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Giovanni Anobile

Post-doc in Developmental Psychology, Stella Maris Scientific Institute, Pisa

Contacts

  • Email: GiovanniAnobile (AT) hotmail.it
  • Telephone:  +39 050 3153175

Research laboratories

  • CNR Institute of Neuroscience, Pisa
  • Department of Psychology, University of Florence
  • Stella Maris Foundation, Pisa, Italy

Education

  • 2009: Italian Master Degree in Experimental Psychology. Summa cum laude. University of Florence.
  • 2007: Italian Degree in Experimental Psychology. University of Florence.

Current research and interests

  • Numerosity perception
  • Multi-sensory perception
  • Dyscalculia
  • Attention

Publications

 2018

Anobile, G., Burr, D. C., Iaia, M., Marinelli, C. V., Angelelli, P. & Turi, M. (2018). Independent adaptation mechanisms for numerosity and size perception provide evidence against a common sense of magnitude, Sci Rep, 1 (8), 13571. PDF

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".

Stievano, P., Cammisuli, D. M., Iaia, M., Michetti, S., Ceccolin,C. & Anobile, G. (2018). Cognitive processes underlying arithmetical skills in primary school: the role of fluency, handwriting, number line and number acuity, Neuropsy Trends, (23). PDF

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.

Anobile, G., Cicchini, G. M., Gasperini, F. & Burr, D. (2018). Typical numerosity adaptation despite selectively impaired number acuity in dyscalculia, Neuropsychologia, PDF

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.

Anobile, G., Arrighi, R. & Burr, D. C. (2019). Simultaneous and sequential subitizing are separate systems, and neither predicts math abilities, Journal of Experimental Child Psychology, (178), 86-103. PDF

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.

2017

Burr, D. C., Anobile, G. & Arrighi, R. (2017). Psychophysical evidence for the number sense, Philos Trans R Soc Lond B Biol Sci, 1740 (373), PDF

It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.This article is part of the discussion meeting issue 'The origins of numerical abilities'.

Anobile, G., Arrighi, R., Castaldi, E., Grassi, E., Pedonese, L., PA, M. M., et al. (2017). Spatial but Not Temporal Numerosity Thresholds Correlate With Formal Math Skills in Children, Dev Psychol, PDF

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.

Anobile, G., Cicchini, G. M., Pomè, A. & Burr, D. (2017). Connecting Visual Objects Reduces Perceived Numerosity and Density for Sparse but not Dense Patterns, Journal of Numerical Cognition, 4 (3), PDF

How is numerosity encoded by the visual system? – directly, or derived indirectly from texture density? We recently suggested that the numerosity of sparse patterns is encoded directly by dedicated mechanisms (which have been described as the “Approximate Number System” ANS). However, at high dot densities, where items become “crowded” and difficult to segregate, “texture-density” mechanisms come into play. Here we tested the importance of item segmentation on numerosity and density perception at various stimulus densities, by measuring the effect of connecting visual objects with thin lines. The results confirmed many previous studies showing that connecting items robustly reduces the apparent numerosity of patterns of moderate density. We further showed that the apparent density of moderate-density patterns is also reduced by connecting the dots. Crucially, we found that both these effects are strongly reduced at higher numerosities. Indeed for density judgments, the effect reverses, so connecting dots in dense patterns increases the apparent density (as expected from the physical characteristics). The results provide clear support for the three-regime framework of number perception, and suggest that for moderately sparse stimuli, numerosity – but not texture-density – is perceived directly.

2016

Anobile, G., Castaldi, E., Turi, M., Tinelli, F. & Burr, D. C. (2016). Numerosity but not texture-density discrimination correlates with math ability in children, Dev Psychol, 8 (52), 1206-1216. PDF

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.

