The Psychology of Mathematics
A Journey of Personal Mathematical Empowerment for Educators and Curious Minds
This book offers an innovative introduction to the psychological basis of mathematics and the nature of mathematical thinking and learning, using an approach that empowers students by fostering their own construction of mathematical structures.
Through accessible and engaging writing, award-winning mathematician and educator Anderson Norton reframes mathematics as something that exists first in the minds of students, rather than something that exists first in a textbook. By exploring the psychological basis for mathematics at every level—including geometry, algebra, calculus, complex analysis, and more—Norton unlocks students’ personal power to construct mathematical objects based on their own mental activity and illustrates the power of mathematics in organizing the world as we know it.
Including reflections and activities designed to inspire awareness of the mental actions and processes coordinated in practicing mathematics, the book is geared toward current and future secondary and elementary mathematics teachers who will empower the next generation of mathematicians and STEM majors. Those interested in the history and philosophy that underpins mathematics will also benefit from this book, as well as those informed and curious minds attentive to the human experience more generally.
Table of Contents
Introduction: Mathematical Empowerment
1: What is Number?
2: Reflections upon Reflections
3: Getting with the Program
4: New Actions, New Units, New Numbers
5: Creating, Transforming, and Obliterating Area
6: The Power of Symbols
7: Seeing Angles from a Different Angle
8: The Geometry of Numbers
9: What Doesn’t Vary as Variables Co-Vary?
10: What’s So Special about Special Triangles?
11: Calculus the Old-Fashioned Way
12: The Wonderful Gift of Mathematics
Anderson Norton is Professor in the Department of Mathematics at Virginia Tech, USA, where he has been teaching mathematics courses for future teachers for 15 years. He is the editor of Constructing Number and the coauthor of Developing Fractions Knowledge and Numeracy for All Learners.