ZDM

, Volume 47, Issue 3, pp 331–343

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?

Original Article

Abstract

The ability to mentally rotate objects in space has been singled out by cognitive scientists as a central metric of spatial reasoning (see Jansen, Schmelter, Quaiser-Pohl, Neuburger, & Heil, 2013; Shepard & Metzler, 1971 for example). However, this is a particularly undeveloped area of current mathematics curricula, especially in North America. In this article we discuss what we mean by mental rotation, why it is important, and how it can be developed with young children in classrooms. We feature results from one team of teacher-researchers in Canada engaged in Lesson Study to develop enhanced theoretical understandings as well as practical applications in a geometry program that incorporates 2D and 3D mental rotations. Children in the Lesson Study classrooms (ages 4–8 years) demonstrated large gains in their mental rotation skills during 4 months of Lesson Study intervention in the Math for Young Children research program. The results of this study suggest that young children from a wide range of ability levels can engage in, and benefit from, classroom-based mental rotation activities. The study contributes to bridging a gap between cognitive science and mathematics education literature.

Keywords

Spatial reasoning Mental rotation Mathematics Young children Geometry 

References

  1. Bauer, B., & Jolicoeur, P. (1996). Stimulus dimensionality effects in mental rotation. Journal of Experimental Psychology: Human Performance and Perception, 22(1), 82–94.Google Scholar
  2. Bruce, C. & Flynn, T. (2012). Integrating instruction and play in a Kindergarten to Grade 2 lesson study project. In L.R. Van Zoest, J.J. Lo, & J.L. Kratky, (Eds.), Proceedings of the 34th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Kalamazoo: Western Michigan University.Google Scholar
  3. Bruce, C., Flynn, T. & Moss, J. (2013). A “no-ceiling” approach to young children’s mathematics: preliminary results of an innovative professional learning program. In Proceedings of the 35th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Chicago: University of Chicago.Google Scholar
  4. Bruce, C., Flynn, T., Ross, J., & Moss, J. (2011). Promoting teacher and student mathematics learning through lesson study: a design research approach. In B. Ubuz (Ed.), Proceedings of the thirty-fifth conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 193–200). Ankara: PME.Google Scholar
  5. Bruce, C., & Ladky, M. (2011). What’s going on backstage? Revealing the work of lesson study. In L. Hart, A. Alston, & A. Murata (Eds.), Lesson-study research and practice in mathematics education: learning together (pp. 243–249). New York: Springer.CrossRefGoogle Scholar
  6. Bruce, C., Moss, J., & Flynn, T. (2012). Report on year 1 of the Math for Young Children Lesson Study research project. Toronto: Literacy and Numeracy Secretariat.Google Scholar
  7. 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
  8. Cheng, Y. L., & Mix, K. S. (2013). Spatial training improves children’s mathematics. Journal of Cognition and Development (advanced online publication). doi:10.1080/15248372.2012.725186.
  9. Clements, D., & Sarama, J. (2004). Engaging Young children in mathematics: standards for early childhood mathematics education. Mahwah: Erlbaum.Google Scholar
  10. Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: the case of geometry. Journal of Mathematics Teacher Education, 14(2), 133–148.CrossRefGoogle Scholar
  11. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale: Lawrence Erlbaum Associates.Google Scholar
  12. Cooper, M. (1992). Three-dimensional symmetry. Educational Studies in Mathematics, 23(2), 179–202.CrossRefGoogle Scholar
  13. Copley, J. V. (2000). The young child and mathematics. Washington, DC: National Association for the Education of Young Children. http://www.naeyc.org/store/files/store/TOC/167.pdf. Accessed 11 March 2014.
  14. Delgado, A. R., & Prieto, G. (2004). Cognitive mediators and sex-related differences in mathematics. Intelligence, 32(1), 25–32.CrossRefGoogle Scholar
  15. Erhlich, S. B., Levine, S., & Goldin-Meadow, S. (2006). The importance of gesture in children’s spatial reasoning. Developmental Psychology, 42(6), 1259–1268.CrossRefGoogle Scholar
  16. Farmer, G., Verdine, B., Lucca, K., Davies, T., Dempsey, R., Newcombe, N., et al. (2013). Putting the pieces together: spatial skills at age 3 predict spatial and math performance at age 5. Seattle: SRCD poster presentation.Google Scholar
  17. Feng, J., Spence, I., & Pratt, J. (2007). Playing an action video game reduces gender differences in spatial cognition. Association for Psychological Science, 18(10), 850–855.CrossRefGoogle Scholar
  18. Frick, A., Ferrara, K., & Newcombe, N. S. (2013). Using a touch screen paradigm to assess the development of mental rotation between 3½ and 5½ years of age. Cognitive Processing (advance online publication). doi:10.1007/s10339-012-0534-0.
  19. Geary, D. C., Saults, S. J., Liu, F., & Hoard, M. K. (2000). Sex differences in cognition, computational fluency, and arithmetical reasoning. Journal of Experimental Child Psychology, 77, 337–353.CrossRefGoogle Scholar
  20. Harris, J., Newcombe, N. S., & Hirsh-Pasek, K. (2013). A new twist on studying the development of dynamic spatial transformations: mental paper folding in young children. Mind, Brain, and Education, 7(1), 49–55.CrossRefGoogle Scholar
