Numerical and Arithmetical Cognition: A Longitudinal Study of Process and Concept Deficits in Children with Learning Disability

Abstract

Based on the stability and level of performance on standard achievement tests in first and second grade (mean age in first grade ϭ 82 months), children with IQ scores in the low-average to high-average range were classified as learning disabled (LD) in mathematics (MD), reading (RD), or both (MD/RD). These children (n ϭ 42), a group of children who showed variable achievement test performance across grades (n ϭ 16), and a control group of academically normal peers (n ϭ 35) were administered a series of experimental and psychometric tasks. The tasks assessed number comprehension and production skills, counting knowledge, arithmetic skills, working memory, the ease of activation of phonetic representations of words and numbers, and spatial abilities. The children with variable achievement test performance did not differ from the academically normal children in any cognitive domain, whereas the children in the LD groups showed specific patterns of cognitive deficit, above and beyond the influence of IQ. Discussion focuses on the similarities and differences across the groups of LD children.

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…Moreover, in studies focusing on children with mathematical learning disabilities, school children showed deficits in these quantity-number competencies (Gaupp, Zoelch, & Schumann-Hengsteler, 2004;Geary, Hamson, & Hoard, 2000;Geary, Hoard, Byrd-Craven, & DeSoto, 2004;Landerl, Bevan, & Butterworth, 2004). Confirming the special importance of the quantity to number-word linkage, for instance, the 7-year-olds with Williams Syndrome in the study by Ansari, Donlan, Thomas, Ewing, Peen, and Karmiloff-Smith (2003) demonstrated an extremely delay in the understanding of the cardinality principle (Level II), despite the fact that they could recite the number-word sequence (Level I) in the assessed number range almost without errors.…”

“…For instance, indicators of working memory have been identified as potentially relevant unspecific predictors of both literacy and mathematics development in school (see Berg, 2008;Bull, Espy, & Wiebe, 2008;Geary, Hamson, & Hoard, 2000;Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Hecht, Torgesen, Wagner, & Rashotte, 2001;Landerl, Bevan, & Butterworth, 2004;Swan & Goswami, 1997;Wolf, 1984). Phonological aspects of working memory, in particular, phonological recoding and phonological rehearsal processes as conceptualized in Baddeley's (1986) working memory model have been shown to affect subsequent literacy development during elementary school (see Daneman, 1987;Schneider & Näslund, 1999;Schuchardt, Kunze, Grube, & Hasselhorn, 2006;Swanson & Howell, 2001;Wagner & Torgesen, 1987).…”

Mathematics deficiencies in children with very low birth weight or very preterm birth

“…Studies of developmental MLD also show that the nature of mathematics problems varies in relation to presence or absence of comorbid reading disability. Children with isolated MLD have more circumscribed deficits in fact retrieval and progress more rapidly in mathematics than children with combined disabilities (Geary et al, 2000;Jordan et al, 2003). Postulated mechanisms for poor fact retrieval include deficient phonological representations, failure to inhibit memory for closely related facts, difficulties in manipulating nonverbal representations, and generally slow information processing (Jordan et al, 2003;Barnes et al, 2006).…”

Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia

“…The question of whether this difficulty in learning mathematics is due to a single impairment of a basic number specific core competence ('number sense') or a combination of impairments in a more general cognitive system is still open (Butterworth, 2004;Mix & Sandhofer, 2007). One impediment to research on DD is the complexity of the numerical domain that includes verbal, visual-spatial, memory, and executive functions (Ardila, Galeano, & Rosselli, 1998;Geary, Hamson, & Hoard, 2000;von Aster, 2000). This wide array of cognitive factors that could contribute to DD poses a special challenge to investigate this disorder.…”