The Language of Mathematics (eBook)

Telling Mathematical Tales

Bill Barton (Autor)

eBook Download: PDF

2007 | 2008
X, 186 Seiten
Springer US (Verlag)
978-0-387-72859-9 (ISBN)

Infos

The book emerges from several contemporary concerns in mathematics, language, and mathematics education. However, the book takes a different stance with respect to language by combining discussion of linguistics and mathematics using examples from each to illustrate the other. The picture that emerges is of a subject that is much more contingent, much more relative, much more subject to human experience than is usually accepted. Another way of expressing this, is that the thesis of the book takes the idea of mathematics as a human creation, and, using the evidence from language, comes to more radical conclusions than most writers allow.

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Abstract: An outline of the structure of the book is presented, making the argument that the language we use for everyday mathematical ideas presents us with valuable evidence and insights into the nature of mathematics. Keywords: mathematical discourse, nature of mathematics I begin the book by looking at the way people speaking different languages talk about mathematical ideas in their everyday conversation. I end up questioning some common beliefs about mathematics, its history, and its pedagogy. The way we (English speakers) use numbers, the way we give directions, the way we express relationships, are all so commonplace that it is hard to imagine any other way of expressing these ideas. We take for granted the structures of the following sentences: There are four people in the room. The book costs forty-five dollars. Two and three are five. Turn left. Go straight on. The sun rises in the east. A dog is a mammal. He is not my father. I will either go shopping or read my book this afternoon.

Inhalt

Acknowledgements 7
Contents 8
PRELUDE: MAORI MATHEMATICS VOCABULARY 10
INTRODUCTION 16
PART I SPEAKING MATHEMATICS DIFFERENTLY 21
Chapter 1 SPACE: POINTS OF REFERENCE 22
1. WAYS OF LOCATING: LINGUISTIC FEATURES 23
2. WAYS OF LOCATING: MATHEMATICAL SYSTEMS 25
3. LINKING THE LINGUISTIC AND MATHEMATICAL SYSTEMS 26
Chapter 2 SPACE: STATIC AND DYNAMIC WORLD VIEWS 34
1. WHAT ARE VERBAL SHAPES? 35
2. BIRDS AND ORBITS 37
3. EUROPEAN AND PACIFIC NAVIGATION 40
4. LINKING THE LINGUISTIC AND MATHEMATICAL SYSTEMS 43
Chapter 3 QUANTITY: TRAPPING NUMBERS IN GRAMMATICAL NETS 47
1. EMERGING NUMBERS: POLYNESIAN LANGUAGES 48
2. NUMBERS TRAPPED AS ADJECTIVES: KANKANA- EY 49
Français Québécois 52
3. FUNCTIONING NUMBERS: DHIVEHI 52
4. CONGRUENCE OF LANGUAGE WITH MATHEMATICS 56
PART II LANGUAGE AND MATHEMATICS 60
Chapter 4 THE EVIDENCE FROM LANGUAGE 61
1. TWO WORD STORIES: NORMAL AND OPEN 61
2. REVIEWING THE EVIDENCE 65
Chapter 5 MUMBLING, METAPHORS, & MINDLOCKS: THE ORIGINS OF MATHEMATICS
1. GOSSIP & MATHEMATICAL TALK
2. COGNITIVE SCIENCE CONTRIBUTIONS 74
3. FRACTION SYSTEMS 77
4. HISTORICAL EVIDENCE 82
5. SOCIAL INFLUENCE ON CHOICE 84
6. THE ROLE OF COMMUNICATION 86
7. METAPHORS 92
8. MINDLOCKS 98
Chapter 6 A NEVER-ENDING BRAID: THE DEVELOPMENT OF MATHEMATICS 102
1. PACIFIC NAVIGATION: IS IT MATHEMATICS? 104
2. A RIVER OR A BRAID? 108
3. SNAPPING TO GRID AND OTHER MECHANISMS 111
4. REJECTION AND ISOLATION 116
5. MATHEMATICS, SOCIETY & CULTURE
Chapter 7 WHAT IS MATHEMATICS? PHILOSOPHICAL COMMENTS 123
1. MIDDLE EARTH 123
2. MATHEMATICAL WORLDS 126
3. WITTGENSTEINIAN MATHEMATICAL WORLDS 129
4. MATHEMATICS AND EXPERIENCE 132
5. RECURRENT HISTORY: BACHELARD 134
6. UNIVERSAL OR RELATIVE 136
7. EVIDENCE, REFLECTIONS, & CONSEQUENCES
PART III IMPLICATIONS FOR MATHEMATICS EDUCATION 141
Chapter 8 LEARNING MATHEMATICS 142
1. CONCLUSIONS THROUGH EDUCATIONAL EYES 142
2. BECOMING A BETTER GOSSIP 147
3. FROM 1 TO 100: PLAYING & EXPLORING
4. CREATING MATHEMATICS THROUGH TALKING 153
5. SOME THOUGHTS ABOUT TEACHING MATHEMATICS 155
6. NOTES ON ASSESSMENT 158
Chapter 9 MULTILINGUAL AND INDIGENOUS MATHEMATICS EDUCATION 161
1. UNTOLD RICHES 162
2. MATHEMATICAL DISCOURSE 164
3. MATHEMATICS EDUCATION FOR INDIGENOUS PEOPLES 166
END WORDS 172
REFERENCES 174
Index to Names 181
Index to Subjects 183

Produkt-Details

• Erscheint lt. Verlag: 24.12.2007
• Reihe/Serie: Mathematics Education Library
• Reihe/Serie: Mathematics Education Library
• Zusatzinfo: X, 186 p. 12 illus.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Schulbuch / Wörterbuch ► Lektüren / Interpretationen
• Themenwelt: Schulbuch / Wörterbuch ► Wörterbuch / Fremdsprachen
• Themenwelt: Geisteswissenschaften ► Sprach- / Literaturwissenschaft ► Sprachwissenschaft
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Sozialwissenschaften ► Pädagogik ► Erwachsenenbildung
• Themenwelt: Sozialwissenschaften ► Pädagogik ► Schulpädagogik / Grundschule
• Themenwelt: Technik
• Schlagworte: Barton • Development of Mathematics • Education • Implications for Mathematics Education • language • Language and Mathematics • Learning Mathematics • Mathematics • mathematics education • Multilingual and Indigenous Maths Education • Origins of Mathematics • Points of Reference • space • Speaking Mathematic • Telling
• ISBN-10: 0-387-72859-7 / 0387728597
• ISBN-13: 978-0-387-72859-9 / 9780387728599