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This study investigated the direct and indirect effects of general intelligence and 7 broad cognitive abilities on mathematics achievement. Structural equation modeling was used to investigate the simultaneous effects of both general and broad cognitive abilities on students' mathematics achievement. A hierarchical model of intelligence derived from the Cattell-Horn-Carroll (CHC) taxonomy of intelligence was used for all analyses. The participants consisted of 4 age-differentiated subsamples (ranging from ages 5 to 19) from the standardization sample of the Woodcock-Johnson III (WJ III; Woodcock, McGrew, & Mather, 2001). Data from each of the 4 age-differentiated subsamples were divided into 2 data sets. At each age level, one data set was used for model testing and modification, and a second data set was used for model validation. The following CHC broad cognitive ability factors demonstrated statistically significant direct effects on the mathematics achievement variables: Fluid Reasoning, Crystallized Intelligence, and Processing Speed. In contrast, across all age levels, the general intelligence factor demonstrated indirect effects on the mathematics achievement variable.

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For many decades, discussions regarding the definition and identification of learning disabilities have been contentious; one result is the varied practices across states and school districts. This study reviewed learning disability (LD) regulations and guidelines from the 50 United States and the District of Columbia that were employed during 2013. Two authors independently coded components of all LD regulations and guidelines. Results showed considerable variability in the state policies and practices governing LD identification. Only 67% of states allow for use of the ability-achievement discrepancy approach, and 20% of states explicitly prohibit its use. Approximately 16% of states require the sole use of response to intervention (RtI) models in LD identification, and there is considerable variability in the guidance states provide regarding how to implement RtI models to identify LD. Finally, about half of states do not allow use of "pattern of strengths and weaknesses" (PSW) models, and most states allowing these models provide little information regarding ideal identification practices. These results can inform school psychology practice, training, and related research.