.7 Language, Context and Ideology......Page 101
4.1 Mathematical Symbolism......Page 107
4.2 Language-Based Approach to Mathematical Symbolism......Page 109
4.3 SF Framework for Mathematical Symbolism......Page 110
4.4 Contraction and Expansion of Experiential Meaning......Page 116
4.5 Contraction of Interpersonal Meaning......Page 127
4.6 A Resource for Logical Reasoning......Page 131
4.7 Specification of Textual Meaning......Page 134
4.8 Discourse, Grammar and Display......Page 138
4.9 Concluding Comments......Page 141
5.1 The Role of Visualization in Mathematics......Page 142
5.2 SF Framework for Mathematical Visual Images......Page 146
5.3 Interpersonally Orientating the Viewer......Page 152
5.4 Visual Construction of Experiential Meaning......Page 155
5.5 Reasoning through Mathematical Visual Images......Page 158
5.6 Compositional Meaning and Conventionalized Styles of Organization......Page 159
5.7 Computer Graphics and the New Image of Mathematics......Page 161
6.1 The Semantic Circuit in Mathematics......Page 171
6.2 Intersemiosis: Mechanisms, Systems and Semantics......Page 176
6.3 Analysing Intersemiosis in Mathematical Texts......Page 184
6.4 Intersemiotic Re-Contexualization in Newton's Writings......Page 190
6.5 Semiotic Metaphor and Metaphorical Expansions of Meaning......Page 192
6.6 Reconceptualizing Grammatical Metaphor......Page 197
7.1 Multisemiotic Analysis of a Contemporary Mathematics Problem......Page 202
7.2 Educational Implications of a Multisemiotic Approach to Mathematics......Page 212
7.3 Pedagogical Discourse in Mathematics Classrooms......Page 218
7.4 The Nature and Use of Mathematical Constructions......Page 221
References......Page 224
D......Page 236
L......Page 237
S......Page 238
W......Page 239
