© 2019

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

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

About the editors

Anderson Norton is Professor in the Department of Mathematics at Virginia Tech. His research focuses on the epistemology of mathematics. This work has generated interdisciplinary collaborations with psychologists and neuroscientists. Prior to this volume, Norton served as chair of the steering committee for the North American Chapter of the International Group for the Psychology of Mathematics Education, chair of the editorial panel for the Journal for Research in Mathematics Education, and guest editor (along with Julie Nurnberger-Haag) for a special issue of the Journal of Numerical Cognition—bridging frameworks from psychology and mathematics education.

Martha W. Alibali is Vilas Distinguished Achievement Professor in the Departments of Psychology and Educational Psychology atthe University of Wisconsin-Madison. Her research investigates processes of knowledge change in cognitive development and mathematics learning. She also conducts basic research on gestures and on communication processes in instructional settings. She collaborates with scholars from a range of fields, including mathematics education, educational psychology, communicative disorders and computer science. She is a recipient of the Friedrich Wilhelm Bessel Research Prize from the Alexander von Humboldt Foundation, and she is co-author (with Robert Siegler) of the cognitive development textbook, Children’s Thinking.

Bibliographic information

  • Book Title Constructing Number
  • Book Subtitle Merging Perspectives from Psychology and Mathematics Education
  • Editors Anderson Norton
    Martha W. Alibali
  • Series Title Research in Mathematics Education
  • Series Abbreviated Title Res. Mathem. Edu.
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Hardcover ISBN 978-3-030-00490-3
  • eBook ISBN 978-3-030-00491-0
  • Series ISSN 2570-4729
  • Series E-ISSN 2570-4737
  • Edition Number 1
  • Number of Pages XXI, 370
  • Number of Illustrations 25 b/w illustrations, 27 illustrations in colour
  • Topics Mathematics Education
    Developmental Psychology
    Educational Psychology
  • Buy this book on publisher's site


“The research reported in this book covers a range of grade levels and I found it interesting as an undergraduate math education researcher. I would recommend this book to researchers at any level that are doing cognitive work around conceptions of number, value, and their representations.” (MAA Reviews, May 24, 2020)

“This is a volume for mathematics education researchers and for anyone who studies the cognitive development of children. Summing Up: Recommended. Graduate students, researchers, faculty.” (R. M. Fischer, Choice, Vol. 57 (4), December, 2019)