Advertisement

Part I Commentary 3: Proposing a Pedagogical Framework for the Teaching and Learning of Spatial Skills: A Commentary on Three Chapters

  • Tom Lowrie
  • Tracy Logan
Chapter
Part of the Research in Mathematics Education book series (RME)

Abstract

Education, generally, and mathematics education specifically, have long-held associations with the field of psychology. Schoenfeld (1987) and Mayer (1992) both described the connections between the two fields and indeed, many educational theories of development evolved from psychology. To this point, one of the longest running groups in mathematics education derived from the field of cognitive psychology, namely, The International Group for the Psychology of Mathematics Education (IGPME). IGPME was established in 1976 under the guidance of Efraim Fischbein, a cognitive psychologist. Initially, the focus was, as the name suggested, on the developmental and psychological complexities of learning various mathematical concepts and processes. However, over the years, the organization has broadened to include new ways of thinking about mathematics learning that go beyond the purely cognitive aspect. In fact, very few cognitive psychologists attend the annual conference these days. Although the direct insights and engagement of cognitive psychology researchers are not commonplace, some overlap remains.

References

  1. Adler, J. (1998). A Language of teaching dilemmas: Unlocking the complex multilingual secondary mathematics classroom. For the Learning of Mathematics, 18(1), 24–33.Google Scholar
  2. Bruce, C. D., Davis, B., Sinclair, N., McGarvey, L., Hallowell, D., Drefs, M., … Woolcott, G. (2017). Understanding gaps in research networks: Using “spatial reasoning” as a window into the importance of networked educational research. Educational Studies in Mathematics, 95(2), 143–161.  https://doi.org/10.1007/s10649-016-9743-2CrossRefGoogle Scholar
  3. Bruce, C. D., & Hawes, Z. (2014). The role of 2D and 3D mental rotation in mathematics for young children: What is it? Why does it matter? And what can we do about it? ZDM—The International Journal on Mathematics Education, 47(3), 331–343.  https://doi.org/10.1007/s11858-014-0637-4CrossRefGoogle Scholar
  4. Burte, H., Gardony, A. L., Hutton, A., & Taylor, H. A. (2017). Think3d!: Improving mathematics learning through embodied spatial training. Cognitive Research: Principles and Implications, 2(13), 1–18.  https://doi.org/10.1186/s41235-017-0052-9CrossRefGoogle Scholar
  5. Casey, B. M., Andrews, N., Schindler, H., Kersh, J. E., Samper, A., & Copley, J. (2008). The development of spatial skills through interventions involving block building activities. Cognition and Instruction, 26(3), 269–309.CrossRefGoogle Scholar
  6. Cheng, Y. L., & Mix, K. S. (2014). Spatial training improves children’s mathematics ability. Journal of Cognition and Development, 15(1), 2–11.CrossRefGoogle Scholar
  7. Cobb, P. (1988). The tension between theories of learning and instruction in mathematics education. Educational Psychologist, 23(2), 87.CrossRefGoogle Scholar
  8. Hargittai, M., & Hargittai, I. (2009). Symmetry through the eyes of a chemist (3rd ed.). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  9. Lerman, S. (2003). Cultural, discursive psychology: A sociocultural approach to studying the teaching and learning of mathematics learning discourse. In C. Kieran, E. Forman, & A. Sfard (Eds.), Learning discourse: Sociocultural approaches to research in mathematics education (pp. 87–113). Dordrecht, The Netherlands: Springer.CrossRefGoogle Scholar
  10. Livio, M. (2006). The equation that couldn’t be solved: How mathematical genius discovered the language of symmetry. New York: Simon and Schuster.Google Scholar
  11. Lowrie, T., & Kay, R. (2001). Task representation: The relationship between visual and nonvisual solution methods and problem difficulty in elementary school mathematics. Journal of Educational Research, 94(4), 248–253.CrossRefGoogle Scholar
  12. Lowrie, T., & Patahuddin, S. M. (2015). ELPSA as a lesson design framework. Journal of Mathematics Education, 6(2), 1–15.Google Scholar
  13. Lowrie, T., Logan, T., & Ramful, A. (2017). Visuospatial training improves elementary students’ mathematics performance. British Journal of Educational Psychology, 87(2), 170–186. https://doi.org/10.1111/bjep.12142CrossRefGoogle Scholar
  14. Mayer, R. E. (1992). A series of books in psychology. Thinking, problem solving, cognition (2nd ed.). New York, NY: W H Freeman/Times Books/Henry Holt and Company.Google Scholar
  15. Martin, L. C. (2008). Folding back and the dynamical growth of mathematical understanding: Elaborating on the Pirie-Kieren Theory. Journal of Mathematical Behavior, 27, 64–85.CrossRefGoogle Scholar
  16. Mix, K., & Cheng, Y. (2018, April). More than just numbers: Varied predictors of mathematical knowledge. Paper presented at the American Education Research Association Conference, New York, NY.Google Scholar
  17. Mix, K., Levine, S., Cheng, Y., Young, C., Hambrick, D., & Konstantopoulos, S. (2017). The latent structure of spatial skills and mathematics: A replication of the two-factor model. Journal of Cognition and Development, 18(4), 465–492.  https://doi.org/10.1080/15248372.2017.1346658CrossRefGoogle Scholar
  18. Pillay, H. (1998). Cognitive processes and strategies employed by children to learn spatial representations. Learning and Instruction, 8(1), 1–18.CrossRefGoogle Scholar
  19. Schoenfeld, A. H. (Ed.). (1987). Cognitive science and mathematics education. Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  20. Stieff, M. (2007). Mental rotation and diagrammatic reasoning in science. Learning and Instruction, 17, 219–234.CrossRefGoogle Scholar
  21. Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Alden, A. R., Warren, C., & Newcombe, N. S. (2013). The malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of CanberraBruceAustralia

Personalised recommendations