Composition and Decomposition of 2D Shapes
Although the research on children's composition and decomposition of 3D shapes is limited, it is consistent with research on children's composition and decomposition of two-dimensional (2D) shapes. The composition and decomposition of 2D shapes involves separating structures from embedded figures or finding hidden shapes in complex diagrams.This can be very challenging, even for adults, especially since embedded pictures can be so complex. The ability to compose and decompose 2D shapes can also help with the learning trajectory of 3D shapes as the two trajectories take place simultaneously.
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Learning Trajectory
Piece Assembler
Age 4 Makes Pictures in which each shape represents a unique role (e.g., one shape for each body part) and shapes touch. Fills simple "Pattern Block Puzzles" using trial and error. At this stage, Pattern Block Puzzles begin with each shape clearly outlined and touching the other shapes only at the point to make matching as easy as possible. Later, the puzzles become more difficult and combine shapes by matching their sides, although each shape mainly serves separate roles. |
Picture Maker
Age: 5 Puts several shapes together to make one part of a picture (e.g. two shapes for one leg). Uses trial and error, and does not anticipate creation of new geometric shape. Chooses shapes using “general shape” or side length. Fills “easy” “Pattern Block Puzzles” that suggest the placement of each shape. Pattern Block Puzzles begin with those where shapes are combined to make one "part" but internal lines are still available. |
Shape Composer
Age: 5 Composes shapes with anticipation ("I know what will fit"). Chooses shapes using angles as well as side lengths. Rotation and flipping are used intentionally to select and place shapes. Pattern Block Puzzles at this stage have no internal lines and larger areas; therefore, children must compose shapes accurately. |
Substitution Composer
Age: 6 Makes new shapes out of smaller shapes, and uses trial and error to substitute groups of shapes for other shapes to create new shapes in different ways. Video http://earlymath.erikson.edu/composing-shapes-with-child-12-math-challenge-puzzles/ |
Shape Composer--Units of Units
Age: 8 Builds and applies units of units (shapes made from other shapes). For example, in constructing spatial patterns, extends patterning activity to create a tiling with a new unit shape--a unit of unit shapes that they recognize and consciously construct. In this picture, the child repeatedly build "Ts" out of four squares, used four "Ts" to build squares and used the squares to tile a rectangle (p. 182). |
Activities
Geometric Shape Stamping
http://www.thecrafttrain.com/1/post/2014/06/geometric-shape-stamping-an-invitation-to-create.html
http://www.thecrafttrain.com/1/post/2014/06/geometric-shape-stamping-an-invitation-to-create.html