1st Edition
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.
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
Biography
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.
"The Psychology of Mathematics offers an innovative introduction to the often-ignored and less-discussed psychology of mathematics. The author—an award-winning mathematician, educator, and writer—uses an engaging and accessible style, thereby making the reading experience both enriching and revealing. The book, by virtue of its style and simplicity, is accessible to a nonmathematical audience, too."
- Firdous Ahmad Mala, World Literature Today
"The Psychology of Mathematics: A Journey of Personal Mathematical Empowerment for Educators and Curious Minds, by Anderson Norton, provides a path for readers to rebuild their relationship with mathematics. The author offers perspectives on what mathematics is, and he helps us, the reader, see the humanity in mathematics. Norton shows us how mathematics is inherently a part of how we think and act in the world, and he illustrates how mathematical thinking connects us all through broader cultural and historical practices. Throughout this book, Norton takes readers through a journey of connections and relationships in the world of mathematics. He also keeps equity in mind throughout the book."
- Amanda Jansen, The Mathematics Educator
"In The Psychology of Mathematics: A Journey of Personal Empowerment for Educators and Curious Minds, Anderson Norton presents a comprehensive theory of what mathematics is, how mathematics is done, and why mathematics works."
- Keith Weber, Research in Mathematics Education
