Continuous visual properties explain neural responses to nonsymbolic number

Learning to integrate versus inhibiting information is modulated by age

Cognitive training aiming at improving learning is often successful, but what exactly underlies the observed improvements and how these differ across the age spectrum are currently unknown. Here we asked whether learning in young and older people may reflect enhanced ability to integrate information required to perform a cognitive task or whether it may instead reflect the ability to inhibit task-irrelevant information for successful task performance. We trained 30 young and 30 aging human participants on a numerosity discrimination task known to engage the parietal cortex and in which cue-integration and inhibitory abilities can be distinguished. We coupled training with parietal, motor, or sham transcranial random noise stimulation, known for modulating neural activity. Numerosity discrimination improved after training and was maintained long term, especially in the training + parietal stimulation group, regardless of age. Despite the quantitatively similar improvement in the two age groups, the content of learning differed remarkably: aging participants improved more in inhibitory abilities, whereas younger subjects improved in cue-integration abilities. Moreover, differences in the content of learning were reflected in different transfer effects to untrained but related abilities: in the younger group, improvements in cue integration paralleled improvements in continuous quantity (time and space), whereas in the elderly group, improvements in numerosity-based inhibitory abilities generalized to other measures of inhibition and corresponded to a decline in space discrimination, possibly because conflicting learning resources are used in numerosity and continuous quantity processing. These results indicate that training can enhance different, age-dependent cognitive processes and highlight the importance of identifying the exact processes underlying learning for effective training programs.

Multiple object individuation and subitizing in enumeration: a view from electrophysiology

What are the processes involved in determining that there are exactly n objects in the visual field? The core level of representation for this process is based on a mechanism that iteratively individuates each of the set of relevant objects for exact enumeration. In support of this proposal, we review recent electrophysiological findings on enumeration-at-a-glance and consider three temporally distinct responses of the EEG signal that are modulated by object numerosity, and which have been associated respectively with perceptual modulation, attention selection, and working memory. We argue that the neural response associated with attention selection shows the hallmarks of an object individuation mechanism, including the property of simultaneous individuation of a limited number of objects thought to underlie the behavioral subitizing effect. The findings support the view that the core component of exact enumeration is an attention-based individuation mechanism that binds specific features to locations and provides a stable representation of a limited set of relevant objects. The resulting representation is made available for further cognitive operations for exact enumeration.

Assessing the Approximate Number System: no relation between numerical comparison and estimation tasks

Whether our general numerical skills and the mathematical knowledge that we acquire at school are entwined is a debated issue, which many researchers are still striving to investigate. The findings reported in the literature are actually inconsistent; some studies emphasized the existence of a relationship between the acuity of the Approximate Number System (ANS) and arithmetic competence, while some others did not observe any significant correlation. One potential explanation of the discrepancy might stem from the evaluation of the ANS itself. In the present study, we correlated two measures used to index ANS acuity with arithmetic performance. These measures were the Weber fraction (w), computed from a numerical comparison task and the coefficient of variation (CV), computed from a numerical estimation task. Arithmetic performance correlated with estimation CV but not with comparison w. We further investigated the meaning of this result by taking the relationship between w and CV into account. We expected a tight relation as both these measures are believed to assess ANS acuity. Crucially, however, w and CV did not correlate with each other. Moreover, the value of w was modulated by the congruity of the relation between numerical magnitude and non-numerical visual cues, potentially accounting for the lack of correlation between the measures. Our findings thus challenge the overuse of w to assess ANS acuity and more generally put into question the relevance of correlating this measure with arithmetic without any deeper understanding of what they are really indexing.

