First-graders’ spatial-mathematical reasoning about plane and solid shapes and their representations
The primary goal of the study was to explore first-grade children’s reasoning about plane and solid shapes across various kinds of geometric representations. Children were individually interviewed while completing a shape-matching task developed for this study. This task required children to compose and decompose geometric figures to identify geometric shapes that either matched or did not match the stimulus shape. The stimulus shapes were 2D diagrams of plane and solid-shape geometric figures. The results showed that children overestimated the significance of triangular vertices (“pointiness”); certain kinds of scaling demands gave children trouble in shape classification; children had trouble translating lines found in 2D diagrams into 3D visual boundaries, especially where projected curvature was involved; and that children had difficulty reasoning consistently across the task. Implications for future research as well as teaching recommendations are discussed.
KeywordsEarly geometry Spatial reasoning Dimensionality Mathematical diagrams
- Duval, R. (1995). Geometrical pictures: Kinds of representation and specific processings. In Exploiting mental imagery with computers in mathematics education (pp. 142–157). Berlin, Heidelberg: Springer.Google Scholar
- Hegarty, M., Crookes, R. D., Dara-Abrams, D., & Shipley, T. F. (2010). Do all science disciplines rely on spatial abilities? Preliminary evidence from self-report questionnaires. In Spatial Cognition VII (pp. 85–94). Berlin, Heidelberg: Springer.Google Scholar
- IBM Corporation. (2013). IBM SPSS Statistics for Windows, Version 22,0. Armonk: IBM Corp.Google Scholar
- Lonergan, B. (1997). In F. E. Crowe, & R. M. Doran, (Eds.), Verbum: Word and Idea in Aquinas, Vol. 2 of the Collected Works of Bernard Lonergan, Toronto: University of Toronto Press.Google Scholar
- Ng, O., & Sinclair, N. (2015). Young children reasoning about symmetry in a dynamic geometry environment. ZDM Mathematics Education, 47(3). doi:10.1007/s11858-014-0660-5.
- Noldus Information Technology. (2008). The Observer XT 8.0 [Computer software]. Wageningen: Noldus Information Technology.Google Scholar
- Steenpaß, A., & Steinbring, H. (2013). Young students’ subjective interpretations of mathematical diagrams: elements of the theoretical construct “frame-based interpreting competence”. ZDM - The International Journal on Mathematics Education, 46(1), 3–14, doi:10.1007/s11858-013-0544-0.
- Thom, J.S., & McGarvey, L. (2015). The act and artifact of drawing(s): Observing geometric thinking with, in, and through children’s drawings. ZDM Mathematics Education, 47(3) (this issue).Google Scholar
- van Hiele, P. (1986). Structure and insight: a theory of mathematics education. New York.Google Scholar