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Early Algebraization

A Global Dialogue from Multiple Perspectives

  • Book
  • © 2011

Overview

Editors:
  1. Jinfa Cai

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

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    You can also search for this editor in PubMed   Google Scholar

  2. Eric Knuth

    1. University of Wisconsin-Madison, Madison, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Addresses early algebra research from an international perspective
  • Addresses early algebra research from curricular, cognitive, and instructional perspectives
  • Addresses early algebra research from the elementary grades through the middle grades
  • Provides a comprehensive account of current early algebra research
  • Includes supplementary material: sn.pub/extras

Part of the book series: Advances in Mathematics Education (AME)

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Table of contents (29 chapters)

  1. Front Matter

    Pages I-XXIII
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  2. Curricular Perspective

    1. Front Matter

      Pages 1-2
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    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
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    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
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Keywords

About this book

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.

Editors and Affiliations

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

    Jinfa Cai

  • University of Wisconsin-Madison, Madison, USA

    Eric Knuth

About the editors

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

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