Cicchini, G. M., Anobile, G. & Burr, D. C. (2016). Spontaneous perception of numerosity in humans, Nat Commun, (7), 12536. PDF

Humans, including infants, and many other species have a capacity for rapid, nonverbal estimation of numerosity. However, the mechanisms for number perception are still not clear; some maintain that the system calculates numerosity via density estimates-similar to those involved in texture-while others maintain that more direct, dedicated mechanisms are involved. Here we show that provided that items are not packed too densely, human subjects are far more sensitive to numerosity than to either density or area. In a two-dimensional space spanning density, area and numerosity, subjects spontaneously react with far greater sensitivity to changes in numerosity, than either area or density. Even in tasks where they were explicitly instructed to make density or area judgments, they responded spontaneously to number. We conclude, that humans extract number information, directly and spontaneously, via dedicated mechanisms.

Anobile, G., Arrighi, R., Togoli, I. & Burr, D. C. (2016). A shared numerical representation for action and perception, Elife, (5), PDF

Humans and other species have perceptual mechanisms dedicated to estimating approximate quantity: a sense of number. Here we show a clear interaction between self-produced actions and the perceived numerosity of subsequent visual stimuli. A short period of rapid finger-tapping (without sensory feedback) caused subjects to underestimate the number of visual stimuli presented near the tapping region; and a period of slow tapping caused overestimation. The distortions occurred both for stimuli presented sequentially (series of flashes) and simultaneously (clouds of dots); both for magnitude estimation and forced-choice comparison. The adaptation was spatially selective, primarily in external, real-world coordinates. Our results sit well with studies reporting links between perception and action, showing that vision and action share mechanisms that encode numbers: a generalized number sense, which estimates the number of self-generated as well as external events.



2015

Anobile, G., Turi, M., Cicchini, G. M. & Burr, D. (2015). Mechanisms for perception of numerosity or texture-density are governed by crowding-like effects,Journal of Vision, 15(5), 1-12. PDF

We have recently provided evidence that the perception of number and texture density is mediated by two independent mechanisms: numerosity mechanisms at relatively low numbers, obeying Weber’s law, and texture-density mechanisms at higher numerosities, following a square root law. In this study we investigated whether the switch between the two mechanisms depends on the capacity to segregate individual dots, and therefore follows similar laws to those governing visual crowding. We measured numerosity discrimination for a wide range of numerosities at three eccentricities. We found that the point where the numerosity regime (Weber’s law) gave way to the density regime (square root law) depended on eccentricity. In central vision, the regime changed at 2.3 dots/82, while at 158 eccentricity, it changed at 0.5 dots/82, three times less dense. As a consequence, thresholds for low numerosities increased with eccentricity, while at higher numerosities thresholds remained constant. We further showed that like crowding, the regime change was independent of dot size, depending on distance between dot centers, not distance between dot edges or ink coverage. Performance was not affected by stimulus contrast or blur, indicating that the transition does not depend on low-level stimulus properties. Our results reinforce the notion that numerosity and texture are mediated by two distinct processes, depending on whether the individual elements are perceptually segregable. Which mechanism is engaged follows laws that determine crowding.

Tinelli, F., Anobile, G., Gori, M., Aagten-Murphy, D., Bartoli, M., Burr, D. C., et al. Time, number and attention in very low birth weight children,Neuropsychologia, 2015 PDF

Abstract Premature birth has been associated with damage in many regions of the cerebral cortex, although there is a particularly strong susceptibility for damage within the parieto-occipital lobes (Volpe, 2009). As these areas have been shown to be critical for both visual attention and magnitudes perception (time, space, and number), it is important to investigate the impact of prematurity on both the magnitude and attentional systems, particularly for children without overt white matter injuries, where the lack of obvious injury may cause their difficulties to remain unnoticed. In this study, we investigated the ability to judge time intervals (visual, audio and audio-visual temporal bisection), discriminate between numerical quantities (numerosity comparison), map numbers onto space (numberline task) and to maintain visuo-spatial attention (multiple-object-tracking) in school-age preterm children (N29). The results show that various parietal functions may be more or less robust to prematurity-related difficulties, with strong impairments found on time estimation and attentional task, while numerical discrimination or mapping tasks remained relatively unimpaired. Thus while our study generally supports the hypothesis of a dorsal stream vulnerability in children born preterm relative to other cortical locations, it further suggests that particular cognitive processes, as highlighted by performance on different tasks, are far more susceptible than others.

