Electrophysiological correlates of non-symbolic numerical magnitude processing in children: joining the dots

Electrophysiological Comparison of Cumulative Area and Non-Symbolic Number Judgments

Despite the importance of representing different magnitudes (i.e., number and cumulative area) for action planning and formal mathematics, there is much debate about the nature of these representations, particularly the extent to which magnitudes interact in the mind and brain. Early interaction views suggest that there are shared perceptual processes that form overlapping magnitude representations. However, late interaction views hold that representations of different magnitudes remain distinct, interacting only when preparing a motor response. The present study sheds light on this debate by examining the temporal onset of ratio and congruity effects as participants made ordinal judgments about number and cumulative area. Event-related potentials (ERPs) were recorded to identify whether the onset of such effects aligned with early versus late views. Ratio effects for both magnitudes were observed starting in the P100. Moreover, a congruity effect emerged within the P100. That interactions were observed early in processing, at the same time that initial ratio effects occurred, suggests that number and cumulative area processes interacted when magnitude representations were being formed, prior to preparing a decision response. Our findings are consistent with an early interaction view of magnitude processing, in which number and cumulative area may rely on shared perceptual mechanisms.

Neurophysiological signatures of approximate number system acuity in preschoolers

BACKGROUND

A hallmark of the approximate number system (ANS) is ratio dependence. Previous work identified specific event-related potentials (ERPs) that are modulated by numerical ratio throughout the lifespan. In adults, ERP ratio dependence was correlated with the precision of the numerical judgments with individuals who make more precise judgments showing larger ratio-dependent ERP effects. The current study evaluated if this relationship generalizes to preschoolers.

METHOD

ERPs were recorded from 56 4.5 to 5.5-year-olds while they compared the numerosity of two sequentially presented dot arrays. Nonverbal numerical precision, often called ANS acuity, was assessed using a similar behavioral task.

RESULTS

Only children with high ANS acuity exhibited a P2p ratio-dependent effect onsetting ∼250 ms after the presentation of the comparison dot array. Furthermore, P2p amplitude positively correlated with ANS acuity across tasks.

CONCLUSION

Results demonstrate developmental continuity between preschool years and adulthood in the neural basis of the ANS.

Spatial and chromatic properties of numerosity estimation in isolation and context

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.

Shape facilitates number: brain potentials and microstates reveal the interplay between shape and numerosity in human vision

Recognition of simple shapes and numerosity estimation for small quantities are often studied independently of each other, but we know that these processes are both rapid and accurate, suggesting that they may be mediated by common neural mechanisms. Here we address this issue by examining how spatial configuration, shape complexity, and luminance polarity of elements affect numerosity estimation. We directly compared the Event Related Potential (ERP) time-course for numerosity estimation under shape and random configurations and found a larger N2 component for shape over lateral-occipital electrodes (250–400 ms), which also increased with higher numbers. We identified a Left Mid Frontal (LMF; 400–650 ms) component over left-lateralised medial frontal sites that specifically separated low and high numbers of elements, irrespective of their spatial configuration. Different luminance-polarities increased N2 amplitude only, suggesting that shape but not numerosity is selective to polarity. Functional microstates confined numerosity to a strict topographic distribution occurring within the LMF time-window, while a microstate responding only to shape-configuration was evidenced earlier, in the N2 time-window. We conclude that shape-coding precedes numerosity estimation, which can be improved when the number of elements and shape vertices are matched. Thus, numerosity estimation around the subitizing range is facilitated by a shape-template matching process.

The relationship between non-verbal systems of number and counting development: a neural signatures approach

Two non-verbal cognitive systems, an approximate number system (ANS) for extracting the numerosity of a set and a parallel individuation (PI) system for distinguishing between individual items, are hypothesized to be foundational to symbolic number and mathematics abilities. However, the exact role of each remains unclear and highly debated. Here we used an individual differences approach to test for a relationship between the spontaneously evoked brain signatures (using event-related potentials) of PI and the ANS and initial development of symbolic number concepts in preschool children as displayed by counting. We observed that individual differences in the neural signatures of the PI system, but not the ANS, explained a unique portion of variance in counting proficiency after extensively controlling for general cognitive factors. These results suggest that differences in early attentional processing of objects between children are related to higher-level symbolic number concept development.

