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

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.