Early Algebraization

1. Front Matter

   Pages I-XXIII

   PDF

2. Curricular Perspective

   1. Front Matter

      Pages 1-2

      PDF

   2. Preface to Part I

      • Jinfa Cai, Eric Knuth

      Pages 3-4

   3. Functional Thinking as a Route Into Algebra in the Elementary Grades

      • Maria L. Blanton, James J. Kaput

      Pages 5-23

   4. Developing Students’ Algebraic Thinking in Earlier Grades: Lessons from China and Singapore

      • Jinfa Cai, Swee Fong Ng, John C. Moyer

      Pages 25-41

   5. Developing Algebraic Thinking in the Context of Arithmetic

      • Susan Jo Russell, Deborah Schifter, Virginia Bastable

      Pages 43-69

   6. The Role of Theoretical Analysis in Developing Algebraic Thinking: A Vygotskian Perspective

      • Jean Schmittau

      Pages 71-85

   7. The Arithmetic-Algebra Connection: A Historical-Pedagogical Perspective

      • K. Subramaniam, Rakhi Banerjee

      Pages 87-107

   8. Shiki: A Critical Foundation for School Algebra in Japanese Elementary School Mathematics

      • Tad Watanabe

      Pages 109-124

   9. Commentary on Part I

      • Jeremy Kilpatrick

      Pages 125-130

3. Cognitive Perspective

   1. Front Matter

      Pages 131-133

      PDF

   2. Preface to Part II

      • Eric Knuth, Jinfa Cai

      Pages 135-136

   3. Algebraic Thinking with and without Algebraic Representation: A Pathway for Learning

      • Murray S. Britt, Kathryn C. Irwin

      Pages 137-159

   4. Examining Students’ Algebraic Thinking in a Curricular Context: A Longitudinal Study

      • Jinfa Cai, John C. Moyer, Ning Wang, Bikai Nie

      Pages 161-185

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

      • Tom J. Cooper, Elizabeth Warren

      Pages 187-214

   6. Algebra in the Middle School: Developing Functional Relationships Through Quantitative Reasoning

      • Amy B. Ellis

      Pages 215-238

   7. Representational Competence and Algebraic Modeling

      • Andrew Izsák

      Pages 239-258

   8. Middle School Students’ Understanding of Core Algebraic Concepts: Equivalence & Variable

      • Eric J. Knuth, Martha W. Alibali, Nicole M. McNeil, Aaron Weinberg, Ana C. Stephens

      Pages 259-276

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

      • Joan Moss, Susan London McNab

      Pages 277-301

   10. Grade 2 Students’ Non-Symbolic Algebraic Thinking

       • Luis Radford

       Pages 303-322

In this volume, the authors address the development of students’ algebraic thinking in the elementary and middle school grades from curricular, cognitive, and instructional perspectives. The volume is also international in nature, thus promoting a global dialogue on the topic of early Algebraization.

• curriculum
• early Algebraization
• international perspective
• learning and instruction
• mathematics education

• Dept. Mathematical Sciences, University of Delaware, Newark, USA

  Jinfa Cai

• University of Wisconsin-Madison, Madison, USA

  Eric Knuth

Jinfa Cai is professor at the University of Delaware, USA. Eric Knuth is professor at the University of Wisconsin,  USA.

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