Children's partial knowledge of the cognitive skill of counting

Abstract

Acquiring the knowledge that constitutes a cognitive skill is the issue examined in this research—in particular, the skill of counting. Two theories guided the research, one concerning partial knowledge during cognitive growth and the other concerning children's understanding of number. Preschool children were given four tasks involving counting skills in two identical testing sessions, using problem sizes ranging from 3 to 26 items. Stochastic models of data from these tasks separated two sources of instability in the children's performance: measurement error in the tools of assessment and, more interestingly, variability intrinsic to the way the children's knowledge was structured. It was hypothesized that the children's knowledge was organized as separate, modular components for knowing how to tag, partition, and stop. The results showed that development of skilled counting during the preschool years rests primarily on learning to merge and coordinate these components, rather than on acquiring the components themselves. When a task required very few components, the children consistently performed well. When relatively many components had to be coordinated, the children's performance was both lower in absolute level and more variable over testing sessions. Supplementary data suggested that preschool children also have difficulty coordinating their knowledge of cardinality with their execution of the counting process proper.