Mathematics and Beauty : Aesthetic Approaches to Teaching Children

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  • Format: Paperback
  • Copyright: 2006-08-30
  • Publisher: Teachers College Pr

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Supplemental Materials

What is included with this book?


In this innovative book, Nathalie Sinclair makes a compelling case for the inclusion of the aesthetic in the teaching and learning of mathematics. Using a provocative set of philosophical, psychological, mathematical, technological, and educational insights, she illuminates how the materials and approaches we use in the mathematics classroom can be enriched for the benefit of all learners. While ranging in scope from the young learner to the professional mathematician, there is a particular focus on middle school, where negative feelings toward mathematics frequently begin. Offering specific recommendations to help teachers evoke and nurture their students' aesthetic abilities, this book: Features powerful episodes from the classroom that show students in the act of developing a sense of mathematical aesthetics. Analyzes how aesthetic sensibilities to qualities such as connectedness, fruitfulness, apparent simplicity, visual appeal, and surprise are fundamental to mathematical inquiry. Includes examples of mathematical inquiry in computer-based learning environments, revealing some of the roles they play in supporting students' aesthetic inclinations. Book jacket.

Author Biography

Nathalie Sinclair is an assistant professor in the Department of Mathematics at Michigan State University.

Table of Contents

Forewordp. vii
Acknowledgmentsp. xi
Introductionp. 1
Where Beautiful Mathematics Comes Fromp. 1
The Aesthetic as a Vital Lens on Learningp. 4
Plan for the Bookp. 9
A Background Notep. 12
Beauty and Pleasure in Human Experience
Reclaiming the Aesthetic from the Artsp. 17
The Fluidity of Human Facultiesp. 17
The Aesthetic Nature of Inquiryp. 21
Connecting the Aesthetic to Learning: First Stepsp. 26
Fitting the Pieces Togetherp. 28
"Wired" for Beauty and Pleasurep. 29
Homo Aestheticusp. 29
A "Sense of Order"p. 33
Beauty and Pleasure in Mathematics
Developing a Mathematical Aesthetic Lensp. 39
The Aestheticp. 39
The Mathematical Aestheticp. 42
The Mathematical Aesthetic in Actionp. 43
The Aesthetics of Detachmentp. 56
Aesthetics and the Development of Mathematicsp. 59
Debriefing the Kissing Trianglesp. 59
The Importance of the Mathematical Aestheticp. 61
Fitting the Pieces Togetherp. 65
Focusing the Aesthetic Lens On Students
The Motivational Role of the Aestheticp. 69
The Aesthetic Dimension of Problem Selectionp. 71
The Aesthetic Dimension of Problem Posingp. 74
Coloring with Numbersp. 83
Fitting the Pieces Togetherp. 97
The Generative Role of the Aestheticp. 99
Three Examples of the Generative Rolep. 100
Mindful Mathematicsp. 108
Fitting the Pieces Togetherp. 109
The Evaluative Role of the Aestheticp. 113
Which Solution Is Better?p. 117
Wonder and the Aestheticp. 129
Valuing the Aestheticp. 131
Fitting the Pieces Together: Aesthetics and Inquiryp. 133
Aesthetic Enculturation
Peering Inside the Mathematics Culturep. 139
From Outside to Inside the Culturep. 139
What Do Mathematicians Value?p. 140
The Aesthetic Dimension of Mathematical Valuesp. 144
Mathematical Values in Teachingp. 153
Revealing Values in Topics, Tasks, and Toolsp. 154
Communicating Values in the Classroomp. 162
Some Closing Wordsp. 175
Notesp. 177
Referencesp. 183
Indexp. 191
About the Authorp. 196
Table of Contents provided by Ingram. All Rights Reserved.

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