Covering shapes with tiles: Primary students’ visualisation and drawing
- 203 Downloads
- 2 Citations
Abstract
Students’ early area concepts were investigated by an analysis of responses to a worksheet of items that involved visualising the tiling of given figures. Students in Years 2 and 4 in four schools attempted the items on three occasions and some of the students completed ten classroom spatial activities. Half the students had difficulty visualising the tiling of shapes, but students who participated in spatial activities were generally more successful in determining the number of tiles that would cover a shape. Students’ drawings indicated a varying awareness of structural features such as alignment and tile size. Students who drew the tilings were more likely to be successful on the items involving trapezia. The tiling items were part of a test of spatial thinking, Thinking About 2D Shapes, and scores on the overall test were very highly correlated with results for the tiling items.
Keywords
Equilateral Triangle Concrete Material Tile Size Spatial Activity Pattern BlockPreview
Unable to display preview. Download preview PDF.
References
- Andrich, D. (1988).Rasch models for measurement. Newbury Park, CA: Sage.Google Scholar
- Clements, M. A. (1995). The rhetoric/reality gap in school mathematics.Reflections, 20(1), 2–9.Google Scholar
- Doig, B., Cheeseman, J., & Lindsey, J. (1995). The medium is the message: Measuring area with different media. In B. Atweh & S. Flavel (Eds.),Galtha (Proceedings of 18th annual conference of Mathematics Education Research Group of Australasia, pp. 229–234). Darwin: MERGA.Google Scholar
- Gagné, R. M., & White, R. T. (1978). Memory structures and learning outcomes.Review of Educational Research, 48,187–222.Google Scholar
- Gelman, R., & Gallistel, C. R. (1978).The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
- Haft, K., & Sinkinson, A. (1988). Forging the link between practical and formal mathematics. In A. Borbas (Ed.),Proceedings of 12th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 380–384). Vesprem, Hungary: Program Committee.Google Scholar
- Mansfield, H., & Scott, J. (1990). Young children solving spatial problems. In G. Booker, P. Cobb, & T. N. de Mendicuti (Eds.),Proceedings of 14th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 275–282). Oaxtepec, Mexico: Program Committee.Google Scholar
- Mitchelmore, M. C. (1983). Geometry and spatial learning: Some lessons from a Jamaican experience.For the Learning of Mathematics, 3(3), 2–7.Google Scholar
- Outhred, L. (1993).The development in young children of concepts of rectangular area measurement. Unpublished PhD thesis, Macquarie University.Google Scholar
- Outhred, L., & Mitchelmore, M. C. (1992). Representation of area: A pictorial perspective. In W. Geeslin & K. Graham (Eds.),Proceedings of 16th annual conference of the International Group for the Psychology of Mathematics Education (Vol. 2, pp. 194–201). Durham, NH: Program Committee.Google Scholar
- Owens, K. D. (1992). Spatial mathematics: A group test for primary school students. In M. Stephens & J. Izard (Eds.),Reshaping assessment practices: Assessment in the mathematical sciences under challenge (pp. 333–354). Melbourne: ACER.Google Scholar
- Owens, K. D. (1993a). Factors pertinent to children’s responsiveness in spatial problem-solving activities. In B. Southwell, B. Perry, & K. Owens (Eds.),Space: The first and final frontier (Proceedings of 15th annual conference of Mathematics Education Research Group of Australasia, pp. 421–431). Sydney: MERGA.Google Scholar
- Owens, K. D. (1993b).Spatial thinking employed by primary school students engaged in mathematical problem solving. Unpublished PhD thesis, Deakin University.Google Scholar
- Owens, K. D. (1994a). Concrete materials: Why they do or don’t work. In D. Rasmussen & K. Beesey (Eds.),Mathematics without limits (Proceedings of the 31st annual conference of the Mathematical Association of Victoria, pp. 342–347). Melbourne: MAV.Google Scholar
- Owens, K. D. (1994b). Visualisation as an aspect of spatial problem solving. In R. Killen (Ed.),Educational research: Innovation and practice. (Proceedings of the annual conference of the Australian Association for Research in Education [On-line]. Available: www.swin.edu.au/AARE/conf94.html File: OWENK94.161Google Scholar
- Owens, K. D. (1995). Imagery and concepts in mathematics: Spatial activities for the primary school [Professional development package with video]. Sydney: University of Western Sydney Macarthur, Faculty of Education.Google Scholar
- Owens, K. D., & Outhred, L. (1996). Young children’s understandings of tiling areas.Reflections, 21 (1), 35–40.Google Scholar
- Wheatley, G., & Cobb, P. (1990). Analysis of young children’s spatial constructions. In L. P. Steffe & T. Wood (Eds.),Transforming children’s mathematics education (pp. 161–173). Hillsdale, NJ: Lawrence Erlbaum.Google Scholar