  21. Hawes, Z., LeFevre, J., Chang, X. & Bruce, C. (2014). Mental rotation with tangible three-dimensional objects: a new measure sensitive to developmental differences in 4- to 8-year-old children. Mind, Brain, and Education (in press).Google Scholar
  22. Hoyek, N., Collet, C., Fargier, P., & Guillot, A. (2012). The use of the Vandenberg and Kuse mental rotation test in children. Journal of Individual Differences, 33(1), 62–67.CrossRefGoogle Scholar
  23. Jansen, P., Schmelter, A., Quaiser-Pohl, C., Neuburger, S., & Heil, M. (2013). Mental rotation performance in primary school age children: are there gender differences in chronometric tests? Cognitive Development, 28, 51–62.CrossRefGoogle Scholar
  24. Johnson, W., & Bouchard, T. J, Jr. (2005). The structure of human intelligence: it is verbal, perceptual, and image rotation (VPR), not fluid and crystallized. Intelligence, 33(4), 393–416.CrossRefGoogle Scholar
  25. Jones, K. (2001). Appendix 8: spatial thinking and visualization. In Teaching and learning geometry (pp. 11–19): a report of the Royal Society/Joint Mathematical Council Working Group, edited by The Royal Society.Google Scholar
  26. Jordan, N., & Levine, S. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15, 60–68.CrossRefGoogle Scholar
  27. Kaufman, S. B. (2007). Sex differences in mental rotation and spatial visualization ability: can they be accounted for by differences in working memory capacity? Intelligence, 35, 211–223.CrossRefGoogle Scholar
  28. Kinach, B. M. (2012). Fostering spatial vs. metric understanding in geometry. The Mathematics Teacher, 105(7), 534–540.CrossRefGoogle Scholar
  29. Kyttälä, M., & Lehto, J. (2008). Some factors underlying mathematical performance: the role of visuospatial working memory and non-verbal intelligence. European Journal of Psychology of Education, XXI(1), 77–94.CrossRefGoogle Scholar
  30. Levine, S. C., Huttenlocher, J., Taylor, A., & Langrock, A. (1999). Early sex differences in spatial skill. Developmental Psychology, 35(4), 940–949.CrossRefGoogle Scholar
  31. Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of gender differences in spatial abilities: a meta-analysis. Child Development, 56, 1479–1498.CrossRefGoogle Scholar
  32. Mix, K & Cheng, Y. (2012). The relation between space and math: developmental and educational implications. In J. B. Benson (Ed), Advances in child development and behaviour, Vol 42 (pp. 197–243). Burlington: Academic Press, Elsevier Inc.Google Scholar
  33. Newcombe, N., & Frick, A. (2010). Early education for spatial. Intelligence: why, what, and how. Mind, Brain and Education, 4(3), 102–111.Google Scholar
  34. Örnkloo, H., & von Hofsten, C. (2007) Fitting objects into holes: on the development of spatial cognition skills. Developmental Psychology, 43(2), 404–416.CrossRefGoogle Scholar
  35. Ozdemir, G. (2009). Exploring visuospatial thinking in learning about mineralogy: spatial orientation ability and spatial visualization ability. International Journal of Science and Mathematics Education, 8, 737–759.CrossRefGoogle Scholar
  36. Pazzaglia, F., & Moè, A. (2013). Cognitive styles and mental rotation ability in map learning. Cognitive Processing (advance online publication). doi:10.1007/s10339-013-0572-2.
  37. Sakonidis, C., & Potari, D. (2014). Mathematics teacher educators/researchers’ collaboration with teachers as a context for professional learning. The International Journal on Mathematics Education,. doi:10.1007/s11858-014-0569-z.Google Scholar
  38. Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701–703.CrossRefGoogle Scholar
  39. Shepard, S., & Metzler, D. (1988). Mental rotation: effects of dimensionality of objects and type of task. Journal of Experimental Psychology: Human Perception and Performance, 14, 3–11.Google Scholar
  40. Stylianides, A. J., & Stylianides, G. J. (2013). Seeking research-grounded solutions to problems of practice: classroom-based interventions in mathematics education. ZDMThe International Journal on Mathematics Education, 45(3), 333–340.Google Scholar
  41. Terlecki, M. S., Newcombe, N.S., & Little, M. (2008). Durable and generalized effects of spatial experience on mental rotation: Gender differences in growth patterns. Applied Cognitive Psychology, 22(7), 996–1013.Google Scholar
  42. Tolar, T. D., Lederberg, A. R., & Fletcher, J. M. (2009). A structural model of algebra achievement: computational fluency and spatial visualisation as mediators of the effect of working memory on algebra achievement. Educational Psychology, 29(2), 239–266.CrossRefGoogle Scholar
  43. Uttal, D. H., Miller, D. I., & Newcombe, N. S. (2013). Exploring and enhancing spatial thinking links to achievement in science, technology, engineering, and mathematics? Current Directions in Psychological Science, 22(5), 367–373.CrossRefGoogle Scholar
  44. Verdine, B. N., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2014). Finding the missing piece: blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education, 3(1), 7–13.CrossRefGoogle Scholar
  45. Wai, J., Lubinski, D., & Benbow, C. P. (2009). Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2014

Authors and Affiliations

  1. 1.School of Education and Professional LearningTrent UniversityPeterboroughCanada
  2. 2.Ontario Institute for Studies in EducationUniversity of TorontoTorontoCanada

Personalised recommendations