Patterns of Individual Differences in Conceptual Understanding and Arithmetical Skill: A Meta-Analysis

Abstract 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 that this concept develops. To determine whether these differences are reliable and reflect alternative paths of development, we examined 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. The authors would like to thank Peter Bryant, Jeff Bisanz, Jody Sherman, Carmen Rasmussen, and Katherine Canobi for their assistance in making raw data available for analysis, and Matthew Inglis for helpful comments on an earlier version of this article. Notes 1For one study it was not possible to obtain the raw data to perform this analysis and thus this study was not included in the subsequent analyses.