Neuropsychological aspects of arithmetic performance in children with learning disorders
The present study investigated the neuropsychological predictors of auditory/verbal and visual/written arithmetic performance in a large sample of children with learning disorders. In addition, the efficacy of a cognitive based arithmetic problem solving model (Dinnel, Glover, & Halpain, in press; Dinnel, Glover, & Ronning, 1984) in accounting for neuropsychological functioning in arithmetic performance was considered. Subjects were from a small midwestern school district, and were identified as learning disabled in accord with state (i.e., Rule S-1) and federal guidelines (i.e., PL-94-142). Specifically, subjects' scores on the Halstead-Reitan Neuropsychological Battery (HRNB) (Reitan, 1969) for older children and the Wechsler Intelligence Scale for Children-Revised (WISC-R) (Wechsler, 1974) were used to predict performance on the Wide Range Achievement Test (WRAT) Arithmetic subtest, and WISC-R Arithmetic subtest. Analyses were conducted with criterion measures considered separately and as a composite. In an attempt to examine the utility of the Dinnel et al., (in press; 1984) model, a simple index was formed using the criterion measures. This index was then predicted using the HRNB and WISC-R variables. Neuropsychological variables were found to account for some 31%, and 36% of the variability in visual/written and auditory/verbal arithmetic performance, respectively. However, neuropsychological variables accounted for some 87% of the shared variance when arithmetic measures were considered as a linear composite. Neuropsychological variables predicted a mere 12% of the variability associated with the index designed to test the Dinnel et al. (in press; 1984) arithmetic problem solving model. These data offered some support to Dinnel and others' (Dinnel et al., in press; 1984) formulations accounting for arithmetic performance under visual/stimulus conditions. However, the present findings indicated a more complex neuropsychological underpinning for overall arithmetic problem solving. Moreover, the neuropsychological constructs predicting arithmetic scores varied as a function of the stimulus/performance modes required for problem solving.Auditory-verbal attention and short-term memory, remote verbal memory, symbolic language integration, mental flexibility, and nonverbal abstract reasoning were the common neuropsychological constructs underpinning both auditory/verbal and visual/written arithmetic performance. Verbal facility, verbal abstract reasoning, nonverbal short term memory, and nonverbal concrete concept formation were uniquely implicated in auditory/verbal arithmetic performance. Visual/written arithmetic performance was uniquely related to nonverbal attention and intermediate nonverbal memory functions. In overview, it would seem that neuropsychological measures would be clinically useful in identifying deficits underlying poor arithmetic performance.