Numerical and nonnumerical estimation in children with and without mathematical learning disabilities

There are currently multiple explanations for mathematical learning disabilities (MLD). The present study focused on those assuming that MLD are due to a basic numerical deficit affecting the ability to represent and to manipulate number magnitude (Butterworth, 1999 Butterworth, B. 1999. The mathematical brain, London, , United Kingdom: Macmillan.  [Google Scholar], 2005 Butterworth, B. 2005. “Developmental dyscalculia”. In Handbook of mathematical cognition, Edited by: Campbell, J. I. D. 455–467. New York, NY: Psychology Press.  [Google Scholar]; A. J. Wilson &; Dehaene, 2007 Wilson, A. J. and Dehaene, S. 2007. “Number sense and developmental dyscalculia”. In Human behavior, learning, and the developing brain: Atypical development, 2nd, Edited by: Coch, D., Dawson, G. and Fischer, K. 212–237. New York, NY: Guilford Press.  [Google Scholar]) and/or to access that number magnitude representation from numerical symbols (Rousselle &; Noël, 2007 Rousselle, L. and Noël, M. P. 2007. Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3): 361–395. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]). The present study provides an original contribution to this issue by testing MLD children (carefully selected on the basis of preserved abilities in other domains) on numerical estimation tasks with contrasting symbolic (Arabic numerals) and nonsymbolic (collection of dots) numbers used as input or output. MLD children performed consistently less accurately than control children on all the estimation tasks. However, MLD children were even weaker when the task involved the mapping between symbolic and nonsymbolic numbers than when the task required a mapping between two nonsymbolic numerical formats. Moreover, in the estimation of nonsymbolic numerosities, MLD children relied more than control children on perceptual cues such as the cumulative area of the dots. Finally, the task requiring a mapping from a nonsymbolic format to a symbolic format was the best predictor of MLD. In order to explain these present results, as well as those reported in the literature, we propose that the impoverished number magnitude representation of MLD children may arise from an initial mapping deficit between number symbols and that magnitude representation.