Anobile, G., Cicchini, G. M. & Burr, D. C. (2015). Number as a primary perceptual attribute: a review, Perception 1-27 DOI: 10.1177/0301006615602599. PDF

Although humans are the only species to possess language-driven abstract mathematical capacities, we share with many other animals a nonverbal capacity for estimating quantities or numerosity. For some time, researchers have clearly differentiated between small numbers of items—less than about four—referred to as the subitizing  range, and larger numbers, where counting or estimation is required. In this review, we examine more recent evidence suggesting a further division, between sets of items greater than the subitizing range, but sparse enough to be individuated as single items; and densely packed stimuli, where they crowd each other into what is betterconsidered as a texture. These two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws and show different dependencies on eccentricity and on luminance levels. But provided the elements are not too crowded (less than about two items per square degree in central vision, less in the periphery), there is little evidence that estimation of numerosity depends on mechanisms responsive to texture. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.

2014

Cicchini, G. M., Anobile, G. & Burr, D. C. (2014). Compressive mapping of number to space reflects dynamic encoding mechanisms, not static logarithmic transform,Proc Natl Acad Sci U S A, 21 (111), 7867-7872. PDF

The mapping of number onto space is fundamental to measurement and mathematics. However, the mapping of young children, unschooled adults, and adults under attentional load shows strong compressive nonlinearities, thought to reflect intrinsic logarithmic encoding mechanisms, which are later "linearized" by education. Here we advance and test an alternative explanation: that the nonlinearity results from adaptive mechanisms incorporating the statistics of recent stimuli. This theory predicts that the response to the current trial should depend on the magnitude of the previous trial, whereas a static logarithmic nonlinearity predicts trialwise independence. We found a strong and highly significant relationship between numberline mapping of the current trial and the magnitude of the previous trial, in both adults and school children, with the current response influenced by up to 15% of the previous trial value. The dependency is sufficient to account for the shape of the numberline, without requiring logarithmic transform. We show that this dynamic strategy results in a reduction of reproduction error, and hence improvement in accuracy.

Anobile, G., Cicchini, G. M. & Burr, D. C. (2014). Separate mechanisms for perception of numerosity and density,Psychol Sci, 1 (25), 265-270. PDF

Despite the existence of much evidence for a number sense in humans, several researchers have questioned whether number is sensed directly or derived indirectly from texture density. Here, we provide clear evidence that numerosity and density judgments are subserved by distinct mechanisms with different psychophysical characteristics. We measured sensitivity for numerosity discrimination over a wide range of numerosities: For low densities (less than 0.25 dots/deg(2)), thresholds increased directly with numerosity, following Weber's law; for higher densities, thresholds increased with the square root of texture density, a steady decrease in the Weber fraction. The existence of two different psychophysical systems is inconsistent with a model in which number is derived indirectly from noisy estimates of density and area; rather, it points to the existence of separate mechanisms for estimating density and number. These results provide strong confirmation for the existence of neural mechanisms that sense number directly, rather than indirectly from texture density.

2013

Anobile, G., Stievano, P. & Burr, D. C. (2013). Visual sustained attention and numerosity sensitivity correlate with math achievement in children,J Exp Child Psychol, 2 (116), 380-391. PDF

In this study, we investigated in school-age children the relationship among mathematical performance, the perception of numerosity (discrimination and mapping to number line), and sustained visual attention. The results (on 68 children between 8 and 11years of age) show that attention and numerosity perception predict math scores but not reading performance. Even after controlling for several variables, including age, gender, nonverbal IQ, and reading accuracy, attention remained correlated with math skills and numerosity discrimination. These findings support previous reports showing the interrelationship between visual attention and both numerosity perception and math performance. It also suggests that attentional deficits may be implicated in disturbances such as developmental dyscalculia.

