Some theories from cognitive psychology and mathematics education suggest that children's understanding of mathematical concepts develops together with their knowledge of mathematical procedures. However, previous research into children's understanding of the inverse relationship between addition and subtraction suggests that there are individual differences in the way this concept develops. To determine whether these differences are reliable and reflect alternative paths of development, we

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... ined data from 14 studies of children's understanding of inversion. Cluster analyses and meta-analytic techniques were used to quantify the size of the inversion effect and examine factors influencing its size and to test the stability of patterns of individual differences across the studies. Evidence was found for reliable patterns of individual differences, which have implications for current theories of concept development. Individual Differences Meta-Analysis 3 Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis An enduring question in mathematical cognition concerns how children develop understanding of mathematical concepts. This has attracted attention from researchers in both cognitive psychology and mathematics education. One of the key questions for both fields is how children's understanding of mathematical concepts develops in relation to their ability to perform mathematical procedures.