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...

Humans and other animals are able to make rough estimations of quantities using what has been termed the approximate number system (ANS). Much evidence suggests that sensitivity to numerosity correlates with symbolic math capacity, leading to the suggestion that the ANS may serve as a start-up tool to develop symbolic math. Many experiments have demonstrated that numerosity perception transcends the sensory modality of stimuli and their presentation format (sequential or simultaneous), but it remains an open question whether the relationship between numerosity and math generalizes over stimulus format and modality. Here we measured precision for estimating the numerosity of clouds of dots and sequences of flashes or clicks, as well as for paired comparisons of the numerosity of clouds of dots. Our results show that in children, formal math abilities correlate positively with sensitivity for estimation and paired-comparisons of the numerosity of visual arrays of dots. However, precision of numerosity estimation for sequences of flashes or sounds did not correlate with math, although sensitivities in all estimations tasks (for sequential or simultaneous stimuli) were strongly correlated with each other. In adults, we found no significant correlations between math scores and sensitivity to any of the psychophysical tasks. Taken together these results support the existence of a generalized number sense, and go on to demonstrate an intrinsic link between mathematics and perception of spatial, but not temporal numerosity. (PsycINFO Database Record

When asked to estimate the number of items in a visual array, educated adults and children are more precise and rapid if the items are clustered into small subgroups rather than randomly distributed. This phenomenon, termed “groupitizing”, is thought to rely on the recruitment of the subitizing system (dedicated to the perception of very small numbers), with the aid of simple arithmetical calculations. The aim of current study is to verify whether the advantage for clustered stimuli does rely on subitizing, by manipulating attention, known to strongly affect attention. Participants estimated the numerosity of grouped or ungrouped arrays in condition of full attention or while attention was diverted with a dual-task. Depriving visual attention strongly decreased estimation precision of grouped but not of ungrouped arrays, as well as increasing the tendency for numerosity estimation to regress towards the mean. Additional explorative analyses suggested that calculation skills correlated with the estimation precision of grouped, but not of ungrouped, arrays. The results suggest that groupitizing is an attention-based process that leverages on the subitizing system. They also suggest that measuring numerosity estimation thresholds with grouped stimuli may be a sensitive correlate of math abilities.

Like most perceptual attributes, the perception of numerosity is susceptible to adaptation, both to prolonged viewing of spatial arrays and to repeated motor actions such as hand-tapping. However, the possibility has been raised that adaptation may reflect response biases rather than modification of sensory processing. To disentangle these two possibilities, we studied visual and motor adaptation of numerosity perception while measuring confidence and reaction times. Both sensory and motor adaptation robustly distorted numerosity estimates, and these shifts in perceived numerosity were accompanied by similar shifts in confidence and reaction-time distributions. After adaptation, maximum uncertainty and slowest response-times occurred at the point of subjective (rather than physical) equality of the matching task, suggesting that adaptation acts directly on the sensory representation of numerosity, before the decisional processes. On the other hand, making reward response-contingent, which also caused robust shifts in the psychometric function, caused no significant shifts in confidence or reaction-time distributions. These results reinforce evidence for shared mechanisms that encode the quantity of both internally and externally generated events, and advance a useful general technique to test whether contextual effects like adaptation and serial dependence really affect sensory processing.