Studies on developmental dyscalculia (DD) have tried to identify a basic numerical deficit that could account for this specific learning disability. The first proposition was that the number magnitude representation of these children was impaired. However, Rousselle and Noel (2007) brought data showing that this was not the case but rather that these children were impaired when processing the magnitude of symbolic numbers only. Since then, incongruent results have been published. In this paper, we will propose a developmental perspective on this issue. We will argue that the first deficit shown in DD regards the building of an exact representation of numerical value, thanks to the learning of symbolic numbers, and that the reduced acuity of the approximate number magnitude system appears only later and is secondary to the first deficit.

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Developmental Changes in the Profiles of Dyscalculia: An Explanation Based on a Double Exact-and-Approximate Number Representation Model

Weak task-related modulation and stimulus representations during arithmetic problem solving in children with developmental dyscalculia.

Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition.

What basic number processing measures in kindergarten explain unique variability in first-grade arithmetic proficiency?

Dot enumeration (DE) and number comparison (NC) abilities are considered markers of core number competence. Differences in DE/NC reaction time (RT) signatures are thought to distinguish between typical and atypical number development. Whether a child's DE and NC signatures change or remain stable over time, relative to other developmental signatures, is unknown. To investigate these issues, the DE and NC RT signatures of 159 children were assessed 7 times over 6 years. Cluster analyses identified within-task and across-age subgroups. DE signatures comprised 4 parameters: (a) the RT slope within the subitizing range, (b) the RT slope for the counting range, (c) the subitizing range (indicated by the point of slope discontinuity), and (d) the overall average DE RT response. NC RT signatures comprised 2 parameters (NC intercept and slope) derived from RTs comparing numbers 1 to 9. Analyses yielded 3 distinct DE and NC profiles at each age. Within-age subgroup profiles reflected differences in 3 of the 4 DE parameters and only 1 NC parameter. Systematic changes in parameters were observed across ages for both tasks, and both tasks broadly identified the same subgroups. Sixty-nine percent of children were assigned to the same subgroup across age, even though parameters themselves changed across age. Subgroups did not differ in processing speed or nonverbal reasoning, suggesting that DE and NC do not tap general cognitive abilities but reflect individual differences specific to the domain of numbers. Indeed, both DE and NC subgroup membership at 6 years predicted computation ability at 6 years, 9.5 years, and 10 years.

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Stability and Change in Markers of Core Numerical Competencies

Enumeration performance in standard dot counting paradigms was investigated for different age groups with typical and atypically poor development of arithmetic skills. Experiment 1 showed a high correspondence between response times and saccadic frequencies for four age groups with typical development. Age differences were more marked for the counting than the subitizing range. In Experiment 2 we found a discontinuity between subitizing and counting for dyscalculic children; however, their subitizing slopes were steeper than those of typically developing control groups, indicating a dysfunctional subitizing mechanism. Across both experiments a number of factors could be identified that affect enumeration in the subitizing and the counting range differentially. These differential patterns further support the assumption of two qualitatively different enumeration processes.

Patrick Schleifer

Papers

Subitizing and Counting in Typical and Atypical Development.