© 2018

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

The Global Evolution of an Emerging Field of Research and Practice

  • Carolyn Kieran

Part of the ICME-13 Monographs book series (ICME13Mo)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Theoretical Perspectives for Developing Early Algebraic Thinking

    1. Front Matter
      Pages 1-1
    2. Maria Blanton, Bárbaras M. Brizuela, Ana Stephens, Eric Knuth, Isil Isler, Angela Murphy Gardiner et al.
      Pages 27-49
    3. David W. Carraher, Analúcia D. Schliemann
      Pages 107-138
  3. Learning to Think Algebraically in Primary and Lower Middle School

  4. Teaching for the Development of Early Algebraic Thinking

    1. Front Matter
      Pages 281-281
    2. Susanne Strachota, Eric Knuth, Maria Blanton
      Pages 351-378
    3. Jodie Hunter, Glenda Anthony, David Burghes
      Pages 379-401

About this book


This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings.

The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.


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Editors and affiliations

  • Carolyn Kieran
    • 1
  1. 1.Département de MathématiquesUniversité du Québec à MontréalMontréalCanada

Bibliographic information

  • Book Title Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds
  • Book Subtitle The Global Evolution of an Emerging Field of Research and Practice
  • Editors Carolyn Kieran
  • Series Title ICME-13 Monographs
  • Series Abbreviated Title ICME-13 Monographs
  • DOI
  • Copyright Information Springer International Publishing AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Hardcover ISBN 978-3-319-68350-8
  • Softcover ISBN 978-3-319-88586-5
  • eBook ISBN 978-3-319-68351-5
  • Series ISSN 2520-8322
  • Series E-ISSN 2520-8330
  • Edition Number 1
  • Number of Pages XIII, 443
  • Number of Illustrations 130 b/w illustrations, 9 illustrations in colour
  • Topics Mathematics Education
    Learning & Instruction
    Teaching and Teacher Education
  • Buy this book on publisher's site


“This book is an excellent resource in the teaching of early algebra. … The reader can certainly have a broad and international perspectives on teaching early algebra by reading this book and can be motivated to try out and conduct their own research study. I’m certainly motivated by this book.” (Peter T. Olszewski, MAA Reviews, March, 2018)