Teaching and Learning Mathematics through Variation

Confucian Heritage Meets Western Theories

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Volume Editors: and
Efforts to improve mathematics teaching and learning globally have led to the ever-increasing interest in searching for alternative and effective instructional approaches from others. Students from East Asia, such as China and Japan, have consistently outperformed their counterparts in the West. Yet, Bianshi Teaching (teaching with variation) practice, which has been commonly used in practice in China, has been hardly shared in the mathematics education community internationally. This book is devoted to theorizing the Chinese mathematical teaching practice, Bianshi teaching, that has demonstrated its effectiveness over half a century; examining its systematic use in classroom instruction, textbooks, and teacher professional development in China; and showcasing of the adaptation of the variation pedagogy in selected education systems including Israel, Japan, Sweden and the US. This book has made significant contributions to not only developing the theories on teaching and learning mathematics through variation, but also providing pathways to putting the variation theory into action in an international context.

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Introduction
Pages: 1–11
‘Bianshi’ and the Variation Theory of Learning
Illustrating Two Frameworks of Variation and Invariance in the Teaching of Mathematics
Pages: 43–67
Variation in Tool-Based Mathematics Pedagogy
The Case of Dynamic Virtual Tool
Pages: 69–84
Pedagogy of Variations
Synthesis of Various Notions of Variation Pedagogy
Pages: 85–103
Introduction
Pages: 105–109
Characteristics of Teaching Mathematical Problem Solving in China
Analysis of a Lesson from the Perspective of Variation
Pages: 111–125
Teaching Geometrical Concepts through Variation
A Case Study of a Shanghai Lesson
Pages: 151–168
Teaching Algebra through Variations
Contrast, Generalization, Fusion, and Separation
Pages: 187–205
Introduction
“The Lesson Plan Is Only the Teacher’s Hypothesis of Students’ Learning”
Pages: 207–212
Introduction
Putting Variation Theory to Work
Pages: 295–300
Improving Teaching through Variation
A Japanese Perspective
Pages: 301–320
Learning to Teach with Variation
Experiences from Learning Study in Sweden
Pages: 355–372
Teaching through Variation
An Asian Perspective – Is the Variation Theory of Learning Varying?
Pages: 373–388
Teaching through Variation
A European Perspective
Pages: 389–406
About the Authors
Pages: 439–450
Subject Index
Pages: 451–459
“This book paints a richly detailed and elaborated picture of both teaching mathematics and learning to teach mathematics with variation. Teaching with variation and variation as a theory of learning are brought together to be theorized and exemplified through analysis of teaching in a wide variety of classrooms and targeting both the content and processes of mathematical thinking. Highly recommended.” —Kaye Stacey, Emeritus Professor of Mathematics Education, University of Melbourne, Australia
“Many teachers in England are excited by the concept of teaching with variation and devising variation exercises to support their pupils’ mastery of mathematics. However, fully understanding and becoming proficient in its use takes time. This book provides a valuable resource to deepen understanding through the experiences of other teachers shared within the book and the insightful reflections of those who have researched this important area. —Debbie Morgan, Director for Primary Mathematics, National Centre for Excellence in the Teaching of Mathematics, United Kingdom
Educational Researchers and their students
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