LOGICAL OPERATIONS IN AREA AND LENGTH MEASUREMENT: AGE AND TRAINING EFFECTS1

Abstract

The measurement of length and area represent major achievements for the child. These achievements, however, are a part of a larger development: the construction of Euclidian space. According to Piaget, Inhelder, and Szeminska (4), true measurement becomes possible when a part belonging to a whole is compared with the remainder by successive superposition of the part on the whole. This is known as unit iteration and may be accomplished with the part itself or with a common measure used transitively. Such measurement represents the fusion of the operations of subdivision (of line or area) and change of position (in space) into a single operation. The operations basic to true measurement are developed in a series of stages more specifically denoted by Piaget et al. (4) as follows: