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Teaching and Learning of Knot Theory in School Mathematics

Akio Kawauchi and Tomoko Yanagimoto, editors
Publication Date: 
Number of Pages: 
[Reviewed by
Charles Ashbacher
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This book is an explanation of an interesting way to get students excited about mathematics. In many ways it borrows an activity that was long a staple of the American Boy Scout organization. The subject is knot theory; it has the advantages in that the principles can be demonstrated using very inexpensive materials such as string or craft grade pipe cleaners.

This book is a report on a joint venture between Akio Kawauchi, an expert in knot theory, and the Osaka study group of mathematics education. The opening chapter is an introduction to knot theory, followed by two chapters on the educational aspects of developing and delivering educational content in knot theory.

Subsequent chapters contain separate reports on the results of introducing knot theory into the elementary school, junior high, high school and then in the mathematics education curriculum at a liberal arts college. All of the schools where the introduction was done and studied are in Japan.

There is no question that knot theory is an excellent way to introduce mathematics. Like origami, it is a subject that allows the student to develop spatial understanding as well as manual dexterity and abstract thinking. I strongly recommend this book of consideration by all people involved in teaching the next generation of educators. It should also be examined by all instructors of mathematics working in K–12 education.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.

1. ​What is Knot Theory?---Why Is It in Mathematics?2. The Evolution of Mathematics Education---forwarding the research and practice of teaching knot theory in mathematics education---3. The Background of Developing Teaching Contents of Knot Theory 4. Education Practice in Elementary School 5. Education Practices in Junior High School 6. Education Practices in Senior High School 7. Education Practice at the University as Liberal Arts and Teacher Education-Index