previous work has shown that when arrays of objects are grouped within clusters, participants can enumerate their numerosity more rapidly than when objects are randomly scattered, a phenomenon termed "groupitizing". importantly, the magnitude of the grouping advantage correlates with math abilities in children. Here we show that sensory precision of numerosity estimation is also improved when grouping cues are available, by up to 20%. The grouping can be induced by color and/or spatial proximity, and occurs in temporal sequences as well as spatial arrays. the improvement is strongest for participants with the highest thresholds in the random, ungrouped conditions. taken together with previous research, our data suggest that measurements correlations between numerosity estimation and formal math skills may be driven by grouping strategies, which require a minimal level of basic arithmetic. When counting is not possible, humans and other animals can rapidly estimate the number of items in any scene to achieve an approximate assessment of their numerosity. The system sustaining this ability is often termed the Approximate Number System (ANS) and, like all sensory systems, is error-prone, with errors increasing proportionally with numerosity, obeying Weber Law 1-4. Importantly, many studies have found a correlation between ANS precision (measured by Weber fraction or Coefficient of variation) and child math abilities, with lower precision associated with poorer performance in math 5-8. Children with dyscalculia, a neurodevelopmental disorder affecting mathematical and numerical learning, often show higher Weber fractions compared to typically developing children 6,9,10. Based on this evidence it has been proposed that the ANS may constitute a foundational non-symbolic system on which the language-based mathematical system could subsequently be built 6. Jevons 11 first reported that estimates of numerosities less than four are fast and error-free, subsequently termed subitizing by Kaufman and Lord 12. Subitizing is robust, and occurs for both sequential and simultaneous stimuli, in all sensory modalities 3,13-16. Subitizing is highly dependent on attention 17-24 , and seems to work in parallel with the estimation system, boosting performance at low numerosities. More recently, Starkey and McCandliss 25 suggested that subitizing mechanisms may also come into play for higher numerosities, a process they term "groupitizing". This is very much like George Miller's well-known notion of "chunking", where complex sets of information such as long telephone numbers can be more easily recalled if parsed into three or four smaller "chunks". Starkey et al. 25 measured counting speed of spatially clustered arrays in school-age children, and found that clustering, or grouping, increased performance. Crucially, both the number of clusters and the number of elements within each cluster was limited to the subitizing range (e.g. 7 = 2 + 2 + 3). Interestingly, the grouping advantage increased with age and correlated with arithmetic abil...

Psychophysical studies have shown that numerosity is a sensory attribute susceptible to adaptation. Neuroimaging studies have reported that, at least for relatively low numbers, numerosity can be accurately discriminated in the intra-parietal sulcus. Here we developed a novel rapid adaptation paradigm where adapting and test stimuli are separated by pauses sufficient to dissociate their BOLD activity. We used multivariate pattern recognition to classify brain activity evoked by non-symbolic numbers over a wide range (20–80), both before and after psychophysical adaptation to the highest numerosity. Adaptation caused underestimation of all lower numerosities, and decreased slightly the average BOLD responses in V1 and IPS. Using support vector machine, we showed that the BOLD response of IPS, but not in V1, classified numerosity well, both when tested before and after adaptation. However, there was no transfer from training pre-adaptation responses to testing post-adaptation, and vice versa, indicating that adaptation changes the neuronal representation of the numerosity. Interestingly, decoding was more accurate after adaptation, and the amount of improvement correlated with the amount of perceptual underestimation of numerosity across subjects. These results suggest that numerosity adaptation acts directly on IPS, rather than indirectly via other low-level stimulus parameters analysis, and that adaptation improves the capacity to discriminate numerosity.

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively sparse, segregatable items (24 dots); numerosity of very dense textured patterns (250 dots); and discrimination of direction of motion. Thresholds in all tasks improved with age, but at different rates, implying the action of different mechanisms: In particular, in young children, thresholds were lower for sparse than textured patterns (the opposite of adults), suggesting earlier maturation of numerosity mechanisms. Importantly, numerosity thresholds for sparse stimuli correlated strongly with math skills, even after controlling for the influence of age, gender and nonverbal IQ. However, neither motion-direction discrimination nor numerosity discrimination of texture patterns showed a significant correlation with math abilities. These results provide further evidence that numerosity and texture-density are perceived by independent neural mechanisms, which develop at different rates; and importantly, only numerosity mechanisms are related to math. As developmental dyscalculia is characterized by a profound deficit in discriminating numerosity, it is fundamental to understand the mechanism behind the discrimination. (PsycINFO Database Record

Between 1-5:100 people worldwide has never experienced normotypic vision due to a condition called amblyopia, and about 1:4000 suffer from inherited retinal dystrophies that progressively lead them to blindness. While a wide range of technologies and therapies are being developed to restore vision, a fundamental question still remains unanswered: would the adult visual brain retain a sufficient plastic potential to learn how to 'see' after a prolonged period of abnormal visual experience? In this review we summarize studies showing that the visual brain of sighted adults retains a type of developmental plasticity, called homeostatic plasticity, and this property has been recently exploited successfully for adult amblyopia recover. Next, we discuss how the brain circuits reorganizes when visual stimulation is partially restored by means of a 'bionic eye' in late blinds with Retinitis Pigmentosa. The primary visual cortex in these patients slowly became activated by the artificial visual stimulation, indicating that sight restoration therapies can rely on a considerable degree of spared plasticity in adulthood.