Cognitive Mechanisms Underlying Achievement Deficits in Children With Mathematical Learning Disability

Abstract

Using strict and lenient mathematics achievement cutoff scores to define a learning disability, respective groups of children who are math disabled (MLD, n=15) and low achieving (LA, n=44) were identified. These groups and a group of typically achieving (TA, n=46) children were administered a battery of mathematical cognition, working memory, and speed of processing measures (M=6 years). The children with MLD showed deficits across all math cognition tasks, many of which were partially or fully mediated by working memory or speed of processing. Compared with the TA group, the LA children were less fluent in processing numerical information and knew fewer addition facts. Implications for defining MLD and identifying underlying cognitive deficits are discussed.

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, as was found for phonological awareness, the visual-spatial component of working memory had no direct impact on math competencies in school, but exerted an indirect influence on school achievement mediated by higher-order domain-specific precursor variables such as the understanding of quantity to number-word linkage at QNC Level II and III (cf. Geary et al, 2007;Berg, 2008;Bull, Espy, & Wiebe, 2008;Simmons, Singleton, & Horne, 2008). Consequently, the visual-spatial sketch pad seems particularly relevant when the task is to create the link from number words to quantities (cf.…”

“…Here, effects of the central executive seem particularly strong (Bull, Espy, & Wiebe, 2008;Geary, Brown, & Samaranayake, 1991;Geary & Hoard, 2001;Gersten, Jordan, & Flojo, 2005;Leather & Henry, 1994;Lee, Ng, Ng, & Lim, 2004;Lemaire, Abdi, & Fayol, 1996;Logie, Gilhooly, & Wynn, 1994;Passolunghi, & Siegel, 2004;Passolunghi, Vercelloni, & Schadee, 2007;Rammelaere, Stuyven, & Vandierendonck, 2001;Swanson, 2006;Swanson & Beebe-Frankenberger, 2004;Thomas, Zoelch, Seitz-Stein, & Schumann-Hengsteler, 2006). In a recent study by Geary, Hoard, Byrd-Graven, Nugent, and Numtee (2007) it was shown that all components of working memory, including the visual-spatial sketch pad, are related to math performance in school. The impact of the visual-spatial sketch pad on math achievement was also confirmed in recent cross-sectional and longitudinal studies (Berg, 2008;Bull, Espy, & Wiebe, 2008;Simmons, Singleton, & Horne, 2008; but see Leather & Henry, 1994;Lee, Ng, Ng, & Lim, 2004;Seitz & Schumann-Hengsteler, 2002;Swanson, 2006, for inconsistent results).…”

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

“…Moreover, structural (Isaacs, Edmonds, Lucas, & Gadian, 2001;Rotzer et al, 2008) and functional (Mussolin et al, 2010;Price, Holloway, Rasanen, Vesterinen, & Ansari, 2007) There exists considerable evidence that representations of magnitude are impaired in children with mathematical difficulties (De Smedt, Reynvoet, et al, 2009;Geary et al, 2007Geary et al, , 2008Iuculano et al, 2008;Jordan, Kaplan, Olah, & Locuniak, 2006;Landerl et al, 2004Passolunghi & Siegel, 2004;Rousselle & Noël, 2007). However, the majority of these studies only relied on tasks with a symbolic processing requirement and do not allow us to clarify whether difficulties in mathematics result from difficulties in representing numerical magnitudes, as postulated in the defective number module hypothesis, or from difficulties in the ability to access numerical magnitudes from formal symbols, such as Arabic numerals, as assumed in the access deficit hypothesis.…”

“…This cut-off score for mathematical difficulties is rather lenient and might result in a sample of children with potentially severe and potentially mild forms of mathematical difficulties, which both may show different cognitive profiles (Geary et al, 2007(Geary et al, , 2008Murphy, Mazzocco, Hanich, & Early, 2007). Against this background, we divided our sample of children with mathematical difficulties into children with low achievement (LA) in mathematics, if they had math achievement scores between the 16 th and 25 th percentile, and children with mathematics learning disabilities (MLD), if they had math achievement scores below the 16 th percentile.…”

“…Indeed, studies have demonstrated that children with mathematical difficulties have particular impairments in understanding and processing numerical magnitudes (De Smedt, Reynvoet, et al, 2009;Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Geary, Hoard, Nugent, & Byrd-Craven, 2008;Landerl, Bevan, & Butterworth, 2004;Landerl, Fussenegger, Moll, & Willburger, 2009;Passolunghi & Siegel, 2004;Rousselle & Noël, 2007). Two accounts for these impairments have been put forward (Rousselle & Noël, 2007; see also Wilson & Dehaene, 2007).…”