Early Algebraization

Chapter 1 Preface to Part I

Chapter 2 Functional Thinking as a Route Into Algebra in the Elementary Grades

Chapter 3 Developing Students’ Algebraic Thinking in Earlier Grades: Lessons from China and Singapore

Chapter 4 Developing Algebraic Thinking in the Context of Arithmetic

Chapter 5 The Role of Theoretical Analysis in Developing Algebraic Thinking: A Vygotskian Perspective

Chapter 6 The Arithmetic-Algebra Connection: A Historical-Pedagogical Perspective

Chapter 7 Shiki : A Critical Foundation for School Algebra in Japanese Elementary School Mathematics

Chapter 8 Commentary on Part I

Chapter 9 Preface to Part II

Chapter 10 Algebraic Thinking with and without Algebraic Representation: A Pathway for Learning

Chapter 11 Examining Students’ Algebraic Thinking in a Curricular Context: A Longitudinal Study

Chapter 12 Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning

Chapter 13 Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning

Chapter 14 Representational Competence and Algebraic Modeling

Chapter 15 Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable

Chapter 16 An Approach to Geometric and Numeric Patterning that Fosters Second Grade Students’ Reasoning and Generalizing about Functions and Co-variation

Chapter 17 Grade 2 Students’ Non-Symbolic Algebraic Thinking

Chapter 18 Formation of Pattern Generalization Involving Linear Figural Patterns Among Middle School Students: Results of a Three-Year Study

Chapter 19 Commentary on Part II

Chapter 20 Preface to Part III

Chapter 21 Prospective Middle-School Mathematics Teachers’ Knowledge of Equations and Inequalities

Chapter 22 The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School

Chapter 23 Professional Development to Support Students’ Algebraic Reasoning: An Example from the Problem-Solving Cycle Model

Chapter 24 Using Habermas’ Theory of Rationality to Gain Insight into Students’ Understanding of Algebraic Language

Chapter 25 Theoretical Issues and Educational Strategies for Encouraging Teachers to Promote a Linguistic and Metacognitive Approach to Early Algebra

Chapter 26 A Procedural Focus and a Relationship Focus to Algebra: How U.S. Teachers and Japanese Teachers Treat Systems of Equations

Chapter 27 Teaching Algebraic Equations with Variation in Chinese Classroom

Chapter 28 Commentary on Part III

Chapter 29 Overall Commentary on Early Algebraization: Perspectives for Research and Teaching