Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Introduction.- Part I Theoretical Perspectives for Developing Early Algebraic Thinking.- The Emergence of Symbolic Algebraic Thinking in Primary School.- 2 Implementing a Framework for Early Algebra.- 3 New Words and Concepts for Early Algebra Teaching: Sharing with Teachers Epistemological Issues in Early Algebra to Develop Students' Early Algebraic Thinking.- 4 Seeking, Using, and Expressing Structure in Numbers and Numerical Operations: A Fundamental Path to Developing Early Algebraic Thinking.- 5 Cultivating Early Algebraic Thinking.- Part II Learning to Think Algebraically in Primary and Lower Middle School.- 6 Characteristics of Korean Students' Early Algebraic Thinking: A Generalized Arithmetic Perspective.- 7 Function Tasks, Input, Output, and The Predictive Rule: How some Singapore Primary Children Construct the Rule.- 8 Algebraic Understanding of Equalities in Primary Classes .- 9 Observations of Structure within Shape Patterns.- 10 Generalizing Fractional Structures: A Critical Precursor To Algebraic Thinking.- 11 First Encounter with Variables by First and Third Grade Spanish Students.- Part III Teaching for the Development of Early Algebraic Thinking.- 12 Making Implicit Algebraic Thinking Explicit: Exploiting National Characteristics of German Approaches.- 13 Early Algebra as Analysis of Structure: A Focus on Operations.- 14 How Early Is too Early for Thinking Algebraically?.- 15 Cycles of Generalizing Activities in the Classroom.- 16 Scaffolding Teacher Practice to Develop Early Algebraic Reasoning.-  17 Preservice Teachers' Knowledge to Teach Functional Thinking.- Conclusions and Looking Ahead.

"This book is an excellent resource in the teaching of early algebra. ... The reader can certainly have a broad and international perspectives on teaching early algebra by reading this book and can be motivated to try out and conduct their own research study. I'm certainly motivated by this book." (Peter T. Olszewski, MAA Reviews, March, 2018)