# Relationships between the broad and narrow cognitive abilities of Gc and Glr and mathematics achievement within a sample of students with specific learning disability

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Few studies have looked at the relationships between broad and narrow cognitive abilities and mathematics achievement within a sample of students with specific learning disability (SLD). Empirical links between cognition and mathematics abilities must be identified to improve the ability of professionals such as Educational Diagnosticians and School Psychologists in order to accurately identify students with mathematics learning disability. This study examined the relationships between the broad and narrow cognitive abilities of Crystallized-Intelligence (Gc) and Long-term Storage and Retrieval (Glr) and mathematics achievement within a sample of students with SLD at age 9-15 years.

This study also examined the relationships between math calculation skills and math reasoning. Instruments include the Woodcock-Johnson III Tests of Cognitive Abilities and Tests of Achievement. Participant data were split into the two special education math eligibility areas, Math Calculation Skills (n = 90) and Math Reasoning (n = 96). The data were also split into two age groups, 9-12 and 13-15 years to determine if a developmental component exists between the selected broad and narrow abilities and mathematics achievement. Cognitive and achievement data were then used to determine the existence of statistically significant relationships between cognition and mathematics achievement. Correlation analysis found no statistical significance between the broad cognitive abilities of Gc and Glr and mathematics achievement. Math Reasoning and the narrow cognitive ability of Ideational Fluency (FI) were related among all participants and at age 9-12 and 13-15. A positive relationship between Lexical Knowledge (VL) and Math Calculation Skills at age 9-12 and a negative relationship between Lexical Knowledge (VL) and Math Calculation Skills at age 13-15 were revealed. Correlation analysis also found that Math Calculation Skills was a statistically significant predictor of Math Reasoning among all participants and at age 9-12 and 13-15 years.