Deep Thinking: What Mathematics Can Teach Us About the Mind
| Author | : | |
| Rating | : | 4.16 (593 Votes) |
| Asin | : | 9814618039 |
| Format Type | : | paperback |
| Number of Pages | : | 264 Pages |
| Publish Date | : | 2017-10-26 |
| Language | : | English |
DESCRIPTION:
Deep thinking is the essential ingredient in every significant learning experience, which leads to a new way to think about education. It is also essential to the construction of conceptual systems that are at the heart of mathematics and science, and of the technologies that shape the modern world. Most people are familiar with the systematic, rule-based thinking that one finds in a mathematical proof or a computer program. The sources of this study include the cognitive development of numbers in children, neuropsychology, the study of creativity, and the historical development of mathematics and science. The approach is unusual and original. Deep thinking is a different and more basic way of using the mind. There is more than one way to think. Many people suspect that such a gap exists, but find it difficult to make this intuition precise. It is at the heart of every paradigm shift or reframing of a problematic situation. It comes out of the author's lengthy experience as a mathematician, teacher, and writer of books about mathematics and science, such as How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics and The Blind Spot: Science and the Crisis of Uncertainty.. For example, there is an unbridgeable gap between deep thinking and computer simulations of thinking. It results in the discontinuous “aha!” experience, which is the essence of creativity. The identification of deep
"broken thinking" according to berts. The only enjoyable part I found was the nice review of how mathematics thought builds upon itself from elementary through graduate school; it did bring back a lot of memories and I agreed with most of the premises of the discontinuous, difficult, and informal nature of true understanding. The book takes this to some really far fetched conclusions like therefore no algorithm of human level creativity can ever exist and ramblings on how bad the educational system is without giving any new ideas on how to improve it. It was difficult to pay attention to the last third of the book as it just seemed to be rehashing the same points . spock said To boldly think where few minds have gone before. This book is required reading for those who wish to move beyond the superficial or inconsequential ideas of our era.