TABLE 6-1 Space and Shapes in Two Dimensions

Steps/Ages (Level of Thinking)

Goals

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

Step 1 (Ages 2 and 3)

Thinking visually/holistically

Recognition and informal description (including at least circles, squares, then triangles, rectangles).

Recognize shapes in many different orientations and sizes. Trial-and-error geometric movements (informal, not quantified).

  • Use relational language, including vertical directionality terms as “up” and “down,” referring to a 2-D environment.

  • Informally recognizes area as filling 2-D space (e.g., “I need more papers to cover this table”).

Solve simple puzzles involving things in the world.

Create pictures by representing single objects, each with a different shape.

Thinking about parts

Shapes by number of sides (starting with restricted cases, e.g., prototypical equilateral triangle, square).

 

 

Step 2 (Age 4)

Thinking visually/holistically

Recognition and informal description at multiple orientations, sizes, and shapes (includes circles and half/quarter circles, squares and rectangles, triangles, and others [the pattern block rhombus, trapezoids, hexagons regular]).

Recognize shapes (to the left) in many different orientations, sizes, and shapes (e.g., “long” and “skinny” rectangles and triangles).

  • Match shapes by using geometric motions to superimpose them.

  • Use relational words of proximity, such as “beside,” “next to,” and “between,” referring to a 2-D environment.

 



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