Children's mathematical skills were considered in relation to executive functions. Using multiple measures--including the Wisconsin Card Sorting Task (WCST), dual-task performance, Stroop task, and counting span-it was found that mathematical ability was significantly correlated with all measures of executive functioning, with the exception of dual-task performance. Furthermore, regression analyses revealed that each executive function measure predicted unique variance in mathematics ability. These results are discussed in terms of a central executive with diverse functions (Shallice & Burgess, 1996) and with recent evidence from Miyake, et al. (2000) showing the unity and diversity among executive functions. It is proposed that the particular difficulties for children of lower mathematical ability are lack of inhibition and poor working memory, which result in problems with switching and evaluation of new strategies for dealing with a particular task. The practical and theoretical implications of these results are discussed, along with suggestions for task changes and longitudinal studies that would clarify theoretical and developmental issues related to executive functioning.

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Although early studies of executive functioning in children supported Miyake et al.'s (2000) three-factor model, more recent findings supported a variety of undifferentiated or two-factor structures. Using a cohort-sequential design, this study examined whether there were age-related differences in the structure of executive functioning among 6- to 15-year-olds (N = 688). Children were tested annually on tasks designed to measure updating and working memory, inhibition, and switch efficiency. There was substantial task-based variation in developmental patterns on the various tasks. Confirmatory factor analyses and tests for longitudinal factorial invariance showed that data from the 5- to 13-year-olds conformed to a two-factor structure. For the 15-year-olds, a well-separated three-factor structure was found.

The importance of executive functioning (EF) skills in mathematical achievement is well established, and researchers have moved from just measuring working memory or updating to an inclusion of other EF skills, namely, inhibition and shifting. In this article, we review studies that have taken different approaches to measuring EF (e.g., using single vs. multiple indicators) and those that have applied different analytical techniques to conceptualize the structure of EF (e.g., exploratory vs. confirmatory techniques). Across studies, updating is often a unique predictor of math achievement at many ages; the findings relating to inhibition and switching are less conclusive. We discuss these findings in relation to age‐related variance in EF structure, the nature of inhibitory and shifting task requirements, and the role of updating as a limiting factor or a common resource for inhibition and shifting.

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