Teaching and Learning of Knot Theory in School Mathematics [electronic resource] /
Kawauchi, Akio.editor.
Yanagimoto, Tomoko.editor.
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.
Description based upon print version of record.
Teaching and Learning of Knot Theory in School Mathematics; Foreword; Preface; Notes on the school systems in Japan; Authors; Contents; 1. What Is Knot Theory? Why Is It In Mathematics?; 1.1 Knots, links, and spatial graphs; 1.2 Diagrams and equivalence on knots, links, and spatial graphs; 1.3 A brief history of knot theory; 1.4 The first non-trivial knots; 1.5 Understanding the linking number; 1.5.1. Linking number; 1.5.2. Linking degree; 1.5.3. Computing examples of the linking degree using the meridian loops on the upper crossings; 1.6 Conclusion; 1.7 References
2. The Evolution of Mathematics Education -forwarding the research and practice of teaching knot theory in mathematics education-2.1 Overview; 2.2 Comments to our second issue; 2.3 Historical developments of the arithmetic and mathematics education in our country; 2.3.1 The Earliest Stages; 2.3.2 Modernization period; 2.3.3 The period of the "modernization of mathematics movement"; 2.4 International research interactions of mathematics education; 2.5 What knot theory means to mathematics education; 3. The Background of Developing Teaching Contents of Knot Theory
3.1 Recent trend in the course of study and actual situation of schools in Japan3.1.1 Curriculum arrangement for "the period of integrated study"; 3.1.2 Allowance of introduction of advanced contents in courses of study; 3.1.3 Study for curriculum development for the enrichment of technology, science and mathematics education; 3.2 The introduction of new mathematics into education; 3.2.1 Curriculum arrangement looking at introduction of new mathematics; 3.2.2 What we learn from modernization of mathematics education; 3.3 An approach to the development of teaching knot theory; 3.4 Conclusion
References4. Education Practice in Elementary School; 4. 1 A significance of teaching mathematical knot in elementary school; 4.1.1 Looking at a knot from different viewpoints; 4.2 Investigation of the pupils' drawing; 4.2.1 Questions for investigation; 4.2.2 The result of the investigation; 4.3 Education practice on knot as a 3-dimensional figure; 4.4 Education practice on reducing crossing number of a knot; 4.4.1 Lessons and the pupils' work; 4.5 Conclusion; References; 5. Education Practices in Junior High School
5.1 Education practice in junior high school attached to Osaka Kyoiku University5.1.1 Tri-colorability and Linking number; Tri-colorability; Linking number; 5.1.2 Education Practice; 5.1.3 Teaching plan (1); The 1st period; The 2nd period; The 3rd period; The 4th period; Impressions of pupils; 5.1.4 Teaching plan (2); The 1st period; The 2nd period; The 3rd period (This practice is not yet tried.); The 4th period (This practice is not yet tried.); Impression of pupils; 5.1.5 Conclusion; On teaching "tri-colarability"; On teaching "linking number"; References
5.2 Education practice in public junior high school
Includes bibliographical references and index.
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.
Geometry.
Topology.
Mathematics—Study and teaching .
Geometry.
Topology.
Mathematics Education.