We have not included either proof or history, only because we see them as part of all areas of mathematics. The remainder of this section focuses on shape as a sample of how one of these themes can be developed. Basic geometric shapes like circles, triangles, rectangles, balls, rectangular blocks, pyramids, cones, cylinders are part of the vocabulary of everyone and form a foundation for communication and understanding the world around us. While classification of shapes is an important activity, we are concerned that an emphasis on classification may leave less room for other important activities, and recommend that students not be asked to memorize endless lists of geometrical figures including kites, scalene versus obtuse versus acute triangles, rhombus, rhomboid, etc. Pre-school children have sets of shapes that fit in correspondingly shaped holes.
Young children connect dots in booklets to draw figures they can color.
In upper elementary grades and middle grades, students learn properties of shapes. They learn that a tripod is stable, but a four-legged table may be woggly on an uneven floor. They start building three dimensional shapes from folded paper or sticks and connectors. They learn to measure and compute characteristics associated with shapes such as perimeter, area, and volume. In addition to being able to compute the perimeter of a rectangle one meter by five meters and get an answer of twelve meters, we would like them to be able to list the possible rectangles whose sides are an integral number of meters and whose perimeter is twelve meters.