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

Authors

  • Michèle M.M. Mazzocco,

    1. Department of Psychiatry and Behavioral Sciences, Johns Hopkins University School of Medicine, USA
    2. Department of Population and Family Health Sciences, Johns Hopkins Bloomberg School of Public Health, USA
    3. Math Skills Development Project, Kennedy Krieger Institute, USA
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  • Kathleen T. Devlin

    1. Math Skills Development Project, Kennedy Krieger Institute, USA
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Address for correspondence: Michèle Mazzocco, Kennedy Krieger Institute, Math Skills Development Project, 3825 Greenspring Avenue, Painter Building, Top Floor, Baltimore, MD 21211, USA; e-mail: mazzocco@jhu.edu

Abstract

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 =inline image); 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.

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