Parts and 'holes': gaps in rational number sense among children with vs. without mathematical learning disabilities.

Many middle-school students struggle with decimals and fractions, even if they do not have a mathematical learning disability (MLD). In the present longitudinal study, we examined whether children with MLD have weaker rational number knowledge than children whose difficulty with rational numbers occurs in the absence of MLD. We found that children with MLD failed to accurately name decimals, to correctly rank order decimals and/or fractions, and to identify equivalent ratios (e.g. 0.5 = 1/2); they also 'identified' incorrect equivalents (e.g. 0.05 = 0.50). Children with low math achievement but no MLD accurately named decimals and identified equivalent pairs, but failed to correctly rank order decimals and fractions. Thus failure to accurately name decimals was an indicator of MLD; but accurate naming was no guarantee of rational number knowledge - most children who failed to correctly rank order fractions and decimals tests passed the naming task. Most children who failed the ranking tests at 6th grade also failed at 8th grade. Our findings suggest that a simple task involving naming and rank ordering fractions and decimals may be a useful addition to in-class assessments used to determine children's learning of rational numbers.

Is it a fact? Timed arithmetic performance of children with mathematical learning disabilities (MLD) varies as a function of how MLD is defined.

Poor fact retrieval is a frequently reported characteristic of children with mathematical learning disability (MLD). To better understand the nature and specificity of poor fact retrieval in MLD, in the present study, we examined eighth graders' accuracy on timed addition and multiplication problems of varying levels of difficulty. We compared the performance of 16 children with deficient math achievement (MLD), 19 children with below average (but not deficient) math achievement (LA), and 100 typically achieving (TA) children. Children in all three groups made errors. Errors made by children in the LA group were more numerous, but comparable in type, to those observed for typically developing children. Errors made by children with MLD were more numerous still, and included errors that differ qualitatively from those in the LA and TA groups. Thus the way in which performance linked to "math difficulties" differs from that of typically achieving children varies as a function of how we define math disabilities (MLD vs. LA). Moreover, the frequency and types of errors made by individuals varied within the MLD group, highlighting group heterogeneity even when using strict criteria to define this group of children. Finally, the types of errors made by children with MLD reflect reliance on processes other than retrieval to solve these alleged "math facts."