Each year, whether I was teaching kindergarten or fourth grade, I would pull out the tub of pattern blocks and wooden solids when it was time for geometry. Year after year, the students were exposed to the same shapes and manipulatives. By fourth grade, many students had played with the same pattern blocks for five years straight. I knew teaching geometry (especially 3-dimensional shapes) through a worksheet wasn’t the best way to learn. I was convinced I could change the trend of low achievement in geometry through constant use of these manipulatives. Little did I know, I was only perpetuating many misconceptions that students have about shapes. This was made particularly clear after I asked my fourth grade students to identify which shape had a hexagonal face. After a few minutes of silence, one student finally responded with, “It’s the yellow one. Hexagons are yellow.” And he was right. In his experience, the most consistent image he was given of a hexagon was the yellow pattern block. That regular, yellow hexagon had become his definition of all hexagons.
Students develop mental prototypes of shapes based on the examples and non-examples they are exposed to. If a child is only shown limited examples of a shape, deep understanding of the defining attributes will not be learned. Thus, a student is likely to recognize a shape by its non-defining attributes. It is common for children to think a triangle is upside down or too skinny because it does not match the mental image of the equilateral triangle they are used to. This mental image was formed from shape posters, textbooks and manipulatives that all show a triangle the same way. Why do students, or even adults, struggle with the concept that a square is a special type of rectangle? A square does not match the mental image we have of a rectangle. Representing a rectangle only as a shape with two long sides and two short sides reinforces this incorrect image.
For students to be ready for the deep thinking required for future geometrical learning, they must be given multiple experiences with a variety of shapes. Students will begin to discover which attributes actually determine what the shape is, thus allowing their mental images to become more flexible. Providing examples and non-examples that clearly show the difference between these defining attributes will create a strong conceptual definition that will not be swayed by a change of color, size or orientation. Students will begin to recognize all six sided polygons as hexagons whether they are yellow or not.