Byers W. Deep Thinking. What Mathematics Can Teach...2015

Textbook in PDF format

"Deep thinking is the process that is at the heart of creativity and learning. It has many names—breakthrough thinking, reframing, and paradigm change. The result of deep thinking is that one comes to see things in a manner that is radically different from the way one previously saw them. Breakthroughs are inevitably difficult to achieve and involve a discontinuity, which is sometimes called the “eureka moment.” This book uses the subject matter of mathematics to describe what deep thinking is and how it differs from the rule-based thinking that is familiar from logic, mathematical proofs, and computer algorithms."
What is Deep Thinking?
Conceptual Systems
Deep Thinking in Mathematics and Science
Deep Thinking in the Mind and the Brain
Deep Thinking and Creativity
Deep Learning
Good Teaching
Undergraduate Mathematics
What the Mind Can Teach Us About Mathematics
What Mathematics Can Teach Us About the Mind