International Electronic Journal of Mathematics Education

Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Kenan KX. Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems. Int Elect J Math Ed. 2018;13(2), 57-60. https://doi.org/10.12973/iejme/2695
APA 6th edition
In-text citation: (Kenan, 2018)
Reference: Kenan, K. X. (2018). Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems. International Electronic Journal of Mathematics Education, 13(2), 57-60. https://doi.org/10.12973/iejme/2695
Chicago
In-text citation: (Kenan, 2018)
Reference: Kenan, Kok Xiao-Feng. "Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems". International Electronic Journal of Mathematics Education 2018 13 no. 2 (2018): 57-60. https://doi.org/10.12973/iejme/2695
Harvard
In-text citation: (Kenan, 2018)
Reference: Kenan, K. X. (2018). Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems. International Electronic Journal of Mathematics Education, 13(2), pp. 57-60. https://doi.org/10.12973/iejme/2695
MLA
In-text citation: (Kenan, 2018)
Reference: Kenan, Kok Xiao-Feng "Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems". International Electronic Journal of Mathematics Education, vol. 13, no. 2, 2018, pp. 57-60. https://doi.org/10.12973/iejme/2695
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Kenan KX. Seeing and the Ability to See: A Framework for Viewing Geometric Cube Problems. Int Elect J Math Ed. 2018;13(2):57-60. https://doi.org/10.12973/iejme/2695

Abstract

Perceiving a 3-dimensional (3D) diagram on a 2-dimensional (2D) surface or plane can be a challenging endeavor for students at the elementary or primary grade levels. Adding to this challenge are the intricacies present in understanding the processes involved in geometric problems of such a nature. To ease the comprehension of these processes, this paper proposes a framework that traces the processes in viewing 3D diagrams represented on a 2D plane. This framework, abbreviated as SMS, espouses three main processes; (1) Seeing the 2D plane, (2) Making sense of the 3D diagram on the 2D plane, and (3) Seeing the 3D diagram. Implications for teaching and learning are also offered.

References

  • Battista, M. T., & Clements, D. H. (1996). Students’ Understanding of Three-Dimensional Rectangular Arrays of Cubes. Journal for Research in Mathematics Education, 27(3), 258-292.
  • Ben-Haim, D., Lappan, G., & Houang, R. T. (1985). Visualizing Rectangular Solids Made of Small Cubes: Analyzing and Effecting Students’ Performance. Educational Studies in Mathematics, 16(4), 389-409. https://doi.org/10.1007/BF00417194
  • Duval, R. (1999). Representation, vision and visualization: Cognitive functions in mathematical thinking. Basic issues for learning. In F. Hitt & M. Santos (Eds.), Proceedings of the 21st North American PME Conference, 1, 3-26.
  • Hirstein, J. J. (1981). The second national assessment in mathematics: Area and volume. The Mathematics Teacher, 74(9), 704–708.
  • McGee, M. G. (1979). Human spatial abilities: Sources of sex differences. New York: Praeger.
  • National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, Va.: NCTM, 2000.
  • Zazkis, R., Dubinsky, E., & Dauterman, E. (1996). Using visual and analytic strategies: A study of students’ understanding of permutation and symmetry groups. Journal for Research in Mathematics Education, 27, 435-475. https://doi.org/10.2307/749876

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.