Development of Number Line Representations in Children With Mathematical Learning Disability

Abstract

Children with a mathematical learning disability (MLD, n = 19) and low achieving (LA, n = 43) children were identified using mathematics achievement scores below the 11th percentile and between the 11th and 25th percentiles, respectively. A control group of typically achieving (TA, n = 50) children was also identified. Number line and speed of processing tasks were administered in 1st and 2nd grade and a working memory battery in 1st grade. In both grades, the MLD children were less accurate in their number line placements and more reliant on a natural numbermagnitude representational system to make these placements than were TA children. The TA children were more reliant on the school-taught linear system in both grades. The performance of the LA children was similar to that of the MLD children in first grade and to the TA children in second. The central executive component of working memory contributed to across-grade improvements in number line performance and to group differences in this performance.Several large-scale population-based, prospective studies and a number of smaller-scale studies have consistently found that between 5% and 10% of children and adolescents will experience a substantive learning deficit-not attributable to low cognitive ability-in at least one area of mathematics before graduating from high school (Badian, 1983;Barbaresi, Katusic, Colligan, Weaver, & Jacobsen 2005;Ostad, 1998;Shalev, 2007;Shalev, Manor, & Gross-Tsur, 2005). These individuals are considered to have a mathematical learning disability (MLD), and are joined by another 5% and perhaps many more children and adolescents who experience more mild and circumscribed learning difficulties in mathematics (for recent reviews see Berch & Mazzocco, 2007). The mathematics achievement of this latter group of low achieving children (LA) is below expectations based on their cognitive ability and reading achievement, and the mechanisms contributing to their difficulties with mathematics learning may differ from those underlying MLD (Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007;Murphy, Mazzocco, Hanich, & Early, 2007). The central executive component of working memory has been implicated as a core mechanism underlying differences in the mathematical cognition of children with MLD but not their LA peers, but this remains to be confirmed. Moreover, the mathematical areas in which these groups may be similar or different are not well understood. HHS Public Access Author Manuscript Author ManuscriptAuthor Manuscript Author ManuscriptChildren with MLD have deficits in a wide range of basic mathematical domains, including a delayed understanding of counting concepts (Geary, Bow-Thomas, & Yao, 1992), difficulties remembering arithmetic facts (Geary, 1993;Jordan, Hanich, & Kaplan, 2003;Jordan & Montani, 1997), and poor conceptual knowledge of rational numbers (Mazzocco & Devlin, in press). The delayed learning of LA children, in contrast, may center on basic numerical representations, including the number line (Geary et al., 20...

Intuitive proportion judgment in number-line estimation: Converging evidence from multiple tasks

“…For example, children characterized as linear estimators do better on standardized math tests and other measures of mathematical ability (Ashcraft & Moore, 2012;Booth & Siegler, 2006) and children with mathematical learning disability (MLD) produce linear estimates later than comparison groups (Geary, Hoard, Nugent, & Byrd-Craven, 2008) -behaviors that have been attributed to differences in children's numerical magnitude representations. These findings have also led researchers to develop effective interventions to improve formal math performance (e.g.…”

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).…”

Development of numerical estimation in Chinese preschool children

“…This law is believed to describe representations of numerical as well as physical magnitudes (Bank & Hill, 1974;Dehaene, 1997). One of the widely used tasks to examine how the human mind represents numbers is the number line estimation task, in which participants are asked to place a given number on a straight line anchored with numbers at the two ends (e.g., 0 on the left end and 10 or 100 on the right end; Dehaene, Izard, Spelke, & Pica, 2008;Ebersbach, Luwel, Frick, Onghena, & Verschaffel, 2008;Geary, Hoard, Nugent, & Byrd-Craven, 2008;Moeller, Pixner, Kaufmann, & Nuerk, 2009;Muldoon, Simms, Towse, Menzies, & Yue, 2011;Opfer, Siegler, & Young, 2011;Siegler & Booth, 2004;Siegler & Opfer, 2003;Slusser, Santiago, & Barth, 2013;Whyte & Bull, 2008;.…”