A componential analysis of an early learning deficit in mathematics

Abstract

This study was designed to assess strategy choice and information-processing differences in normal and mathematically disabled first and second grade children. Twenty-three normal and 29 learning disabled (LD) children solved 40 computerpresented simple addition problems. Strategies, and their associated solution times, used in problem solving were recorded on a trial-by-trial basis and each was classified in accordance with the distributions of associations model of strategy choices. Based on performance in a remedial education course, as indexed by achievement test scores, the LD sample was reclassified into an LDimproved group and an LD-no-change group. No substantive differences comparing the normal and LD-improved groups occurred in the distribution of strategy choices, strategy characteristics (e.g., error rates), or rate of information processing. The performance characteristics of the LD-no-change group, as compared to the two remaining groups, included frequent counting and memory retrieval errors, frequent use of an immature computational strategy, poor strategy choices, and a variable rate of information processing. These performance characteristics were discussed in terms of the strategy choice model and in terms of potential long-term memory and working memory capacity deficits. In addition, implications for remedial education in mathematics were discussed. o 1990 ACademic Press, Inc.A learning disability in mathematics achievement is characterized by the failure to acquire grade appropriate knowledge and problem-solving skills (Schoenfeld, 1987a). While traditional achievement measures allow for the identification of learning disabled (LD) students, they do not

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

“…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 final set of analyses in this section sought to determine if the use of the backup strategies was related to problem difficulty, as is the case for children (Geary, 1990;Geary & Brown, 1991;Siegler & Shrager, 1984). To achieve this end, the frequency (across problems) with which the backup strategies were used for problem solving was correlated with the value of the problem's correct sum.…”

“…First, the array of problem-solving strategies used for this task is well documented. In fact, at least for children, problemsolving strategies can be reliably classified on a trial-by-trial basis (Geary, 1990;Siegler & Shrager, 1984). Second, for each of the strategies, the overall solution times can be decomposed into more elementary information processes that might index, for example, the rate of retrieving facts from long-term memory (Geary & Burlingham-Dubree, 1989).…”

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.…”

Examination of Addition and Subtraction Performances of Students with and without Learning Disabilities

“…Brown and Burton (1978) found in their study that the students forget the place they count after a while since they use immature strategies like finger counting, and therefore make this error. Geary (1990), Siegler and Robinson (1982) indicated that this error was particularly common in addition operations. Because students count as 4, 5, 6 instead of 5, 6, 7 in an addition operation of 4+3, they get the incorrect result.…”