Cognitive addition: Comparison of learning disabled and academically normal elementary school children

Abstract

Simple addition problems were presented using a true/false reaction time (RT) verification paradigm to 77 academically normal and 46 learning disabled (LD) subjects in the second, fourth, or sixth grade. The experiment was designed to determine the potential process deficits associated with a learning disability in mathematics achievement. Structural models representing alternative process strategies were fit to RT data. Across grade level and academic status, RT was best fitted by structural variables representing either an implicit counting strategy or a memory retrieval process. The majority of normal and LD second-grade subjects used the implicit counting strategy for problem solution; however, LD subjects required a greater amount of time to execute this process and appeared to be deficient in the ability to self-monitor the problem-solving process. A clear shift from reliance on the implicit counting strategy to the memory-retrieval process was evident from the second to sixth grade for normal subjects. No such shift was evident for LD subjects, as the majority of these subjects relied on the counting strategy in the second, fourth, and sixth grade. Subjects having a specific learning disability in mathematics achievement appear to differ from academically normal

A componential analysis of an early learning deficit in mathematics

“…The remaining performance deficits of the LD-no-change group might be explained in terms of poor self-monitoring of the problem-solving process (Geary et al, 1987;Goldman et al, 1988) or in terms of a deficit in the attentional allocation aspect of working memory capacity (Woltz, 1988). Poor self-monitoring of problem solving could result in under-or over-counting and therefore frequent verbal counting errors.…”

“…For each of the three groups, no single variable clearly provided the best representation of retrieval trial RTs. So, to make these analyses comparable to those of a previous study (Geary et al, 1987), the product (prod) variable was used to represent average retrieval trial RTs for the normal and LD-improved groups. The resulting regression equations are presented in the bottom portion of Table 4.…”

“…The information-processing approach to the study of human abilities provides a methodology which should enable a more accurate representation of the factors which contribute to a learning disability. Indeed, several studies of mathematically disabled children have followed the information-processing approach and have identified a number of potential underlying deficits (Fleischner, Garnett, & Shepherd, 1982;Garnett & Fleischner, 1983;Geary, Widaman, Little, & Cormier 1987;Goldman, Pellegrino, & Mertz, 1988;Svenson & Broquist, 1975).…”

“…These studies have focused on addition and suggest that the performance characteristics of young mathematically disabled students, relative to their academically normal peers, include the frequent use of inefficient problem-solving strategies, rather long solution times, and frequent computational and memory-related errors (Geary et al, 1987;Goldman et al, 1988). Moreover, this pattern of deficits which characterizes poor achievement in arithmetic in young children appears to parallel the deficits associated with the lack of mastery of more abstract domains, such as calculus (Schoenfeld, 1987b).…”

“…Rather, it was assumed with these studies that each individual subject employed the same strategy (e.g., counting) to solve each individual problem (Fleischner et al, 1982;Garnett & Fleischner, 1983;Geary et al, 1987). or a general distribution of strategies (e.g., 50% counting and 50% memory retrieval) was inferred based upon patterns of performance on reaction time (RT) measures (Goldman et al, 1988).…”