Pathways to Number: Children's Developing Numerical Abilities

By Jacqueline Bideaud; Claire Meljac et al. | Go to book overview

4
Learning Stages in the Construction of the Number Sequence

Leslie P. Steffe University of Georgia

To those individuals interested in the construction of mathematics by children, The Child's Conception of Number (La Genèse du Nombre chez l'Enfant) by Piaget and Szeminska ( 1941) will always be a classic work in genetic epistemology. The finding that human beings can construct a rational system of numerical operations in early childhood using their conceptual operations and the sensory material that is available to them is even more relevant today than it was in 1941 because of the international search for improvements in the mathematical education of children ( Steffe & Wood, 1990). My enthusiasm for this classic work has not waned, but I now view the picture of the child's numerical concepts as painted by Piaget and Szeminska as serving more to help solve the problems in genetic epistemology than those in mathematics education. This is no criticism because any model of the knowledge of the child is formulated to meet certain goals of the investigators. However, after working for a period of ten years within the framework of Piagetian stage theory to understand how it might be used to foster mathematics education of children (e.g., Steffe, Hirstein, & Spikes, 1976), I developed an internal necessity to formulate a model of the child's conception of number that would be compatible with the Piagetian model, but would also account for experiential phenomena that seemed to be inexplicable within that model.

When teaching 6- and 7-year-old children in teaching experiments,1 it became evident to me that the counting scheme was one of their fundamental numerical

____________________
1
The term teaching experiment does not mean an investigation of teaching a predetermined or accepted way of operating. Instead, it is primarily an exploratory tool, derived from Piaget's clinical interview but aimed at investigating children's constructive processes ( Cobb & Steffe, 1983).

-83-

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