Rapid and Direct Encoding of Numerosity in the Visual Stream

Humans are endowed with an intuitive number sense that allows us to perceive and estimate numerosity without relying on language. It is controversial, however, as to whether there is a neural mechanism for direct perception of numerosity or whether numerosity is perceived indirectly via other perceptual properties. In this study, we used a novel regression-based analytic method, which allowed an assessment of the unique contributions of visual properties, including numerosity, to explain visual evoked potentials of participants passively viewing dot arrays. We found that the human brain is uniquely sensitive to numerosity and more sensitive to changes in numerosity than to changes in other visual properties, starting extremely early in the visual stream: 75 ms over a medial occipital site and 180 ms over bilateral occipitoparietal sites. These findings provide strong evidence for the existence of a neural mechanism for rapidly and directly extracting numerosity information in the human visual pathway.

Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement

A central question in cognitive and educational neuroscience is whether brain operations supporting nonlinguistic intuitive number sense (numerosity) predict individual acquisition and academic achievement for symbolic or "formal" math knowledge. Here, we conducted a developmental functional magnetic resonance imaging (MRI) study of nonsymbolic numerosity task performance in 44 participants including 14 school age children (6-12 years old), 14 adolescents (13-17 years old), and 16 adults and compared a brain activity measure of numerosity precision to scores from the Woodcock-Johnson III Broad Math index of math academic achievement. Accuracy and reaction time from the numerosity task did not reliably predict formal math achievement. We found a significant positive developmental trend for improved numerosity precision in the parietal cortex and intraparietal sulcus specifically. Controlling for age and overall cognitive ability, we found a reliable positive relationship between individual math achievement scores and parietal lobe activity only in children. In addition, children showed robust positive relationships between math achievement and numerosity precision within ventral stream processing areas bilaterally. The pattern of results suggests a dynamic developmental trajectory for visual discrimination strategies that predict the acquisition of formal math knowledge. In adults, the efficiency of visual discrimination marked by numerosity acuity in ventral occipital-temporal cortex and hippocampus differentiated individuals with better or worse formal math achievement, respectively. Overall, these results suggest that two different brain systems for nonsymbolic numerosity acuity may contribute to individual differences in math achievement and that the contribution of these systems differs across development.

Numerical discrimination is mediated by neural coding variation

One foundation of numerical cognition is that discrimination accuracy depends on the proportional difference between compared values, closely following the Weber-Fechner discrimination law. Performance in non-symbolic numerical discrimination is used to calculate individual Weber fraction, a measure of relative acuity of the approximate number system (ANS). Individual Weber fraction is linked to symbolic arithmetic skills and long-term educational and economic outcomes. The present findings suggest that numerical discrimination performance depends on both the proportional difference and absolute value, deviating from the Weber-Fechner law. The effect of absolute value is predicted via computational model based on the neural correlates of numerical perception. Specifically, that the neural coding "noise" varies across corresponding numerosities. A computational model using firing rate variation based on neural data demonstrates a significant interaction between ratio difference and absolute value in predicting numerical discriminability. We find that both behavioral and computational data show an interaction between ratio difference and absolute value on numerical discrimination accuracy. These results further suggest a reexamination of the mechanisms involved in non-symbolic numerical discrimination, how researchers may measure individual performance, and what outcomes performance may predict.

The Neural Mechanism Underlying Ordinal Numerosity Processing

Changes in the sensory properties of numerosity stimuli have a direct effect on the outcomes of nonsymbolic number tasks. This suggests a prominent role of sensory properties in numerosity processing. However, the current consensus holds that numerosity is processed independent of its sensory properties. To investigate the role of sensory cues in ordinal number processes, we manipulated both dimensions orthogonally. Participants passively viewed the stimuli while their brain activity was measured using EEG. The results revealed an interaction between numerosity and its sensory properties in the absence of main effects. Different neural responses were present for trials where numerosity and sensory cues changed in the same direction compared with trials where they changed in opposite directions. These results show that the sensory cues are expected to change in concert with numerosity and support the notion that the visual cues are taken into account when judging numerosity.

