Children's drawings of objects about to be moved in space (anticipatory images) were studied in relation to their judgments about Euclidean spatial relations. Tasks assessing Euclidean geometric operations were administered to 102 girsl between the ages of 4 and 13 years. 5 operative levels resulted: (a) failure on all operations tasks, (b) success on conservation of length, (c) success on conservation and 1-dimensional measurement, (d) success on the latter 2 tasks plus measurement in 2 dimensions, and (e) success on the latter 3 tasks and coordination of internal and external reference frames. The same children performed on 6 imaginal tasks involving movements of objects. Results confirmed several theoretical expectations: (a) children who were unable to measure had difficulty imaging successive positions for 1-dimensional movement; (b) children who were unable to coordinate a point in space by reference to 2 axes were unable to draw states of movement correctly for 2-dimensional movement; (c) children's errors in drawing successive positions of moving objects were related to the structure of operations at the lower levels; and (d) the coordination of object positions over successive states was dependent on the ability to measure from an external frame. The results were interpreted as support for Piaget and Inhelder's theory of imagery development.
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