Typical numerosity adaptation despite selectively impaired number acuity in dyscalculia, Neuropsychologia.

It has been suggested that a core deficit of the “number sense” may underlie dyscalculia. We test this idea by measuring perceptual adaptation and discrimination thresholds for numerosity and object size in a group of dyscalculic and typical preadolescents (N=71, mean age 12). We confirmed that numerosity discrimination thresholds are higher in evelopmental dyscalculia, while size thresholds are not affected. However, dyscalculics adapted to numerosity in a similar way to typicals. This suggests that although numerosity thresholds are selectively higher in dyscalculia, the mechanisms for perceiving numerosity are otherwise similar, suggesting that that have a similar, but perhaps noisier, number sense.

Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude, Sci Rep, 1 (8), 13571.

How numerical quantity is processed is a central issue for cognition. On the one hand the “number sense theory” claims that numerosity is perceived directly, and may represent an early precursor for acquisition of mathematical skills. On the other, the “theory of magnitude” notes that numerosity correlates with many continuous properties such as size and density, and may therefore not exist as an independent feature, but be part of a more general system of magnitude. In this study we examined interactions in sensitivity between numerosity and size perception. In a group of children, we measured psychophysically two sensory parameters: perceptual adaptation and discrimination thresholds for both size and numerosity. Neither discrimination thresholds nor adaptation strength for numerosity and size correlated across participants. This clear lack of correlation (confirmed by Bayesian analyses) suggests that numerosity and size interference effects are unlikely to reflect a shared sensory representation. We suggest these small interference effects may rather result from top-down phenomena occurring at late decisional levels rather than a primary “sense of magnitude”.

Cognitive processes underlying arithmetical skills in primary school: the role of fluency, handwriting, number line and number acuity, Neuropsy Trends, (23).

The aim of the present study is to determine the presence of specific and independent core processes involved in arithmetical skills. We evaluated performances of 68 typically developing school children (8-11 yrs) on numerosity acuity, number line, handwriting (non-math writing skills), phonemic and design fluency as well as math abilities. A principal component analysis on math subtests scores revealed three main factors: Numeracy, Magnitude and Handwriting. Correlations showed that phonemic fluency was associated with the Numeracy factor and the Magnitude factor while design fluency with the Handwriting factor. Number acuity was associated with the Magnitude factor, number line with the Numeracy factor, handwriting with the Handwriting factor. Hierarchical regressions analyses indicated that number acuity, number line, phonemic fluency and handwriting explained unique variance portions on Math test (factors scores). Our study suggests an explanation of the cognitive architecture of processes involved in arithmetical skills in school children.

Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities, Journal of Experimental Child Psychology, (178), 86-103.

Small quantities of visual objects can be rapidly estimated without error, a phenomenon known as subitizing. Larger quantities can also be rapidly estimated, but with error, and the error rate predicts math abilities. This study addressed two issues: (a) whether subitizing generalizes over modalities and stimulus formats and (b) whether subitizing correlates with math abilities. We measured subitizing limits in primary school children and adults for visual and auditory stimuli presented either sequentially (sequences of flashes or sounds) or simultaneously (visual presentations, dot arrays). The results show that (a) subitizing limits for adults were one item larger than those for primary school children across all conditions; (b) subitizing for simultaneous visual stimuli (dots) was better than that for sequential stimuli; (c) subitizing limits for dots do not correlate with subitizing limits for either flashes or sounds; (d) subitizing of sequences of flashes and subitizing of sequences of sounds are strongly correlated with each other in children; and (e) regardless of stimuli sensory modality and format, subitizing limits do not correlate with mental calculation or digit magnitude knowledge proficiency. These results suggest that although children can subitize sequential numerosity, simultaneous and temporal subitizing may be subserved by separate systems. Furthermore, subitizing does not seem to be related to numerical abilities.