Cognitive Development in the Primary School Child: The Relationship between Tests of Combinations and Tests of Concrete Operations

Abstract

Piaget's theory of cognitive development emphasizes the growth of specific structures in thought. The present studies examined a mathematical structure which has been proposed as a basis for conservation. It involved combinations of judgments that certain units were “equal”, “more”, or “less”, than one another. Three tests were designed and, together with tests of concrete operations, were administered to primary school children. Success on the first and third tests came at the same age as did success on the tests of concrete operations, but the second was more difficult. The second test involved use of the abstract terms “equal”, “more”, and “less” on their own, without the direct reference to a numerical basis which was used with the first and third test by presenting appropriate concrete materials. The most adequate test from a theoretical point of view was the third, which contained items developed from a transitivity paradigm. Results indicated that the concrete operational child is able to effect closed mappings, but the preoperational child has difficulty.