Automaticity, cognitive flexibility, and mathematics: A longitudinal study of children with and without learning disabilities

This longitudinal investigation examined specific cognitive and linguistic variables affecting the development of mathematical problem solving in children with and without learning disabilities. The first goal was to investigate the possible links between early automatic retrieval processes and later mathematical problem solving. The second goal was to examine the connections between early set-switching and later problem solving strategies used in solving math problems (i.e., cognitive flexibility). The third goal was to investigate whether the study of word retrieval processes is as effective for the detection of mathematics disorders as it has been for dyslexic children.; The sample consisted of seventy sixth and seventh graders (12-13 years) who had been tested from kindergarten through grade four as part of a longitudinal study of reading and language development (Wolf, 1982). Subjects received a battery of three continuous naming tests of automaticity and set-switching, a confrontational naming test, three problem solving tasks, and three mathematics measures.; Results of multiple regression analyses indicated that continuous naming speed in first grade was an effective index of both seventh grade math fact retrieval and higher levels of mathematical problem solving. In addition, set-switching in first grade (as measured by the Rapid Alternating Stimulus, Wolf, 1986) was a better predictor of mathematical problem solving and sequential reasoning than of cognitive flexibility (as measured by subtests of the Survey of Problem Solving and Educational Skills (SPES), Meltzer, 1987). These results indicated that a broad range of set-switching tasks are needed to examine cognitive flexibility at different points in development.; Findings indicated that specific SPES subtests, continuous naming tests, and the Boston Naming Test constitute a powerful diagnostic battery for differentiating average-to-able from severely impaired math problem solvers. Findings supported the use of the Rapid Alternating Stimulus in first grade as a sensitive test for early detection of potential math problems.; In conclusion, continuous naming speed combined with cognitive strategy measures are effective for the detection and description of learning problems in mathematics. A child-centered process model is needed as a framework for understanding the developmental principles and range of processes used in lower- and higher-levels of mathematical problem solving.