Mathematics and beauty: Aesthetic approaches to teaching children

Cover......Page 1
Mathematics and Beauty: Aesthetic Approaches to Teaching Children......Page 4
Copyright - ISBN: 080774722X......Page 5
Contents......Page 6
Foreword......Page 8
Acknowledgments......Page 12
WHERE BEAUTIFUL MATHEMATICS COMES FROM......Page 14
THE AESTHETIC AS A VITAL LENS ON LEARNING......Page 17
PLAN FOR THE BOOK......Page 22
A BACKGROUND NOTE......Page 25
PART I: Beauty and Pleasure in Human Experience......Page 28
THE FLUIDITY OF HUMAN FACULTIES......Page 30
THE AESTHETIC NATURE OF INQUIRY......Page 34
CONNECTING THE AESTHETIC TO LEARNING: FIRST STEPS......Page 39
FITTING THE PIECES TOGETHER......Page 41
HOMO AESTHETICUS......Page 42
A “SENSE OF ORDER”......Page 46
PART II: Beauty and Pleasure in Mathematics......Page 50
THE AESTHETIC......Page 52
THE MATHEMATICAL AESTHETIC......Page 55
THE MATHEMATICAL AESTHETIC IN ACTION......Page 56
THE AESTHETICS OF DETACHMENT......Page 69
DEBRIEFING THE KISSING TRIANGLES......Page 72
THE IMPORTANCE OF THE MATHEMATICAL AESTHETIC......Page 74
FITTING THE PIECES TOGETHER......Page 78
PART III: Focusing the Aesthetic Lens on Students......Page 80
CHAPTER 6: The Motivational Role of the Aesthetic......Page 82
THE AESTHETIC DIMENSION OF PROBLEM SELECTION......Page 84
THE AESTHETIC DIMENSION OF PROBLEM POSING......Page 87
COLORING WITH NUMBERS......Page 96
FITTING THE PIECES TOGETHER......Page 110
CHAPTER 7: The Generative Role of the Aesthetic......Page 112
THREE EXAMPLES OF THE GENERATIVE ROLE......Page 113
MINDFUL MATHEMATICS......Page 121
FITTING THE PIECES TOGETHER......Page 122
CHAPTER 8: The Evaluative Role of the Aesthetic......Page 126
WHICH SOLUTION IS BETTER?......Page 130
WONDER AND THE AESTHETIC......Page 142
VALUING THE AESTHETIC......Page 144
FITTING THE PIECES TOGETHER: AESTHETICS AND INQUIRY......Page 146
PART IV: Aesthetic Enculturation......Page 150
FROM OUTSIDE TO INSIDE THE CULTURE......Page 152
WHAT DO MATHEMATICIANS VALUE?......Page 153
THE AESTHETIC DIMENSION OF MATHEMATICAL VALUES......Page 157
CHAPTER 10: Mathematical Values in Teaching......Page 166
REVEALING VALUES IN TOPICS, TASKS, AND TOOLS......Page 167
COMMUNICATING VALUES IN THE CLASSROOM......Page 175
SOME CLOSING WORDS......Page 188
Notes......Page 190
References......Page 196
C......Page 204
E......Page 205
L......Page 206
R......Page 207
Y......Page 208
About the Author......Page 209