2012

Anobile, G., Cicchini, G. M. & Burr, D. C. (2012). Linear mapping of numbers onto space requires attention,Cognition, 3 (122), 454-459. PDF

Mapping of number onto space is fundamental to mathematics and measurement. Previous research suggests that while typical adults with mathematical schooling map numbers veridically onto a linear scale, pre-school children and adults without formal mathematics training, as well as individuals with dyscalculia, show strong compressive, logarithmic-like non-linearities when mapping both symbolic and non-symbolic numbers onto the numberline. Here we show that the use of the linear scale is dependent on attentional resources. We asked typical adults to position clouds of dots on a numberline of various lengths. In agreement with previous research, they did so veridically under normal conditions, but when asked to perform a concurrent attentionally-demanding conjunction task, the mapping followed a compressive, non-linear function. We model the non-linearity both by the commonly assumed logarithmic transform, and also with a Bayesian model of central tendency. These results suggest that veridical representation numerosity requires attentional mechanisms.

Anobile, G., Turi, M., Cicchini, G. M. & Burr, D. C. (2012). The effects of cross-sensory attentional demand on subitizing and on mapping number onto space,Vision Res, PDF

Various aspects of numerosity judgments, especially subitizing and the mapping of number onto space, depend strongly on attentional resources. Here we use a dual-task paradigm to investigate the effects of cross-sensory attentional demands on visual subitizing and spatial mapping. The results show that subitizing is strongly dependent on attentional resources, far more so than is estimation of higher numerosities. But unlike many other sensory tasks, visual subitizing is equally affected by concurrent attentionally demanding auditory and tactile tasks as it is by visual tasks, suggesting that subitizing may be amodal. Mapping number onto space was also strongly affected by attention, but only when the dual-task was in the visual modality. The non-linearities in numberline mapping under attentional load are well explained by a Bayesian model of central tendency.

2011

Burr, D. C., Anobile, G. & Turi, M. (2011). Adaptation Affects Both High and Low (Subitized) Numbers Under Conditions of High Attentional Load,Seeing and Perceiving, (24), 141-150. PDF

It has recently been reported that, like most sensory systems, numerosity is subject to adaptation. However, the effect seemed to be limited to numerosity estimation outside the subitizing range. In this study we show that low numbers, clearly in the subitizing range, are adaptable under conditions of high attentional load. These results support the idea that numerosity is detected by a perceptual mechanism that operates over the entire range of numbers, supplemented by an attention-based system for small numbers (subitizing).

2010

Burr, D. C., Turi, M. & Anobile, G. (2010). Subitizing but not estimation of numerosity requires attentional resources,J Vis, 6 (10), 20. PDF

The numerosity of small numbers of objects, up to about four, can be rapidly appraised without error, a phenomenon known as subitizing. Larger numbers can either be counted, accurately but slowly, or estimated, rapidly but with errors. There has been some debate as to whether subitizing uses the same or different mechanisms than those of higher numerical ranges and whether it requires attentional resources. We measure subjects' accuracy and precision in making rapid judgments of numerosity for target numbers spanning the subitizing and estimation ranges while manipulating the attentional load, both with a spatial dual task and the "attentional blink" dual-task paradigm. The results of both attentional manipulations were similar. In the high-load attentional condition, Weber fractions were similar in the subitizing (2-4) and estimation (5-7) ranges (10-15%). In the low-load and single-task condition, Weber fractions substantially improved in the subitizing range, becoming nearly error-free, while the estimation range was relatively unaffected. The results show that the mechanisms operating over the subitizing and estimation ranges are not identical. We suggest that pre-attentive estimation mechanisms works at all ranges, but in the subitizing range, attentive mechanisms also come into play.

 


Conferences

  • Anobile G, Turi M, Burr D C, 2010, "Subitizing but not estimation of numerosity requires attentional resources". Perception, 39 ECVP Abstract Supplement, page 80.
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