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Validation of a Piaget-based hierarchy leading to number conservation Wong, Bernice Yee Lan

Abstract

The main purpose of this dissertation was to validate a developmental hierarchy of component abilities underlying number conservation. This hierarchy or sequence of component abilities was derived from Piaget's theory of children's intellectual development. A secondary purpose of this dissertation was to investigate the extent to which predictions can be made about the performance of children on the proposed sequence of tasks, as a function of the specific Piagetian stages of number conservation, in which they have been classified. The proposed developmental hierarchy consisted of seven tasks. These were constructed to conform to Piaget's conception of what they were purported to measure . The tasks in the predicted hierarchy were: Construction of Equivalence → Cognitive Shift → Hindsight-Foresight → Multiplication of Relations/Multiplication of Classes → Conservation of Number → Conservation of Ordinal Correspondence, where → indicated developmental precedence. These seven tasks were administered to all subjects. The predicted direction in the performance on the proposed hierarchy of Piaget's three stage groups in number conservation was: Stage III > Stage II > Stage I, where > indicates superior performance. One hundred and fifty-nine children, aged four to seven, participated in the study: 53 Nursery, 53 Kindergarten and 53 Grade One children. The results indicated partial support of the proposed sequence of component abilities underlying number conservation. The results also indicated that predictions regarding the performance on the hierarchy of Piaget's Stage III children in number conservation were substantiated except for the prediction on Multiplication of Classes. The predictions regarding the performance on the hierarchy of Piaget's Stage I and Stage II children in number conservation were not substantiated because the results did not attain statistical significance. However, they were consistently in the predicted direction. This dissertation points to the fruitfulness of developmental research for educators in its practical implications for building preschool and primary curricula. Moreover there are implications for special education of mentally handicapped children, as well as for children with arithmetic learning disorders of a specific kind, namely, absence of the concept of one-to-one correspondence and absence of conservation concepts in number and/or quantity.

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