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    • 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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