Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, 2017) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments examining…

The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic…

Differentiation and integration played large roles within classic developmental theories but have been relegated to obscurity within contemporary theories. However, they may have a useful role to play in modern theories as well, if conceptualized as guiding principles for analyzing change rather than as real-time mechanisms. In the present study,…

Children's thinking is highly variable at every level of analysis, from neural and associative levels to the level of strategies, theories, and other aspects of high-level cognition. This variability exists within people as well as between them; individual children often rely on different strategies or representations on closely related problems…