Academic literature on the topic 'Groupitizing'

Enumeration of a dot array is faster and easier if the items form recognizable subgroups. This phenomenon, which has been termed “groupitizing,” appears in children after one year of formal education and correlates with arithmetic abilities. We formulated and tested the hypothesis that groupitizing reflects an ability to sidestep counting by using arithmetic shortcuts, for instance, using the grouping structure to add or multiply rather than just count. Three groups of students with different levels of familiarity with mathematics were asked to name the numerosity of sets of 1–15 dots in various arrangements, for instance, 9 represented as a single group of 9 items, three distinct groups of 2, 3, and 4 items (affording addition 2 + 3 + 4), or three identical groups of 3 items (affording multiplication 3 × 3). Grouping systematically improved enumeration performance, regardless of whether the items were grouped spatially or by color alone, but only when an array was divided into subgroups with the same number of items. Response times and error patterns supported the hypothesis of a multiplication process. Our results demonstrate that even a simple enumeration task involves mental arithmetic.

Numerosity estimation around the subitizing range is facilitated by a shape-template matching process and shape-coding mechanisms are selective to visual features such as colour and luminance contrast polarity. Objects in natural scenes are often embedded within other objects or textured surfaces. Numerosity estimation is improved when objects are grouped into small clusters of the same colour, a phenomenon termed groupitizing, which is thought to leverage on the subitizing system. Here we investigate whether numerosity mechanisms around the subitizing range are selective to colour, luminance contrast polarity and orientation, and how spatial organisation of context and target elements modulates target numerosity estimation. Stimuli consisted of a small number (3-to-6) of target elements presented either in isolation or embedded within context elements. To examine selectivity to colour, luminance polarity and orientation, we compared target-only conditions in which all elements were either the same or different along one of these feature dimensions. We found comparable performance in the same and different feature conditions, revealing that subitizing mechanism do not depend on ‘on-off’ luminance-polarity, colour or orientation channel interactions. We also measured the effect of varying spatial organisation of (i) context, by arranging the elements either in a grid, mirror-symmetric, translation-symmetric or random; (ii) target, by placing the elements either mirror-symmetric, on the vertices of simple shapes or random. Our results indicate higher accuracy and lower RTs in the grid compared to all other context types, with mirror symmetric, translation and random arrangements having comparable effects on target numerosity. We also found improved performance with shape-target followed by symmetric and random target arrangements in the absence and presence of context. These findings indicate that numerosity mechanisms around the subitizing range are not selective to colour, luminance polarity and orientation, and that symmetric, translation and random contexts organisations inhibit target-numerosity encoding stronger than regular/grid context.

Groupitizing is a recently described phenomenon of numerosity perception where clustering items of a set into smaller “subitizable” groups improves discrimination. Groupitizing is thought to be rooted on the subitizing system, with which it shares several properties: both phenomena accelerate counting and decrease estimation thresholds irrespective of stimulus format (for both simultaneous and sequential numerosity perception) and both rely on attention. As previous research on groupitizing has been almost completely limited to vision, the current study investigates whether it generalizes to other sensory modalities. Participants estimated the numerosity of a series of tones clustered either by proximity in time or by similarity in frequency. We found that compared with unstructured tone sequences, grouping lowered auditory estimation thresholds by up to 20%. The groupitizing advantage was similar across different grouping conditions, temporal proximity and tone frequency similarity. These results mirror the groupitizing effect for visual stimuli, suggesting that, like subitizing, groupitizing is an a-modal phenomenon.

AbstractWhen asked to estimate the number of items in the visual field, neurotypical adults are more precise and rapid if the items are clustered into subgroups compared to when they are randomly distributed. It has been suggested that this phenomenon, termed “groupitizing”, relies on the recruitment of arithmetical calculation strategies and subitizing. Here the role of arithmetical skills in groupitizing was investigated by measuring the groupitizing effect (or advantage) in a sample of children and adolescents with and without math learning disability (dyscalculia). The results showed that when items were grouped, both groups of participants showed a similar advantage on sensory precision and response time in numerosity estimates. Correlational analyses confirmed a lack of covariation between groupitizing advantage and math scores. Bayesian statistics on sensory precision sustained the frequentist analyses providing decisive evidence in favor of no groups difference on groupitizing advantage magnitude (LBF = − 0.44) and no correlation with math scores (LBF = − 0.57). The results on response times, although less decisive, were again in favor of the null hypothesis. Overall, the results suggest that the link between groupitizing and mathematical abilities cannot be taken for granted, calling for further investigations on the factors underlying this perceptual phenomenon.

AbstractThe number of items in an array can be quickly and accurately estimated by dividing the array into subgroups, in a strategy termed “groupitizing.” For example, when memorizing a telephone number, it is better to do so by divide the number into several segments. Different forms of visual grouping can affect the precision of the enumeration of a large set of items. Previous studies have found that when groupitizing, enumeration precision is improved by grouping arrays using visual proximity and color similarity. Based on Gestalt theory, Palmer (Cognit Psychol 24:436, 1992) divided perceptual grouping into intrinsic (e.g., proximity, similarity) and extrinsic (e.g., connectedness, common region) principles. Studies have investigated groupitizing effects on intrinsic grouping. However, to the best of our knowledge, no study has explored groupitizing effects for extrinsic grouping cues. Therefore, this study explored whether extrinsic grouping cues differed from intrinsic grouping cues for groupitizing effects in numerosity perception. The results showed that both extrinsic and intrinsic grouping cues improved enumeration precision. However, extrinsic grouping was more accurate in terms of the sensory precision of the numerosity perception.

