Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children.

Abstract

Sixty young and 60 elderly adults completed a pencil-and-paper addition test and solved 40 computer-presented simple addition problems. Strategies and problem solution times were recorded on a trial-by-trial basis and were classified in accordance with the distributions of associations model of strategy choices. The elderly group showed a performance advantage on the ability measure and for the developmental maturity of the mix of problem-solving strategies, but the young group showed an advantage for overall solution times. A componential analysis of the overall solution times for memory retrieval trials, however, showed no reliable age difference for rate of retrieving addition facts from long-term memory but did suggest that the elderly adults might have been slower than the younger adults for rate of encoding digits and verbally producing an answer. Overall results are interpreted within the context of the strategy choice model.

Cognitive addition: Strategy choice and speed-of-processing differences in gifted, normal, and mathematically disabled children.

“…In other words, many of the young adults had not yet achieved the level of expert in simple addition. Within the context of the strategy choice model, the low proportion of retrieval errors combined with the relatively high proportion of backup strategy trials by the young adults suggests a rather rigorous confidence criterion (Geary & Brown, 1991;Siegler, 1988). The finding that the use of the backup strategies increased with increases in the difficulty of the problem indicates that the backup strategies were probably used when an answer was not readily retrievable from long-term memory.…”

“…Recall that Cerella and Fozard found no age difference in the rate of retrieving the meaning of single words from long-term memory. In fact, data from converging areas, such as psychometrics, mental chronometry, learning disabilities, and neuropsychology, support the position that the long-term memory representation of arithmetic facts is a semantic language-like system (Ashcraft & Battaglia, 1978;Billet & Grafman, 1983;Geary, 1990;Geary & Brown, 1991;Geary et al, in press;Horn, 1968;Luria, 1980;Richman, 1983). Thus, the finding of no age difference in the rate of addition fact retrieval might be interpreted as a replication, albeit with a different content, of the Cerella and Fozard finding.…”

“…The use of counting and in fact other backup procedures, such as decomposition, therefore leads to their extinction by ensuring that memory retrieval becomes the dominant problem-solving process (Siegler & Jenkins, 1989). Nevertheless, some form of confidence criterion probably also influences whether a retrieved answer is stated or whether a backup strategy is used to verify the accuracy of the retrieved answer (Geary & Brown, 1991;Siegler, 1988). In all, within the context of the strategy choice model, for the simple addition task, expert or developmentally mature performance would be represented by the error-free retrieval of all basic facts.…”

Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: differences between children and adults?

“…SpeciWcally, working memory is most important during the initial phase of arithmetic-skill acquisition and its role declines as procedures are used less frequently and facts become represented in long-term memory. Working-memory resources might thus be needed to achieve a complete representation of number facts in long-term memory (e.g., Geary, 1990;Geary & Brown, 1991;Hitch & McAuley, 1991;Siegler & Shrager, 1984), which explains the correlation between working-memory span and retrieval use in the younger children. However, once the number facts are completely represented in longterm memory, fact retrieval becomes more automatic and less eVortful, resulting in smaller arithmetic-performance diVerences between high-span children and low-span children.…”

Role of Cognitive Theory in the Study of Learning Disability in Mathematics

“…To illustrate the challenge, a mathematical disability can result from deficits in the ability to represent or process information in one or several of the many subareas of mathematics (e.g., base-10 arithmetic versus geometric theorems) or in one or a set of procedural or conceptual features within each subarea (e.g., use of base-10 arithmetic for trading versus conceptual understanding of this system). To narrow the focus of the search for LD, our approach has been to apply theory and methods used to study mathematical development in academically typical children to the study of children with low achievement in mathematics (e.g., Geary & Brown, 1991).…”