Steps/Ages (Level of Thinking)


A. Perceive, Say, Describe/Discuss, and Construct Objects in 2-D Space

B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 2-D Space

C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 2-D Space

Thinking about parts

Shape by number of sides and corners (including new shapes).

Create and record original compositions made using squares, right triangles, and rectangles on grid paper. Extend to equilateral grids and pattern blocks (those with multiples of 60° and 120° angles).

  • Begin to use relational language of “right” and “left.”

  • Draw a complete covering of a rectangle area. Count squares in rectangular arrays correctly and (increasingly) systematically.


Relating parts and wholes

Measure of sides (simple units), gross comparison of angle sizes.

Compare area using superimposition.

  • For rectangular regions, draw and count by rows (initially may only count some rows as rows).

  • Identify and create symmetric figures using motions (e.g., paper folding; also mirrors as reflections).

Composition on grids and in puzzles with systematicity and anticipation, using a variety of shape sets (e.g., pattern blocks; rectangular grids with squares, right triangles, and rectangles; tangrams).

NOTE: Most of the time should be spent on 2-D, about 85 percent (there are many beneficial overlapping activities).

equality of angles another relation). Owing usually to a lack of good experiences, many students do not reach this level until late in their schooling. However, with appropriate learning experiences, even preschoolers can begin to develop this level of thinking. In Table 6-1 this is called the “relating parts and wholes” level.

Development of Shape Concepts

What ideas do preschool children form about common shapes? Decades ago, Fuson and Murray (1978) reported that, by 3 years of age, over

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