Constructing Number

Merging Perspectives from Psychology and Mathematics Education

  • Anderson Norton
  • Martha W. Alibali

Part of the Research in Mathematics Education book series (RME)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Anderson Norton, Martha W. Alibali
    Pages 1-10
  3. Natural Numbers and Operations on Natural Numbers

    1. Front Matter
      Pages 11-11
    2. Douglas H. Clements, Julie Sarama, Beth L. MacDonald
      Pages 13-45
    3. Jake McMullen, Jenny Yun-Chen Chan, Michèle M. M. Mazzocco, Minna M. Hannula-Sormunen
      Pages 69-86
    4. Kelly S. Mix, Linda B. Smith, Sandra Crespo
      Pages 87-121
  4. Fractions and Operations on Fractions

  5. Integers and Operations on Integers

    1. Front Matter
      Pages 249-249
    2. Laura Bofferding
      Pages 251-277
    3. Nicole M. Wessman-Enzinger
      Pages 279-305
    4. Sashank Varma, Kristen P. Blair, Daniel L. Schwartz
      Pages 307-327
    5. Martha W. Alibali, Anderson Norton
      Pages 341-353
  6. Back Matter
    Pages 355-370

About this book


The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.


Approximate Number System Educational Neuroscience Fractions Integers Number Number Operations Numerical Cognition Subitzing

Editors and affiliations

  • Anderson Norton
    • 1
  • Martha W. Alibali
    • 2
  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of PsychologyUniversity of Wisconsin–MadisonMadisonUSA

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Education
  • Print ISBN 978-3-030-00490-3
  • Online ISBN 978-3-030-00491-0
  • Series Print ISSN 2570-4729
  • Series Online ISSN 2570-4737
  • Buy this book on publisher's site