Part II Commentary 1: Mathematics Educators’ Perspectives on Spatial Visualization and Mathematical Reasoning

  • Beth M. CaseyEmail author
Part of the Research in Mathematics Education book series (RME)


The chapter by Lowrie and Logan (this volume) on spatial visualization and mathematics reasoning stands out from the chapters written by the other mathematics education researchers, because Lowrie and Logan address the importance of spatial reasoning across a range of mathematics content areas, rather than restricting their focus primarily to measurement or geometry mathematics content. They propose that spatial reasoning is important for content across mathematics because it supports both internal encoding and external decoding of spatial representations through the use of graphics.


  1. Boonen, A. J. H., van der Schoot, M., van Wesel, F., DeVries, M. H., & Jolles, J. (2013). What underlies successful word problem solving? A path analysis in sixth grade students. Contemporary Educational Psychology, 38, 271–279. Scholar
  2. Casey, B. M., Lombardi, C., Pollock, A., Fineman, B., & Pezaris, E. (2017). Girls’ spatial skills and arithmetic strategies in first grade as predictors of fifth grade analytical mathematics reasoning. Journal of Cognition and Development, 18(5), 530–555. Scholar
  3. Casey, B. M., Pezaris, E., Fineman, B., Pollock, A., Demers, L., & Dearing, E. (2015). A longitudinal analysis of early spatial skills compared to arithmetic and verbal skills as predictors of fifth-grade girls’ mathematics reasoning. Learning and Individual Differences, 40, 90–100. Scholar
  4. Frick, A. (2018). Spatial transformation abilities and their relation to later mathematics. performance. Psychological Research. Published online: April 10, 2018.
  5. Gonsalves, N., & Krawec, J. (2014). Using number lines to solve mathematics word problems: A strategy for students with learning disabilities. Learning Disabilities Research and Practice, 29(4), 160–170. Scholar
  6. Hegarty, M., & Kozhevnikov, M. (1999). Types of visual-spatial representations and mathematical problem solving. Journal of Educational Psychology, 91(4), 684–689. Scholar
  7. Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32. Scholar
  8. Ho, S. Y., & Lowrie, T. (2014). The model method: Students’ performance and its effectiveness. The Journal of Mathematical Behavior, 35, 87–100. Scholar
  9. Jitendra, A. K., Nelson, G., Pulles, S. M., Kiss, A. J., & Houseworth, J. (2016). Is mathematical representation of problems an evidence-based strategy for students with mathematical difficulties? Exceptional Children, 83(1), 8–25. Scholar
  10. Kingsdorf, S., & Krawec, J. (2016). A broad look at the literature on mathematics word problem-solving interventions for third graders. Cogent Education, 3(1), 1–12. Scholar
  11. Lowrie, T., Logan, T., & Ramful, A. (2016). Cross cultural comparison of grade 6 students’ performance and strategy use on graphic and non-graphic tasks. Learning and Individual Differences, 52, 97–108. Scholar
  12. Lowrie, T., & Logan, T. (this volume). The interaction between spatial reasoning constructs and mathematics understandings in elementary classrooms. In K. S. Mix & M. T. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought. New York: Springer.Google Scholar
  13. Mix, K. S., & Cheng, U. L. (2012). The relation between space and mathematics: Developmental and educational implications. In J. B. Benson (Ed.), Advances in child development and behavior (Vol. 42, pp. 199–243). Waltham, MA: Academic.Google Scholar
  14. Murata, A. (2008). Mathematics teaching and learning as a mediating process: The case of tape diagrams. Mathematical Thinking and Learning, 10(4), 374406. Scholar
  15. Peters, M., Laeng, B., Latham, K., Jackson, M., Zaiyouna, R., & Richardson, C. (1995). A redrawn Vandenberg and Kuse mental rotations test: Different versions and factors that affect performance. Brain and Cognition, 28(1), 39–58. Scholar
  16. Piaget, J., & Inhelder, B. (1956). The child’s conception of space. London: Routledge & Kegan Paul.Google Scholar
  17. Polya, G. (1965). Mathematical discovery; on understanding and teaching problem solving. Hoboken, NJ: Wiley.Google Scholar
  18. Sinclair, N., Moss, J., Hawes, Z., & Stephenson, C. (this volume). Learning with and from drawing in early years geometry. In K. S. Mix & M. T. Battista (Eds.), Visualizing mathematics: The role of spatial reasoning in mathematical thought. New York: Springer.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Lynch School of EducationBoston CollegeBostonUSA

Personalised recommendations