Comparisons of numerical magnitudes in children with different levels of mathematical achievement. An ERP study

The ability to map between non-symbolic and symbolic magnitude representations is crucial in the development of mathematics and this map is disturbed in children with math difficulties. In addition, positive parietal ERPs have been found to be sensitive to the number distance effect and skills solving arithmetic problems. Therefore we aimed to contrast the behavioral and ERP responses in children with different levels of mathematical achievement: low (LA), average (AA) and high (HA), while comparing symbolic and non-symbolic magnitudes. The results showed that LA children repeatedly failed when comparing magnitudes, particularly the symbolic ones. In addition, a positive correlation between correct responses while analyzing symbolic quantities and WRAT-4 scores emerged. The amplitude of N200 was significantly larger during non-symbolic comparisons. In addition, P2P amplitude was consistently smaller in LA children while comparing both symbolic and non-symbolic quantities, and correlated positively with the WRAT-4 scores. The latency of P3 seemed to be sensitive to the type of numerical comparison. The results suggest that math difficulties might be related to a more general magnitude representation problem, and that ERP are useful to study its timecourse in children with different mathematical skills.

Neural substrates of numerosity estimation in autism

Visual skills, including numerosity estimation are reported to be superior in autism spectrum disorders (ASD). This phenomenon is attributed to individuals with ASD processing local features, rather than the Gestalt. We examined the neural correlates of numerosity estimation in adults with and without ASD, to disentangle perceptual atypicalities from numerosity processing. Fourteen adults with ASD and matched typically developed (TD) controls estimated the number of dots (80-150) arranged either randomly (local information) or in meaningful patterns (global information) while brain activity was recorded with magnetoencephalography (MEG). Behavioral results showed no significant group difference in the errors of estimation. However, numerical estimation in ASD was more variable across numerosities than TD and was not affected by the global arrangement of the dots. At 80-120 ms, MEG analyses revealed early significant differences (TD > ASD) in source amplitudes in visual areas, followed from 120 to 400 ms by group differences in temporal, and then parietal regions. After 400 ms, a source was found in the superior frontal gyrus in TD only. Activation in temporal areas was differently sensitive to the global arrangement of dots in TD and ASD. MEG data show that individuals with autism exhibit widespread functional abnormalities. Differences in temporal regions could be linked to atypical global perception. Occipital followed by parietal and frontal differences might be driven by abnormalities in the processing and conversion of visual input into a number-selective neural code and complex cognitive decisional stages. These results suggest overlapping atypicalities in sensory, perceptual and number-related processing during numerosity estimation in ASD.

Toward a visuospatial developmental account of sequence-space synesthesia

Sequence-space synesthetes experience some sequences (e.g., numbers, calendar units) as arranged in spatial forms, i.e., spatial patterns in their mind's eye or even outside their body. Various explanations have been offered for this phenomenon. Here we argue that these spatial forms are continuous with varieties of non-synesthetic visuospatial imagery and share their central characteristics. This includes their dynamic and elaborative nature, their involuntary feel, and consistency over time. Drawing from literatures on mental imagery and working memory, we suggest how the initial acquisition and subsequent elaboration of spatial forms could be accounted for in terms of the known developmental trajectory of visuospatial representations. This extends from the formation of image-based representations of verbal material in childhood to the later maturation of dynamic control of imagery. Individual differences in the development of visuospatial style also account for variation in the character of spatial forms, e.g., in terms of distinctions such as visual versus spatial imagery, or ego-centric versus object-based transformations.

An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities

INTRODUCTION

The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months).

METHODS

EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed.

RESULTS

In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences.

CONCLUSION

Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range.

Continuous visual properties explain neural responses to nonsymbolic number

Nonsymbolic number and its continuous visual properties are confounded in everyday life: When number changes, its continuous visual properties also change. It could therefore be efficient to rely on the visual properties to judge number. The current consensus, however, holds that number is processed independent of its visual properties. In this study, we pitched these two opposing theories against each other. We used electroencephalography to look at the components suggested to process number. The first experiment showed that number and visual cues affect the N1 and/or the P2 component. To disentangle number and visual processes, we controlled the visual cues in the second experiment. Now, no number-related effects were present. When the data were reorganized according to visual cue instead of number size, N1 and P2 effects emerged. These results argue against the idea that number is processed independent of its continuous visual variables.

Developmental neuroscience of time and number: implications for autism and other neurodevelopmental disabilities

Estimations of time and number share many similarities in both non-humans and man. The primary focus of this review is on the development of time and number sense across infancy and childhood, and neuropsychological findings as they relate to time and number discrimination in infants and adults. Discussion of these findings is couched within a mode-control model of timing and counting which assumes time and number share a common magnitude representation system. A basic sense of time and number likely serves as the foundation for advanced numerical and temporal competence, and aspects of higher cognition-this will be discussed as it relates to typical childhood, and certain developmental disorders, including autism spectrum disorder. Directions for future research in the developmental neuroscience of time and number (NEUTIN) will also be highlighted.