Drawing on rich classroom observations of educators teaching in China and the U.S., this book details an innovative and effective approach to teaching algebra at the elementary level, namely, "teaching through example-based problem solving" (TEPS).
Recognizing young children's particular cognitive and developmental capabilities, this book powerfully argues for the importance of infusing algebraic thinking into early grade mathematics teaching and illustrates how this has been achieved by teachers in U.S. and Chinese contexts. Documenting best practice and students' responses to example-based instruction, the text demonstrates that this TEPS approach - which involves the use of worked examples, representations, and deep questions - helps students learn and master fundamental mathematical ideas, making it highly effective in developing algebraic readiness and mathematical understanding.
This text will benefit post-graduate students, researchers, and academics in the fields of mathematics, STEM, and elementary education, as well as algebra research more broadly. Those interested in teacher education, classroom practice, and developmental and cognitive psychology will also find this volume of interest.
Meixia Ding is Associate Professor of mathematics education in the College of Education and Human Development, Temple University, USA.
Chapter 1: Introduction
Chapter 2: Inverse Relation between Addition and Subtraction
Chapter 3: Inverse Relation between Multiplication and Division
Chapter 4: Properties of Addition: CP and AP
Chapter 5: Properties of Multiplication: CP, AP, and DP
Chapter 6: Conclusion
Appendix 1: A Chinese G1 Lesson Plan about Fact Family (Additive Inverse)
Appendix 2: A Chinese G1 Lesson Plan about "Making a Ten to Add" (Informal Teaching of the AP)
Appendix 3: A Chinese G4 Lesson Plan about Formal Teaching of the CP and AP of Multiplication