Rediscovering Mathematics is a guide to more effective mathematical education, offering topics and puzzles that can inspire a renewed interest in mathematics among students and enthusiasts.
Suitable for anyone who wants to expand their view of mathematics, the book's topics are linked by the theme of mathematical learning through investigation, challenge, and discovery. It can be used as a text for training mathematics teachers at all levels, and is recommended for anyone interested in mathematics and how mathematics should be taught.
Containing dozens of illustrations, tables, and exercises, the book focuses on problem solving and understanding, subsuming learning by memorization. Topics include number theory and applications to secure Internet communication and to probability in sports and gambling.
A Guide for the Reader
Introduction - how to read mathematics
1. Mathematical discovery in the classroom
2. Don't reach for your calculator (yet)
3. Have another piece of pie, Zeno?
4. Thinking like a mathematician - lessons from a medieval Rabbi
5. What is mathematics good for?
6. Three averages
7. Algorithms - the unexpected role of pure mathematics
8. Pythagoras' Theorem and math by pictures
9. Memorizing versus understanding
10. Games and gambling
11. Soccer balls and counting tricks
12. Pizza Pi and area
13. Back to the classroom
Resources for rediscovering mathematics
Memorizing mathematics without comprehension is often harmful. If you memorize a poem that you don't understand, there is still the chance that the flow of the words may have an effect on you. When you memorize dates of historical events, at least you know the chronological order of those events, even if you may not know their significance. When you memorize mathematics without understanding, you delude yourself into thinking that you know something, when in fact you do not. This delusion compounds the lack of understanding. Your ability to apply the knowledge, generalize it, or even question its truth is compromised.
Shai Simonson (Stonehill College), who has lectured all over the world, has published articles on mathematics education, the history of mathematics, popular mathematics, theoretical computer science, and computer science education.