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Constructing Number

Merging Perspectives from Psychology and Mathematics Education

  • Synergizes research across two disciplines—mathematics education and psychology—to address how children construct number
  • Addresses a range of change mechanisms (e.g., reflective abstraction, analogy), as well as a range of social contexts (e.g., informal interactions, formal educational settings), and a range of tools (e.g., curricular materials, technological tools)
  • Includes co-authored chapters and commentaries at the end of each section to create dialogue among scholars from different disciplines

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

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xxi
  2. Mathematics in Action

    • Anderson Norton, Martha W. Alibali
    Pages 1-10
  3. Natural Numbers and Operations on Natural Numbers

    1. Front Matter

      Pages 11-11
    2. Subitizing: The Neglected Quantifier

      • Douglas H. Clements, Julie Sarama, Beth L. MacDonald
      Pages 13-45
    3. Spontaneous Mathematical Focusing Tendencies in Mathematical Development and Education

      • Jake McMullen, Jenny Yun-Chen Chan, Michèle M. M. Mazzocco, Minna M. Hannula-Sormunen
      Pages 69-86
    4. Leveraging Relational Learning Mechanisms to Improve Place Value Instruction

      • Kelly S. Mix, Linda B. Smith, Sandra Crespo
      Pages 87-121
  4. Fractions and Operations on Fractions

    1. Front Matter

      Pages 133-133
    2. Understanding Fractions: Integrating Results from Mathematics Education, Cognitive Psychology, and Neuroscience

      • Andreas Obersteiner, Thomas Dresler, Silke M. Bieck, Korbinian Moeller
      Pages 135-162
    3. Commentary on Fractions

      • Sybilla Beckmann
      Pages 237-248
  5. Integers and Operations on Integers

    1. Front Matter

      Pages 249-249
    2. Understanding Negative Numbers

      • Laura Bofferding
      Pages 251-277
    3. Integers as Directed Quantities

      • Nicole M. Wessman-Enzinger
      Pages 279-305
    4. Cognitive Science Foundations of Integer Understanding and Instruction

      • Sashank Varma, Kristen P. Blair, Daniel L. Schwartz
      Pages 307-327
    5. Synergizing Research on Constructing Number: Themes and Prospects

      • 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.

Reviews

“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)

Editors and Affiliations

  • Department of Mathematics, Virginia Tech, Blacksburg, USA

    Anderson Norton

  • Department of Psychology, University of Wisconsin–Madison, Madison, USA

    Martha W. Alibali

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

  • DOI: https://doi.org/10.1007/978-3-030-00491-0

  • Publisher: Springer Cham

  • eBook Packages: Education, Education (R0)

  • Copyright Information: Springer Nature Switzerland AG 2019

  • Hardcover ISBN: 978-3-030-00490-3Published: 24 January 2019

  • eBook ISBN: 978-3-030-00491-0Published: 17 December 2018

  • 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 it now

Buying options

eBook USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access