Research on average-IQ children with poor math achievement, that is, math disabled (MD) children, has revealed several sources of their lower than expected (based on IQ) achievement. These children have a poor conceptual understanding of counting, use immature counting procedures to solve arithmetic problems, commit many procedural errors, and have difficulties remembering basic arithmetic facts. The poor counting knowledge of these children appears to contribute to their use of immature counting procedures and their procedural errors, although it is not currently known if this poor counting knowledge extends beyond second grade. Poor working memory resources also appear to contribute to these procedural deficits and it has been argued that these working memory deficits are due to a slow counting speed. The source of the fact-retrieval deficits of these children is unclear, but appears to be related to a combination of difficulties in inhibiting irrelevant associations from entering working memory and from difficulties in lexical access (e.g., retrieving information from semantic memory). Recent theoretical and methodological advances suggest that these working memory and retrieval deficits are more complex than previously conceptualized. Individual differences in working memory appear to be related to ease of inhibiting irrelevant associations, speed of articulating words, speed of scanning the contents of working memory, and ease of regenerating phonetic and semantic traces that are decaying in working memory. The latter, in theory, is related to MD children's difficulties in lexical access and the associated fact-retrieval deficits. The proposed research will be the first to: 1) assess the counting knowledge of first, third and fifth grade MD children and normal controls and examine the relations among counting span (an index of working memory), counting knowledge and procedural competencies in arithmetic; 2) use recent theoretical and methodological advances to provide an assessment of each of the above described components of working memory in first, third and fifth grade MD children and normal controls and relate these competencies to the working memory, counting procedure, and fact-retrieval deficits of MD children; 3) use negative priming methods to test the hypothesis that the fact-retrieval deficit of MD children is related, in part, to difficulties in inhibiting irrelevant associations from entering working memory; and 4) systematically compare the counting and arithmetic competencies of MD children and children with low-IQ scores and low math achievement scores.
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