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…

Using a balance-beam task, studied 48 preschoolers to elucidate the process of knowledge construction from the emergence of new representation to transformed problem solving. Analyses revealed a multifaceted development from the first signs of weight representation to fully elaborated weight-based problem solving. Case studies of five children…

Compared children's performance on initial-unknown and final-unknown problems involving the addition or subtraction of a single item. Found that although 4-year olds responded in a directionally appropriate way to the final-unknown problems but not to the corresponding initial-unknown ones, 5-year olds were able to respond appropriately to both.…

Two experiments examined children's early judgments about numerical relations. Found that children as young as three years old are already adept at reasoning about relations between sets, independently of their ability to form numerical representations. Results support the existence of protoquantitative schemas, or ways of thinking about relations…

Focuses on a single case study of a mentally handicapped child to examine directly the relation between the development of number-after rules and a counting-on from the larger addend (COL) strategy. Examines the development of children's proficiency with n+ and 1+n combinations and the evolution of their counting-on strategies over time. (AA)