Steps/Ages (Levels of Thinking)


A. Perceive, Say, Describe/Discuss, and Construct Objects in 3-D Space

B. Perceive, Say, Describe/Discuss, and Construct Spatial Relations in 3-D Space

C. Perceive, Say, Describe/Discuss, and Construct Compositions and Decompositions in 3-D Space

Relating parts and wholes

Informally describe why some blocks “stack well” and others do not.


Compose building blocks to produce composite shapes. Produce arches, enclosures, corners, and crosses systematically.

Step 3 (Age 5)

Thinking visually/holistically

Name common 3-D shapes with mathematical terms (spheres, cylinder, rectangle, prism, pyramid).



Thinking about parts

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

Fill rectangular containers with cubes, filling one layer at a time.


Relating parts and wholes

Describe congruent faces and, in context (e.g., block building), parallel faces of blocks.

Understand and can replicate the perspective of a different viewer.

Substitution of shapes. Build complex structures.

  • Build structures from pictured models.

NOTE: Less time on 3-D than on 2-D, about 10 percent of the time on 3-D.

*Research indicates that very young children mainly use shape for object identification. Research says children with lower socioeconomic status have difficulty with describing objects and need to learn the vocabulary to do so.

ject pictured). They create pictures with geometric shapes (circles, circle sections, polygons), often representing single objects with different shapes, but eventually combining shapes to make, for example, the body of a vehicle or an animal. That is, initially children manipulate shapes individually, but they are unable to combine them to compose a larger shape. For example, they might use a single shape for a sun, a separate shape for a tree, and another separate shape for a person. Initially, they cannot accurately match shapes to even simple frames.

Later, children learn to place 2-D shapes contiguously to form pictures. In free-form “make a picture” tasks, for example, each shape used repre-

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