Early Algebraization: A Global Dialogue from Multiple Perspectives

Front Matter....Pages I-XXIII
Front Matter....Pages 1-2
Preface to Part I....Pages 3-4
Functional Thinking as a Route Into Algebra in the Elementary Grades....Pages 5-23
Developing Students’ Algebraic Thinking in Earlier Grades: Lessons from China and Singapore....Pages 25-41
Developing Algebraic Thinking in the Context of Arithmetic....Pages 43-69
The Role of Theoretical Analysis in Developing Algebraic Thinking: A Vygotskian Perspective....Pages 71-85
The Arithmetic-Algebra Connection: A Historical-Pedagogical Perspective....Pages 87-107
 Shiki : A Critical Foundation for School Algebra in Japanese Elementary School Mathematics....Pages 109-124
Commentary on Part I....Pages 125-130
Front Matter....Pages 131-133
Preface to Part II....Pages 135-136
Algebraic Thinking with and without Algebraic Representation: A Pathway for Learning....Pages 137-159
Examining Students’ Algebraic Thinking in a Curricular Context: A Longitudinal Study....Pages 161-185
Years 2 to 6 Students’ Ability to Generalise: Models, Representations and Theory for Teaching and Learning....Pages 187-214
Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning....Pages 215-238
Representational Competence and Algebraic Modeling....Pages 239-258
Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable....Pages 259-276
An Approach to Geometric and Numeric Patterning that Fosters Second Grade Students’ Reasoning and Generalizing about Functions and Co-variation....Pages 277-301
Grade 2 Students’ Non-Symbolic Algebraic Thinking....Pages 303-322
Formation of Pattern Generalization Involving Linear Figural Patterns Among Middle School Students: Results of a Three-Year Study....Pages 323-366
Commentary on Part II....Pages 367-373
Front Matter....Pages 375-376
Preface to Part III....Pages 377-378
Front Matter....Pages 375-376
Prospective Middle-School Mathematics Teachers’ Knowledge of Equations and Inequalities....Pages 379-408
The Algebraic Nature of Fractions: Developing Relational Thinking in Elementary School....Pages 409-428
Professional Development to Support Students’ Algebraic Reasoning: An Example from the Problem-Solving Cycle Model....Pages 429-452
Using Habermas’ Theory of Rationality to Gain Insight into Students’ Understanding of Algebraic Language....Pages 453-481
Theoretical Issues and Educational Strategies for Encouraging Teachers to Promote a Linguistic and Metacognitive Approach to Early Algebra....Pages 483-510
A Procedural Focus and a Relationship Focus to Algebra: How U.S. Teachers and Japanese Teachers Treat Systems of Equations....Pages 511-528
Teaching Algebraic Equations with Variation in Chinese Classroom....Pages 529-556
Commentary on Part III....Pages 557-577
Overall Commentary on Early Algebraization: Perspectives for Research and Teaching....Pages 579-593
Back Matter....Pages 595-623