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Jerry P. Becker

Posts: 15,675
Registered: 12/3/04
[ncsm-members] New Book on Knot Theory - School Mathematics
Posted: May 13, 2013 7:04 PM
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This book is available on --
New Book on Knot Theory

Title: Teaching and Learning of Knot Theory in School Mathematics

Editors: Akio Kawauchi and Tomoko Yanagimoto

Book Description [From the website]

Publication Date: June 27, 2012 | ISBN-10: 4431541373 | ISBN-13:
978-4431541370 | Edition: 2012 Springer

This book is the result of a joint venture between Professor Akio
Kawauchi, Osaka City University,
well-known for his research in knot theory, and the Osaka study group
of mathematics education,
founded by Professor Hirokazu Okamori and now chaired by his
successor Professor Tomoko
Yanagimoto, Osaka Kyoiku University. The seven chapters address the
teaching and learning of knot theory from several perspectives.
Readers will find an extremely clear and concise introduction to the
fundamentals of knot theory, an overview of curricular developments
in Japan, and in particular a series of teaching experiments at all
levels which not only demonstrate the creativity and the professional
expertise of the members of the study group, but also give a lively
impression of students learning processes. In addition the reports
show that elementary knot theory is not just a preparation for
advanced knot theory but also an excellent means to develop spatial
thinking. The book can be highly recommended for several reasons:
First of all, and that is the main intention of the book, it serves
as a comprehensive text for teaching and learning knot theory.
Moreover it provides a model for cooperation between mathematicians
and mathematics educators based on substantial mathematics. And
finally it is a thorough introduction to the Japanese art of lesson
studies again in the context of
substantial mathematics.

Preface to book

It was in July, 2004 that a project to study "Teaching Knot Theory in
Mathematics Education" was formed, which was made possible only when
Akio Kawauchi of Osaka City University and Hirokazu Okamori, a
professor emeritus of Osaka Kyoiku University, met together. Okamori
is a researcher of mathematics education. Kawauchi is an expert of
knot theory and then he was the leader of "Constitution of wide-angle
mathematical basis focused on knots," one of the 21st Century Center
of Excellence Programs in Japan from April 2003 to March 2008.

In recent years, knot theory has been making a rapid progress and
contributed to elucidating problems of various fields as a science.
Knot theory experts are hoping to get across its fun and importance
widely to pupils and students in their early years. Also, our
cherished hope is that by so doing, we will pick out students with
high levels of interest and learning ability in knot theory and bring
them up to be excellent experts on it. Experts of mathematics
education have a desire to keep developing teaching contents from
much broader perspectives beyond the bounds of traditional school
mathematics in order to cultivate children's understanding of

In pursuit of the realization of the hopes from these two positions,
the research project with a team work of researchers of mathematics
and mathematics education in university and elementary, junior and
senior high school teachers of mathematics was formed by Tomoko
Yanagimoto and started discussions of introducing knot theory to
education. All the members began to tackle such work by learning the
basics of knot theory. At the same time, we delved into its
educational meanings from the viewpoint of mathematics education.
Elementary, junior and senior high school teachers of mathematics
held their respective meetings at the school levels and developed
teaching materials along with the researchers of mathematics
education. Also, based on this, all the members had meetings once a
month, where they discussed from their own standpoints under mutual
respect as equals and confirmed the systematization of the contents
that can be used as teaching materials. We proceeded to discuss the
exploration into teaching contents based on the following points:

. Making teaching knot theory something meaningful for pupils rather
than something that just propagates knowledge.

. Grasping the real situations of their understanding in their
respective years, to this end.

. Developing effective teaching tools as needed.

The report of our research results has already been compiled in
Japanese into three issues, attracting the attention of
mathematicians, researchers of mathematics education and teachers of
mathematics in Japan. In 2006, our research results on knot theory
with senior high school students from the SSH (Super Science High
School) program, which was one of our experimental practices, won
the highest in the four "first prizes" of the sections of
mathematics, physics, chemistry and biology in Japan. The ex post
facto evaluation as a part of the 21st Century Center of Excellence
Programs of 2008 was of the highest. As one of the reasons for that
evaluation, it was pointed out that we had been steadily educating
elementary, junior and senior high school students on knot theory.
Further, researchers representing mathematics educations not only in
Japan but also abroad showed interests in our research results. In
November 2004, Erich Ch. Witttmann, professor of Dortmund University
in Germany, came to visit Osaka and inspected our experimental
classworks on mathematics education of knot theory conducted at
Tennoji Junior High School and Tennoji Elementary School attached to
Osaka Kyoiku University and showed a deep interest in it. Many times
we received encouragement and letters of research interchanges from
Heinrich Besuden, professor of Oldenburg University in Germany and a
former chairman of the German Mathematics Education Society. Also,
whenever we made presentations of our research on teaching knot
theory at the conferences of mathematics education in Japan and
abroad, including ICME (International Conference of Mathematics
Education), lots of interests were directed to our teaching contents,
children's reactions, the process developing teaching materials, and
the way of proceeding on the research project. Thus, at this time, we
have decided to publish our work as a book in English so that we can
introduce our research results and its process to many people,
including researchers of mathematics education around the world, knot
theory researchers and school teachers of mathematics who have shown
interests in our activity.

This book contains an introduction of knot theory, up-to-date topics
on it, the educational meanings of knot theory from the perspective
of the evolution of mathematics education, the methodology for making
knot theory into curriculum and actual examples of researches and
practices, conducted at elementary, junior and senior high schools
and in university general education. All the researches and practices
have actually been conducted. This book introduces our guidance of
knot theory that takes various forms of not only classworks but also
experimental teachings with several students, club activity guidances
in concerted efforts between senior high schools and universities,
and others.

This work was supported in part by the Priority Research of Osaka
City University "Mathematics of knots and wide-range evolutions to
scientific objects" and the JSPS Grant-in-Aid for Scientific Research
(A) No. 21244005, "Studies in Knot Theory."

Early Spring of 2011

Akio Kawauchi and Tomoko Yanagimoto

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
625 Wham Drive
Mail Code 4610
Carbondale, IL 62901-4610
Phone: (618) 453-4241 [O]
(618) 457-8903 [H]
Fax: (618) 453-4244

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