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

Abstract

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 , 2005 ; A. J. Wilson & Dehaene, 2007 ) and/or to access that number magnitude representation from numerical symbols ( Rousselle & Noël, 2007 ). 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.

Impairment of Arabic- and spoken-number processing in children with mathematical learning disability

“…With respect to number production, our results also confirmed those of studies showing that children with MLD were impaired in tasks consisting of transcoding numerosities in spoken numbers (for example, Olkun et al, 2015;Mazzocco et al, 2011;and Mejias et al, 2012). In the present study, we found that children with MLD were less precise than TD children when asked to produce numbers in both analogic-to-symbolic and symbolicto-analogic number transcoding tasks.…”

“…Some of this uncertainty stems from significant differences in the methods and tasks used to measure numerical skills in children. In previous studies, researchers usually used comparison tasks to assess numerical abilities in children with MLD and mainly found that they presented deficits in processing Arabic numbers (Davidse et al, 2014;De Smedt & Gilmore, 2011;Desoete et al, 2012;Ferreira et al, 2012;Landerl & Kölle, 2009;Mejias et al, 2012;Mussolin et al, 2010;Piazza et al, 2010;Price, Holloway, Räsänen, Vesterinen, & Ansari, 2007;Rousselle & Noël, 2007). Spoken numerals are nonetheless as important as Arabic numerals in school as well as in daily life activities and should also be considered in studies designed to address the functional origin of MLD.…”

“…Furthermore, in most of the reported studies, symbolic number processing was measured with comprehension tasks, while number production and number recognition tasks were used less often. When the production of symbolic numbers was investigated, researchers usually used transcoding tasks (such as analogic-to-symbolic numbers and vice versa) and found that children with MLD had difficulties in transcoding analogic numerosities (e.g., groups of dots) to symbolic spoken numbers (e.g., Mazzocco et al, 2011;Mejias et al, 2012;Olkun, Altun, & Şahin, 2015), without investigating symbolic Arabic numbers. Furthermore, Mejias et al (2012) explored only the reverse transcoding of Arabic numbers from 8 to 64 to analogic numbers and found that 9-10-year-old children with MLD had difficulties in approximately producing a collection corresponding to an Arabic number.…”

“…When the production of symbolic numbers was investigated, researchers usually used transcoding tasks (such as analogic-to-symbolic numbers and vice versa) and found that children with MLD had difficulties in transcoding analogic numerosities (e.g., groups of dots) to symbolic spoken numbers (e.g., Mazzocco et al, 2011;Mejias et al, 2012;Olkun, Altun, & Şahin, 2015), without investigating symbolic Arabic numbers. Furthermore, Mejias et al (2012) explored only the reverse transcoding of Arabic numbers from 8 to 64 to analogic numbers and found that 9-10-year-old children with MLD had difficulties in approximately producing a collection corresponding to an Arabic number. Surprisingly, neither study explored spoken-to-analogic numbers transcoding nor analogic-to-Arabic numbers transcoding in schoolage children with MLD, so that the picture regarding the production of numbers in MLD remains incomplete.…”

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

“…Some studies reported a significant correlation between CV and mathematical skills in children (e.g., Mejias, Mussolin, Rousselle, Grégoire, & Noël, 2012;Mejias and Schiltz, 2013) whereas others (Castronovo & Göbel, 2012, experiments 3 & 4) observed that the veridicity of the estimates correlated with math ability in adults, but found no relationship between individual CVs and math ability. Thus, similarly to the findings based on the Weber fraction, it is still unclear ASSESSING THE APPROXIMATE NUMBER SYSTEM whether there is a relationship between CV and arithmetic skill.…”