Mathematics and Beauty: Aesthetic Approaches to Teaching Children

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Overview

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.

About the Author:
Nathalie Sinclair is an assistant professor in the Department of Mathematics at Michigan State University

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Product Details

  • ISBN-13: 9780807747223
  • Publisher: Teachers College Press
  • Publication date: 9/8/2006
  • Edition description: New Edition
  • Pages: 208
  • Product dimensions: 6.12 (w) x 9.00 (h) x 0.52 (d)

Table of Contents


Foreword   William Higginson     vii
Acknowledgments     xi
Introduction     1
Where Beautiful Mathematics Comes From     1
The Aesthetic as a Vital Lens on Learning     4
Plan for the Book     9
A Background Note     12
Beauty and Pleasure in Human Experience
Reclaiming the Aesthetic from the Arts     17
The Fluidity of Human Faculties     17
The Aesthetic Nature of Inquiry     21
Connecting the Aesthetic to Learning: First Steps     26
Fitting the Pieces Together     28
"Wired" for Beauty and Pleasure     29
Homo Aestheticus     29
A "Sense of Order"     33
Beauty and Pleasure in Mathematics
Developing a Mathematical Aesthetic Lens     39
The Aesthetic     39
The Mathematical Aesthetic     42
The Mathematical Aesthetic in Action     43
The Aesthetics of Detachment     56
Aesthetics and the Development of Mathematics     59
Debriefing the Kissing Triangles     59
The Importance of the Mathematical Aesthetic     61
Fitting the Pieces Together     65
Focusing the Aesthetic Lens On Students
The MotivationalRole of the Aesthetic     69
The Aesthetic Dimension of Problem Selection     71
The Aesthetic Dimension of Problem Posing     74
Coloring with Numbers     83
Fitting the Pieces Together     97
The Generative Role of the Aesthetic     99
Three Examples of the Generative Role     100
Mindful Mathematics     108
Fitting the Pieces Together     109
The Evaluative Role of the Aesthetic     113
Which Solution Is Better?     117
Wonder and the Aesthetic     129
Valuing the Aesthetic     131
Fitting the Pieces Together: Aesthetics and Inquiry     133
Aesthetic Enculturation
Peering Inside the Mathematics Culture     139
From Outside to Inside the Culture     139
What Do Mathematicians Value?     140
The Aesthetic Dimension of Mathematical Values     144
Mathematical Values in Teaching     153
Revealing Values in Topics, Tasks, and Tools     154
Communicating Values in the Classroom     162
Some Closing Words     175
Notes     177
References     183
Index     191
About the Author     196
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