Teaching and Learning Mathematics through Variation: Confucian Heritage Meets Western Theories

Front Matter....Pages i-xv
Front Matter....Pages 1-1
Introduction....Pages 3-11
Theory and Development of Teaching Through Variation in Mathematics in China....Pages 13-41
‘Bianshi’ and the Variation Theory of Learning....Pages 43-67
Variation in Tool-Based Mathematics Pedagogy....Pages 69-84
Pedagogy of Variations....Pages 85-103
Front Matter....Pages 105-105
Introduction....Pages 107-109
Characteristics of Teaching Mathematical Problem Solving in China....Pages 111-125
Teaching the Formula of Perfect Square through Bianshi Teaching....Pages 127-150
Teaching Geometrical Concepts through Variation....Pages 151-168
Teaching Geometry Review Lesson through Variation....Pages 169-186
Teaching Algebra through Variations....Pages 187-205
Front Matter....Pages 207-207
Introduction....Pages 209-212
Strategies for Using Variation Tasks in Selected Mathematics Textbooks in China....Pages 213-239
An Expert Teacher’s Use of Teaching with Variation to Support a Junior Mathematics Teacher’s Professional Learning....Pages 241-266
Teaching and Learning Mathematics through Variation in Lesson Study....Pages 267-293
Front Matter....Pages 295-295
Introduction....Pages 297-300
Improving Teaching Through Variation....Pages 301-320
Developing Algebraic Reasoning through Variation in the U.S.....Pages 321-339
Using Variation of Multiplicity in Highlighting Critical Aspects of Multiple Solution Tasks and Modeling Tasks....Pages 341-353
Learning to Teach with Variation....Pages 355-372
Front Matter....Pages 373-373
Teaching through Variation....Pages 375-388
Teaching through Variation....Pages 389-406
Issues in Variation Theory and How it Could Inform Pedagogical Choices....Pages 407-438
Back Matter....Pages 439-459