Working Memory Capacity and the Development of Quantitative Central Conceptual Structures

Abstract

This article reconsiders Case’s theory of central conceptual structures (CCS), examining the relation between working memory and the acquisition of quantitative CCS. The lead hypothesis is that the development of working memory capacity shapes the development of quantitative concepts (whole and rational numbers). Study I, with 779 children from preschool to grade 5, validated a measure of the whole number CCS and found that children’s understanding of whole number advances by one developmental level per additional unit of working memory capacity. Study II, with 92 sixth- and seventh-graders, found that a test of the rational number CCS was predicted by working memory capacity and, to a lesser extent, by intrusion errors in the listening span. We also identified 2 subsets of items that demand a capacity of 4 or 5 units, respectively. Overall, the results support Case’s CCS theory and clarify the role of working memory in the acquisition of numerical concepts. The relevance of these results in relation to the current debate is discussed, with extensive connections to other current theories of whole or rational number comprehension.

Note

Notes

1 This is not to deny a role of chunking in conceptual development. On the contrary, the idea of chunking simpler schemes into higher-order schemes is inherent to the Piagetian and neo-Piagetian construct of scheme. For instance, it is likely that, having understood the relations that tens have to units in one direction and to hundreds in the other direction, the child can chunk these relations into a higher-order concept of positional value. However, this achievement requires as a prerequisite that hundreds, tens, and units are understood as distinct dimensions. Therefore, the contribution of chunking would follow the necessary contribution of working memory growth.