Indexing the approximate number system

Much recent research attention has focused on understanding individual differences in the approximate number system, a cognitive system believed to underlie human mathematical competence. To date researchers have used four main indices of ANS acuity, and have typically assumed that they measure similar properties. Here we report a study which questions this assumption. We demonstrate that the numerical ratio effect has poor test-retest reliability and that it does not relate to either Weber fractions or accuracy on nonsymbolic comparison tasks. Furthermore, we show that Weber fractions follow a strongly skewed distribution and that they have lower test-retest reliability than a simple accuracy measure. We conclude by arguing that in the future researchers interested in indexing individual differences in ANS acuity should use accuracy figures, not Weber fractions or numerical ratio effects.

Area vs. density: influence of visual variables and cardinality knowledge in early number comparison

Current research in the number development field has focused in individual differences regarding the acuity of children's approximate number system (ANS). The most common task to evaluate children's acuity is through non-symbolic numerical comparison. Efforts have been made to prevent children from using perceptual cues by controlling the visual properties of the stimuli (e.g., density, contour length, and area); nevertheless, researchers have used these visual controls interchangeably. Studies have also tried to understand the relation between children's cardinality knowledge and their performance in a number comparison task; divergent results may in fact be rooted in the use of different visual controls. The main goal of the present study is to explore how the usage of different visual controls (density, total filled area, and correlated and anti-correlated area) affects children's performance in a number comparison task, and its relationship to children's cardinality knowledge. For that purpose, 77 preschoolers participated in three tasks: (1) counting list elicitation to test whether children could recite the counting list up to ten, (2) give a number to evaluate children's cardinality knowledge, and (3) number comparison to evaluate their ability to compare two quantities. During this last task, children were asked to point at the set with more geometric figures when two sets were displayed on a screen. Children were exposed only to one of the three visual controls. Results showed that overall, children performed above chance in the number comparison task; nonetheless, density was the easiest control, while correlated and anti-correlated area was the most difficult in most cases. Only total filled area was sensitive to discriminate cardinal principal knowers from non-cardinal principal knowers. How this finding helps to explain conflicting evidence from previous research, and how the present outcome relates to children's number word knowledge is discussed.

Format-dependent representations of symbolic and non-symbolic numbers in the human cortex as revealed by multi-voxel pattern analyses

Neuroimaging studies in the last 20 years have tried to unravel the neural correlates of number processing across formats in humans and non-human primates. Results point to the intraparietal sulcus as the core area for an abstract representation of numerical quantity. On the other hand, there exist a variety of behavioral and neuroimaging data that are difficult to reconcile with the existence of such an abstract representation. In this study, we addressed this issue by applying multi-voxel pattern analysis (MVPA) to functional Magnetic Resonance Imaging (fMRI) data to unravel the neural representations of symbolic (digits) and non-symbolic (dots) numbers and their possible overlap on three different spatial scales (entire lobules, smaller regions of interest and a searchlight analysis with 2-voxel radius). Results showed that numbers in both formats are decodable in occipital, frontal, temporal and parietal regions. However, there were no overlapping representations between dots and digits on any of the spatial scales. These data suggest that the human brain does not contain an abstract representation of numerical magnitude.

Developmental dyscalculia is related to visuo-spatial memory and inhibition impairment

Developmental dyscalculia is thought to be a specific impairment of mathematics ability. Currently dominant cognitive neuroscience theories of developmental dyscalculia suggest that it originates from the impairment of the magnitude representation of the human brain, residing in the intraparietal sulcus, or from impaired connections between number symbols and the magnitude representation. However, behavioral research offers several alternative theories for developmental dyscalculia and neuro-imaging also suggests that impairments in developmental dyscalculia may be linked to disruptions of other functions of the intraparietal sulcus than the magnitude representation. Strikingly, the magnitude representation theory has never been explicitly contrasted with a range of alternatives in a systematic fashion. Here we have filled this gap by directly contrasting five alternative theories (magnitude representation, working memory, inhibition, attention and spatial processing) of developmental dyscalculia in 9-10-year-old primary school children. Participants were selected from a pool of 1004 children and took part in 16 tests and nine experiments. The dominant features of developmental dyscalculia are visuo-spatial working memory, visuo-spatial short-term memory and inhibitory function (interference suppression) impairment. We hypothesize that inhibition impairment is related to the disruption of central executive memory function. Potential problems of visuo-spatial processing and attentional function in developmental dyscalculia probably depend on short-term memory/working memory and inhibition impairments. The magnitude representation theory of developmental dyscalculia was not supported.

