E-Book, Englisch, Band 44, 186 Seiten
Barton The Language of Mathematics
2008
ISBN: 978-0-387-72859-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
Telling Mathematical Tales
E-Book, Englisch, Band 44, 186 Seiten
Reihe: Mathematics Education Library
ISBN: 978-0-387-72859-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Autoren/Hrsg.
Weitere Infos & Material
1;Acknowledgements;7
2;Contents;8
3;PRELUDE: MAORI MATHEMATICS VOCABULARY;10
4;INTRODUCTION;16
5;PART I SPEAKING MATHEMATICS DIFFERENTLY;21
5.1;Chapter 1 SPACE: POINTS OF REFERENCE;22
5.1.1;1. WAYS OF LOCATING: LINGUISTIC FEATURES;23
5.1.2;2. WAYS OF LOCATING: MATHEMATICAL SYSTEMS;25
5.1.3;3. LINKING THE LINGUISTIC AND MATHEMATICAL SYSTEMS;26
5.2;Chapter 2 SPACE: STATIC AND DYNAMIC WORLD VIEWS;34
5.2.1;1. WHAT ARE VERBAL SHAPES?;35
5.2.2;2. BIRDS AND ORBITS;37
5.2.3;3. EUROPEAN AND PACIFIC NAVIGATION;40
5.2.4;4. LINKING THE LINGUISTIC AND MATHEMATICAL SYSTEMS;43
5.3;Chapter 3 QUANTITY: TRAPPING NUMBERS IN GRAMMATICAL NETS;47
5.3.1;1. EMERGING NUMBERS: POLYNESIAN LANGUAGES;48
5.3.2;2. NUMBERS TRAPPED AS ADJECTIVES: KANKANA- EY;49
5.3.3;Français Québécois;52
5.3.4;3. FUNCTIONING NUMBERS: DHIVEHI;52
5.3.5;4. CONGRUENCE OF LANGUAGE WITH MATHEMATICS;56
6;PART II LANGUAGE AND MATHEMATICS;60
6.1;Chapter 4 THE EVIDENCE FROM LANGUAGE;61
6.1.1;1. TWO WORD STORIES: NORMAL AND OPEN;61
6.1.2;2. REVIEWING THE EVIDENCE;65
6.2;Chapter 5 MUMBLING, METAPHORS, & MINDLOCKS: THE ORIGINS OF MATHEMATICS;69
6.2.1;1. GOSSIP & MATHEMATICAL TALK;69
6.2.2;2. COGNITIVE SCIENCE CONTRIBUTIONS;74
6.2.3;3. FRACTION SYSTEMS;77
6.2.4;4. HISTORICAL EVIDENCE;82
6.2.5;5. SOCIAL INFLUENCE ON CHOICE;84
6.2.6;6. THE ROLE OF COMMUNICATION;86
6.2.7;7. METAPHORS;92
6.2.8;8. MINDLOCKS;98
6.3;Chapter 6 A NEVER-ENDING BRAID: THE DEVELOPMENT OF MATHEMATICS;102
6.3.1;1. PACIFIC NAVIGATION: IS IT MATHEMATICS?;104
6.3.2;2. A RIVER OR A BRAID?;108
6.3.3;3. SNAPPING TO GRID AND OTHER MECHANISMS;111
6.3.4;4. REJECTION AND ISOLATION;116
6.3.5;5. MATHEMATICS, SOCIETY & CULTURE;118
6.4;Chapter 7 WHAT IS MATHEMATICS? PHILOSOPHICAL COMMENTS;123
6.4.1;1. MIDDLE EARTH;123
6.4.2;2. MATHEMATICAL WORLDS;126
6.4.3;3. WITTGENSTEINIAN MATHEMATICAL WORLDS;129
6.4.4;4. MATHEMATICS AND EXPERIENCE;132
6.4.5;5. RECURRENT HISTORY: BACHELARD;134
6.4.6;6. UNIVERSAL OR RELATIVE;136
6.4.7;7. EVIDENCE, REFLECTIONS, & CONSEQUENCES;138
7;PART III IMPLICATIONS FOR MATHEMATICS EDUCATION;141
7.1;Chapter 8 LEARNING MATHEMATICS;142
7.1.1;1. CONCLUSIONS THROUGH EDUCATIONAL EYES;142
7.1.2;2. BECOMING A BETTER GOSSIP;147
7.1.3;3. FROM 1 TO 100: PLAYING & EXPLORING;150
7.1.4;4. CREATING MATHEMATICS THROUGH TALKING;153
7.1.5;5. SOME THOUGHTS ABOUT TEACHING MATHEMATICS;155
7.1.6;6. NOTES ON ASSESSMENT;158
7.2;Chapter 9 MULTILINGUAL AND INDIGENOUS MATHEMATICS EDUCATION;161
7.2.1;1. UNTOLD RICHES;162
7.2.2;2. MATHEMATICAL DISCOURSE;164
7.2.3;3. MATHEMATICS EDUCATION FOR INDIGENOUS PEOPLES;166
8;END WORDS;172
9;REFERENCES;174
10;Index to Names;181
11;Index to Subjects;183
