Young children's understanding of geometric shapes: The role of geometric models

Abstract

This study explores the role of polygonal shapes as geometrical models in teaching mathematics by eliciting and interpreting young children's geometric conceptions and understanding about shapes, through their responses while being involved in relevant activities. More specifically, we examined the cases of polygons or “polytopes” of dimensions 0, 1 and 2 (0-polytopes are points, 1-polytopes are line segments and 2-polytopes are (convex) polygons), by asking children of 4-7 years of age to draw a stairway of figures (triangles, squares and rectangles) with each shape being bigger than its preceding one. Our ultimate aim was to investigate the implications the findings have for advancing children's geometric thinking and understanding, and thus for teaching geometry more efficiently, in early childhood. For the analysis of the collected data, Gras's Implicative Statistical Model was used. Results showed that children were mainly using two strategies while solving the problems: (a) conservation of shape, by increasing both dimensions of the figure and (b), increasing one dimension of the figure. Each strategy seems to reflect a different way of reasoning and understanding, possibly corresponding to a different level of development, as far as geometric thinking, is concerned. Also, children appear to work relatively more flexibly with tasks using rectangles than tasks using squares. This finding suggests that geometry instruction needs to introduce geometric shapes in a mathematically correct manner by using accurate definitions and explanations of relative properties and characteristics, hierarchical commonalities and differences among shapes.