Multiple faces elicit augmented neural activity

How do our brains respond when we are being watched by a group of people?Despite the large volume of literature devoted to face processing, this question has received very little attention. Here we measured the effects on the face-sensitive N170 and other ERPs to viewing displays of one, two and three faces in two experiments. In Experiment 1, overall image brightness and contrast were adjusted to be constant, whereas in Experiment 2 local contrast and brightness of individual faces were not manipulated. A robust positive-negative-positive (P100-N170-P250) ERP complex and an additional late positive ERP, the P400, were elicited to all stimulus types. As the number of faces in the display increased, N170 amplitude increased for both stimulus sets, and latency increased in Experiment 2. P100 latency and P250 amplitude were affected by changes in overall brightness and contrast, but not by the number of faces in the display per se. In Experiment 1 when overall brightness and contrast were adjusted to be constant, later ERP (P250 and P400) latencies showed differences as a function of hemisphere. Hence, our data indicate that N170 increases its magnitude when multiple faces are seen, apparently impervious to basic low-level stimulus features including stimulus size. Outstanding questions remain regarding category-sensitive neural activity that is elicited to viewing multiple items of stimulus categories other than faces.

Multiple Object Individuation and Exact Enumeration

Exact computation of numerosity requires the selective individuation of the elements to be enumerated so that each element is counted once and only once. Such a mechanism should operate not only when the elements to be enumerated are presented in isolation but also when they are presented in cluttered scenes. To uncover the electrophysiological correlates of the level of object representation necessary for exact enumeration, we examined ERP measures during the execution of a target enumeration task. A variable number (1–4) of lateralized targets were presented with or without distracters on the target side. An early nonlateralized response (N1, 120–180 msec) was modulated by target numerosity only when presented without distracters. By contrast, the amplitudes of a lateralized and later response (N2pc, 180–300 msec) increased as a function of target numerosity both with and without distracters, reaching a plateau at three targets. We propose that the stage of processing reflected in the N2pc corresponds to the component of individuation that binds specific indexes to properties and locations and that this provides the representation type necessary for exact enumeration.

Comparing the neural distance effect derived from the non-symbolic comparison and the same-different task

As a result of the representation of numerosities, more accurate and faster discrimination between two numerosities is observed when the distance between them increases. In previous studies, the comparison and same-different task were most frequently used to investigate this distance effect. Recently, it was questioned whether the non-symbolic distance effects derived from these tasks originate at the same level. In the current study, we examined the behavioral and neural distance effects of the comparison and same-different task to assess potential differences between both tasks. Participants were first year university students. Each participant completed both tasks, while their reaction time, accuracy and brain activity on predefined components was measured. The early N1-P2p transition and the P2p component on temporo-occipital (TO) and inferior parietal (IP) electrode groups were considered, as well as the late P3 component on a central (C) electrode group. The results showed that the behavioral distance effects from both tasks were comparable, although participants' performance was worse on the same-different task. The neural results revealed similar effects of distance on the mean amplitudes for the early components for both tasks (all p′s < 0.02) and an additional effect of task difficulty on the mean amplitudes of these components. Similar as in previous studies, we found a (marginally) significant increase in mean amplitude of the later P3 component with increasing distance for the comparison (p = 0.07), but not for the same-different task. Apparently, the initial stages of number processing are comparable for both tasks, but an additional later stage is only present for the comparison task. The P3 effect would be indicative of this decisional stage, which was previously proposed to underlie the comparison distance effect (CDE).