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Table of Contents
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
ᷠPreservice Teachers? Knowledge to Teach Functional Thinking
Conclusions and Looking Ahead.
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
ᷠPreservice Teachers? Knowledge to Teach Functional Thinking
Conclusions and Looking Ahead.