Recent studies showed that kindergarten children solve addition, subtraction, doubling and halving problems using the core system for the approximate representation of numerical magnitude. In Study 1, 34 first-grade students in their first week of schooling solved approximate arithmetic problems in a number range up to 100 regarding all four basic operations. Children solved these problems significantly above chance.In Study 2, 66 first graders were tested for their approximate arithmetic achievement, working memory capacity, groupitizing, phonological awareness, naming speed and early arithmetic concepts at the beginning of first grade and again at the beginning of second grade. It appears that approximate arithmetic achievement is independent from most other cognitive variables and correlates most with other variables of the mathematical domain. Furthermore, regression analyses revealed that school success was only predicted by groupitizing and central executive capacity, but not approximate arithmetic achievement, when controlling for other cognitive variables.

Abstract 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.

The present dissertation investigated visual perception of numerosity. In the first part I reviewed the prominent literature about the topic. In the second chapter I described the first experiment, in which I measured confidence and reaction times to study the origins of the well-established visual and motor adaptation effects on numerosity perception. The results reinforce the evidence for a shared mechanism that encodes the quantity of both internally and externally generated events, and shows that the adaptation effects result from changes in sensory encoding, rather than perceptual decisions. More generally, in the study was introduced a novel and useful technique for investigating the mechanisms of numerosity adaptation and sensory adaptation in general. The third chapter investigated the effects of grouping cues on sensory precision of numerosity estimation. The results provide strong evidence that “grouping”, which can improve performance by up to 20%, can be induced by color and/or spatial proximity and occurs in temporal sequences as well as spatial arrays. In the fourth chapter I further examined the groupitizing phenomenon, by testing the hypothesis that the advantage provided by clustering stimuli relies on subitizing. This was achieved by manipulating attention, which is known to strongly affect the subitizing system. In the same chapter I discussed an additional explorative analysis on the relationship between calculation skills and estimation precision of grouped and ungrouped arrays. Taken together, the results showed that groupitizing is truly an attention-based process that leverages on the subitizing system. Furthermore, the outcome of the study suggested that measuring numerosity estimation thresholds with grouped stimuli may be a sensitive correlate of math abilities. In the fifth chapter I went on investigating the neural correlates of the groupitizing phenomenon with both a behavioral and a fMRI study. Similarly to the previous study I measured acuity in estimation of grouped and ungrouped stimuli and additionally I also examined whether the two tasks shared or not the same neural substrate. The results showed that the estimation of grouped and ungrouped stimuli activates similar regions in the right lateralized fronto-parietal network, however, only the presentation of grouped stimuli in the numerosity task elicited the additional activation of regions linked with calculations strategies, for instance the angular gyrus. Moreover, a multivariate pattern analysis showed that parietal activation patterns for individual numerosities could be accurately decoded in the parietal regions independently of the spatial arrangement of the stimuli. Finally, I correlated fMRI decoding accuracy of primary visual areas and angular gyrus with Wfs calculated in the grouped estimation task. Results suggested that the numerical representation in angular gyrus, but not in primary visual areas, is strongly linked with numerical performance and behavior. Overall, the results confirmed psychophysical studies highlighting that groupitizing shares the same regions and neural pattern mechanism of the estimation of ungrouped stimuli, but, furthermore, it also activates brain regions typically activated during calculation tasks. The last part of the dissertation is dedicated to investigating the link between numerosity precision, math abilities and a non-cognitive factor affecting mathematical learning: mathematical anxiety. To this aim, university students with low (< 25th percentile) and high (> 75th percentile) score in the Abbreviate Math Anxiety Scale were tested in multiple domains: a) math proficiency assessed using a standardized test (Mathematics Prerequisite for Psychometrics), b) visuo-spatial attention capacity, measured via a Multiple Object Tracking task, and c) the sensory precision for non-numerical quantities. The results confirmed previous studies showing that math abilities and numerosity precision correlate in subjects with high math anxiety. Furthermore, neither precision in size-discrimination nor visuo-spatial attentional capacity were found to correlate with math capacities. However, within the group with high MA the data also revealed a relationship between numerosity precision and math anxiety, with math anxiety playing a key role in mediating the correlation between participants’ numerosity precision and their math achievement. Taken together, this last study suggests an interplay between extreme levels of MA and sensory precision in the processing of non-symbolic numerosity, giving further insight into the processes (and the variables affecting these processes) behind the acquisition of formal mathematical abilities. In conclusion, the present work assessed the ability to perceive non-symbolic quantities in adults while providing new experimental evidence suggesting its perceptual nature and its link with cognitive and affective factors.