© 2018

Visualizing Mathematics

The Role of Spatial Reasoning in Mathematical Thought

  • Kelly S. Mix
  • Michael T. Battista


  • Bridges two fields by including authors from psychology and education

  • Appeals to the growing interest among psychologists, education scholars, and mathematics educators in the convergence of psychology and education

  • Features cross-field commentaries


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

Table of contents

  1. Front Matter
    Pages i-xv
  2. Psychological Perspectives

    1. Front Matter
      Pages 1-1
    2. Eliza L. Congdon, Marina Vasilyeva, Kelly S. Mix, Susan C. Levine
      Pages 25-46
    3. Krzysztof Cipora, Philipp Alexander Schroeder, Mojtaba Soltanlou, Hans-Christoph Nuerk
      Pages 77-116
    4. Christopher Young, Susan C. Levine, Kelly S. Mix
      Pages 117-148
  3. Commentaries

  4. Educational Perspectives

  5. Commentaries

About this book


This unique volume surveys recent research on spatial visualization in mathematics in the fields of cognitive psychology and mathematics education. The general topic of spatial skill and mathematics has a long research tradition, but has been gaining attention in recent years, although much of this research happens in disconnected subfields. This volume aims to promote interaction between researchers, not only to provide a more comprehensive view of spatial visualization and mathematics, but also to stimulate innovative new directions in research based on a more coordinated effort. It features ten chapters authored by leading researchers in cognitive psychology and mathematics education, as well as includes dynamic commentaries by mathematics education researchers on cognitive psychology chapters, and by cognitive psychologists on mathematics education chapters. 

Among the topics included:

  •          From intuitive spatial measurement to understanding of units.
  •          Spatial reasoning: a critical problem-solving tool in children’s mathematics strategy tool-kit.
  •          What processes underlie the relation between spatial skill and mathematics?
  •          Learning with and from drawing in early years geometry.
  •          Communication of visual information and complexity of reasoning by mathematically talented students.

Visualizing Mathematics makes substantial progress in understanding the role of spatial reasoning in mathematical thought and in connecting various subfields of research. It promises to make an impact among psychologists, education scholars, and mathematics educators in the convergence of psychology and education.


Spatial reasoning Children Mathematics Psychology Education Visualization Elementary School High School Cognition Learning Space and mathematics Spatial skills STEM Cognitive psychology

Editors and affiliations

  • Kelly S. Mix
    • 1
  • Michael T. Battista
    • 2
  1. 1.Department of Human Development and Quantitative MethodologyUniversity of MarylandCollege ParkUSA
  2. 2.Department of Teaching and LearningThe Ohio State UniversityColumbusUSA

About the editors

Kelly S. Mix, Ph.D., is Professor and Chair of the Department of Human Development and Quantitative Methods at the University of Maryland.  A former elementary school teacher with a specialization in mathematics teaching and learning, she received her Ph.D. in Developmental Psychology from the University of Chicago in 1995.

Michael T. Battista is EHE Distinguished Professor of Mathematics Education at The Ohio State University.  He earned a B.S. degree in mathematics from Kent State University in 1971, an M.S. degree in mathematics from Purdue University in 1973, and a Ph.D. degree in mathematics education from Purdue University in 1977.  

Bibliographic information

  • Book Title Visualizing Mathematics
  • Book Subtitle The Role of Spatial Reasoning in Mathematical Thought
  • Editors Kelly S. Mix
    Michael T. Battista
  • Series Title Research in Mathematics Education
  • Series Abbreviated Title Res. Mathem. Edu.
  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Education Education (R0)
  • Hardcover ISBN 978-3-319-98766-8
  • eBook ISBN 978-3-319-98767-5
  • Series ISSN 2570-4729
  • Series E-ISSN 2570-4737
  • Edition Number 1
  • Number of Pages XV, 378
  • Number of Illustrations 56 b/w illustrations, 86 illustrations in colour
  • Topics Educational Psychology
    Mathematics Education
    Science Education
  • Buy this book on publisher's site