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.

Although mathematical pattern tasks are often found in elementary school curricula and are deemed a building block for algebra, a recent report (National Mathematics Advisory Panel, 2008) suggests the resources devoted to its teaching and assessment need to be rebalanced. We examined whether children's developing proficiency in solving algebraic word problems is related to their proficiencies in patterns, computational, and working memory tasks. Children {N = 151 10-year-olds) were tested twice, 1 year apart, and were administered tests of updating capacities (2 complex span and 1 running span task), computation (from the Wechsler Individual Achievement Test), patterns (function machine, number patterns), and algebraic word problems. Proficiencies on the patterns and computational tasks predicted algebraic proficiency. Proficiencies on the computational and patterns tasks are, in turn, predicted by updating capacity. These findings suggest that algebraic reasoning may be difficult if the child has poor updating capacity and either poor facility with computation or difficulty in recognizing and generalizing rules ahout patterns.