The studies’ results that we have d

The studies’ results that we have described have many implications for geometry instruction. The remainder of this article offers research-based suggestions for improving the teaching of basic shapes and for enhancing children’s understanding of their shapes.
reconsider teaching "basic shapes" only through examples
as we continually contrast squares and rectangles, do we convince children of their separateness? Does teaching shapes mainly by showing examples sometimes build unnecessarily rigid ideas? in one study (kay 1987), a first - grade teacher initially introduced the more general case, quadrilaterals and squares as special rectangles. That is, she discussed the attributes of each category of shapes and their relationships; for example, a rectangle is a special kind of quadrilateral. She informally used terms that reflected this relationship; for example, that “this is a square-rectangle.” At the end of instruc- tion, most of her students identified characteristics of quadrilaterals, rectangles, and squares, and about half identified hierarchical relationships among these classes, even though none had done so previously. This teacher concluded that the typical approach of learning by showing examples is appropriate only for shapes that have few such exemplars, such as circles and possibly squares. For other shapes, especially such hierarchical- based classes as triangles and quadrilaterals, this approach alone is inadequate. We might question how deep these first graders’ understanding of hier- archical relations was (Clements and Battista 1992b). However, we might also question the wis- dom of the traditional, show-examples approach— it may lay groundwork that must be overturned to develop hierarchical, that is, abstract-relational, geometric thinking.