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Foreword
Acknowledgements
Part I: Theoretical Perspectives
Introduction
Theory and Development of Teaching through Variation in Mathematics in China
‘Bianshi’ and the Variation Theory of Learning: Illustrating Two Frameworks of Variation and Invariance in the Teaching of Mathematics
Variation in Tool-Based Mathematics Pedagogy: The Case of Dynamic Virtual Tool
Pedagogy of Variations: Synthesis of Various Notions of Variation Pedagogy
Part II: Variation as a Pedagogical Perspective for Classroom Instruction in China
Introduction
Characteristics of Teaching Mathematical Problem Solving in China: Analysis of a Lesson from the Perspective of Variation
Teaching the Formula of Perfect Square through Bianshi Teaching
Teaching Geometrical Concepts through Variation: A Case Study of a Shanghai Lesson
Teaching Geometry Review Lesson through Variation: A Case Study
Teaching Algebra through Variations: Contrast, Generalization, Fusion, and Separation
Part III: The Pedagogical Perspective of Variations as a Principle for Curriculum Development and Teacher Professional Development in China
Introduction: “The Lesson Plan is Only the Teacher’s Hypothesis of Students’ Learning”
Strategies for Using Variation Tasks in Selected Mathematics Textbooks in China
An Expert Teacher’s Use of Teaching with Variation to Support a Junior Mathematics Teacher’s Professional Learning
Teaching and Learning Mathematics through Variation in Lesson Study
Part IV: Use of the Pedagogy of Variation Around the World
Introduction: Putting Variation Theory to Work
Improving Teaching through Variation: A Japanese Perspective
Developing Algebraic Reasoning through Variation in the U.S.
Using Variation of Multiplicity in Highlighting Critical Aspects of Multiple Solution Tasks and Modeling Tasks
Learning to Teach with Variation: Experiences from Learning Study in Sweden
Part V: Commentary and Conclusion
Teaching through Variation: An Asian Perspective – Is the Variation Theory of Learning Varying?
Teaching through Variation: A European Perspective
Issues in Variation Theory and How It Could Inform Pedagogical Choices
About the Authors
Subject Index.

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