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

In this study we focus on math anxiety, comparing its dimensions, levels, and relationship with mathematics achievement across samples of 6th-grade students from China, Taiwan, and the United States. The results of confirmatory factor analyses supported the theoretical distinction between affective and cognitive dimensions of math anxiety in all 3 national samples. The analyses of structural equation models provided evidence for the differential predictive validity of the 2 dimensions of math anxiety. Specifically, across the 3 national samples, the affective factor of math anxiety was significantly related to mathematics achievement in the negative direction. Gender by nation interactions were also found to be significant for both affective and cognitive math anxiety.

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This study represents an attempt to replicate the results of earlier research comparing U.S. and Japanese 1st graders' cognitive representation of number and understanding of place value. First graders from France, Sweden, and Korea were also included in the study. This investigation examines the idea that variability in mathematics performance may be due, in part, to differences in cognitive representation of number that is affected by numerical language characteristics differentiating Asian-and non-Asian-language groups. Comparison of Asian-and non-Asianlanguage speakers revealed that the performance of the children was different across the 2 groups but similar within the groups. There is strong evidence that cognitive representation of number may differ depending on the language spoken. There were also significant differences in performance on place value tasks related to the language spoken.

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