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In this Monograph, we present a new theory of children's conceptual development and the empirical research on which that theory is based. The main construct in the theory is the notion of a central conceptual structure. These structures are defined as networks of semantic nodes and relations that represent children's core knowledge in a domain and that can be applied to the full range of tasks that the domain entails. Major transformations are hypothesized to take place in these structures as children enter each new stage of their development. Once formed, the new structures are hypothesized to exert a powerful influence on all subsequent knowledge acquisition. The process by which they exert this effect is believed to be a dynamic one, in which general conceptual insights and more specific task understandings become reciprocally coupled, each exerting a bootstrapping effect on the other.In the first chapter, the general theoretical framework that underlies this conception is spelled out in broad strokes and compared to other contemporary views of conceptual development. In subsequent chapters, more detailed models of children's central conceptual structures are presented for three different domains: number, space, and social interaction. These models are then tested using a mixture of new and previously designed cognitive tasks, which are administered to children from four different age groups (4, 6, 8, and 10 years), three different social classes (high, medium, and low), and four different countries (the United States, Canada, Japan, and China). The results of a 6-year program of instructional research are

A new curriculum to introduce rational numbers was devised, using developmental theory as a guide. The 1st topic in the curriculum was percent in a linear-measurement context, in which halving as a computational strategy was emphasized. Two-place decimals were introduced next, followed by 3-and 1-place decimals. Fractional notation was introduced last, as an alternative form for representing decimals. Sixteen 4th-grade students received the experimental curriculum. Thirteen carefully matched control students received a traditional curriculum. After instruction, students in the treatment group showed a deeper understanding of rational numbers than those in the control group, showed less reliance on whole number strategies when solving novel problems, and made more frequent reference to proportional concepts in justifying their answers. No differences were found in conventional computation between the 2 groups.

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