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Applying Piaget's Theory of Cognitive Development to Mathematics Instruction.

This paper is based on a presentation given at National Council of Teachers of Mathematics (NCTM) in 2005 in Anaheim, California. It explicates the developmental stages of the child as posited by Piaget. The author then ties each of the stages to developmentally appropriate mathematics instruction. The implications in terms of not imposing unfamiliar ideas on the child and importance of peer interaction are highlighted. Jean Piaget's work on children's cognitive development, specifically with quantitative concepts, has garnered much attention within the field of education. Piaget explored children's cognitive development to study his primary interest in genetic epistemology. Upon completion of his doctorate, he became intrigued with the processes by which children achieved their answers; he used conversation as a means to probe children's thinking based on experimental procedures used in psychiatric questioning. One contribution of Piagetian theory concerns the developmental stages of children's cognition. His work on children's quantitative development has provided mathematics educators with crucial insights into how children learn mathematical concepts and ideas. This article describes stages of cognitive development with an emphasis on their importance to mathematical development and provides suggestions for planning mathematics instruction. The approach of this article will be to provide a brief discussion of Piaget's underlying assumptions regarding the stages of development. Each stage will be described and characterized, highlighting the stage- appropriate mathematics techniques that help lay a solid foundation for future mathematics learning. The conclusion will incorporate general implications of the knowledge of stages of development for mathematics instruction.