Cattell-Horn-Carroll broad cognitive ability profiles of low math achievers

Abstract

This study extends previous research examining the relations between Cattell-Horn-Carroll cognitive abilities and math achievement. The cognitive profiles of children with normative weaknesses in Math Calculation Skills or Math Reasoning were compared to those of their average-achieving peers. The cognitive profile of the low Math Calculation Skills group (n ϭ 68) was similar to that of their average-achieving peers. The low Math Reasoning group (n ϭ 52) scored lower than their average-achieving peers on the cognitive abilities as a set and on Fluid Reasoning and Comprehension-Knowledge. When individual profiles were considered, approximately half of the children with normative math weaknesses demonstrated commensurate weaknesses in one or more cognitive abilities, which may inform diagnostic models of learning disabilities. © 2005 Wiley Periodicals, Inc.Current estimates indicate that approximately 5 to 7% of the school-age population has remarkable difficulty in math achievement, a statistic that presents a challenge for a society that demands at least minimal math competency for success in formal schooling, daily living, and employment (Geary & Hoard, 2001;Light & DeFries, 1995). However, the complex array of mathematical domains obfuscates understanding of the general population of poor math learners (Geary, Hoard, & Hamson, 1999). A useful schema for thinking parsimoniously about the array of math domains is to group them into two factors: math calculation skills and math reasoning (Flanagan, Ortiz, Alfonso, & Mascolo, 2002; Individuals with Disabilities Education Act, 1997). Math Calculation Skills refers to the application of mathematical operations (e.g., addition, subtraction) and basic axioms (e.g., commutative property, inverse operations) to solve mathematical problems. Math Reasoning, in contrast, refers to the ability to problem solve using knowledge about math operations and axioms, numerical relationships, and quantitative concepts.The origins of proficiency in these two math factors are complex. They include ecological variables such as home environment (Mullis, Dossey, Owen, & Phillips, 1991;Walberg, 1984) and math instruction, including quality of textbooks (Carnine, 1991;Mullis et al., 1991;Russell & Ginsburg, 1984). Far less is known about the underlying cognitive abilities that contribute to math calculation skills and math reasoning (Geary, 1994;Rourke & Conway, 1997). The cognitive abilities that have been the focus of most investigations of math skills are information retrieval (Geary, 1990(Geary, , 1994Geary, Brown, & Samaranayake, 1991), working memory (Geary, 1994Hitch & McAuley, 1991;Shafir & Siegel, 1994;Swanson, 1994), and speed of processing (Bull & Johnston, 1997;Geary, 1994).Assimilating research on the cognitive abilities underlying math performance has been difficult, primarily because researchers have used varying models of cognitive abilities to guide their studies. That is, one researcher may explore the relationship between math and visual-auditory processing whereas anothe...

The effects of Wechsler Intelligence Scale for Children—Fourth Edition cognitive abilities on math achievement

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WISC-V and the Personalized Assessment Approach

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