Empirical Testing of a Cognitive Model to Account for Neuropsychological Functioning Underlying Arithmetic Problem Solving

Abstract

The efficacy of a cognitive-based arithmetic problem-solving model (Dinnel, Glover, & Halpain, in press; Dinnel, Glover, & Ronning, 1984) was tested using 989 students with learning disabilities. Comprehensive neuropsychological test battery information was used to predict composite arithmetic test performance as a means of examining the utility of this model. Results of this study offer support for Dinnel et al.'s (Dinnel, Glover, & Halpain, in press; Dinnel, Glover, & Ronning, 1984) model in accounting for arithmetic performance under continuous visual stimulus conditions. However, these data indicate a more complex neuropsychological underpinning to arithmetic performance in both visual and aural stimulus conditions. The neuropsychological aspects of arithmetic problem solving were discussed in relationship to this cognitive-based model.

Processing Abilities Associated with Math Skills in Adult Learning Disability

“…Since JLO but not Gv predicts math skill, it would seem that spatial perception is more important to math achievement than general visual processing. This interpretation is consistent with past studies that have shown such spatial tasks as Pattern Analysis from the Stanford-Binet IV and WISC-R Block Design to be related to math skills (Assel et al, 2003;Batchelor, Gray, & Dean, 1990).…”

“…However, the WJ-R visual factor (Gv) emphasizes aspects of visual perceptual processing (e.g., closure speed, visual memory) to a greater extent than spatial ability, making the Gv factor perhaps less sensitive to the type of visual abilities (i.e., spatial visualization and spatial relations) important in math skill development (Geary, Hamson, & Hoard, 2000;McGrew, Flanagan, Keith, & Vanderwood, 1997). In support of this interpretation, others using purer measures of visuospatial ability (e.g., WAIS Block Design: Batchelor, Gray, & Dean, 1990; Standford-Binet IV Pattern Analysis and Copying: Assel et al, 2003;Benton Judgment of Line Orientation: Riccio & Hynd, 1992) have found a relationship between visuospatial ability and math skill.…”

“…For example, Geary's (1993) widely cited review of math disability clearly states that the review of research is confined to "lower order numerical skills" and does not consider the role of higher order cognitive processes such as executive function. Likewise, in the testing of Dinnel's model of math ability, Batchelor, Gray, & Dean (1990) note that the model is constrained to dealing with math skills in a situation where continuous visual processing of task-related information is present, such that memory retrieval and some aspects of problem solving skills are minimized. In an attempt to deal with such limitations, Floyd et al (2003) used a Cattell-Horn-Carroll model of intelligence, instantiated by the Woodcock-Johnson battery, to evaluate processing abilities underlying math skill development from the standpoint of all factor analytically-defined facets of intelligence, as proposed by Carroll (1993).…”

“…In contrast to the conceptualization that spatial and executive functions underlie math ability, some researchers have identified verbal conceptual/crystallized intelligence (WJ-R Gc) as important to math skill development by virtue of the relationship between semantic processes and factual mathematical knowledge (Batchelor, Gray, & Dean, 1990;Floyd, Evans, & McGrew, 2003;Geary, 1993). However, Keith (1997) found that "g" ("general intelligence") was strongly related to math achievement, raising the possibility that the relationship of Gc to math skill may be confounded with general intelligence and may not reflect a specific cognitive ability underlying math skill development.…”

A systematic procedure for identifying and classifying children with Dyscalculia among primary school children in India

“…(x) Not all reading disabled children will necessarily have serious arithmetic disability (Guttman, 1937;Goodstein and Kahn, 1974). (xi) Arithmetic disorders frequently co-occur with reading and spelling disorders (Fletcher and Loveland, 1986;Batchelor et al, 1990;Miles and Miles, 1992). (xii) Subtle cognitive deficits in symbolic or representational thinking, temporal-sequential organization, verbal memory, and rate of verbal processing may underlie language deficits in children.…”