Functional imaging of numerical processing in adults and 4-y-old children

Short-term number sense training recapitulates long-term neurodevelopmental changes from childhood to adolescence

Number sense is fundamental to the development of numerical problem-solving skills. In early childhood, children establish associations between non-symbolic (e.g., a set of dots) and symbolic (e.g., Arabic numerals) representations of quantity. The developmental estrangement theory proposes that the relationship between non-symbolic and symbolic representations of quantity evolves with age, with increased dissociation across development. Consistent with this theory, recent research suggests that cross-format neural representational similarity (NRS) between non-symbolic and symbolic quantities is correlated with arithmetic fluency in children but not in adolescents. However, it is not known if short-term training (STT) can induce similar changes as long-term development. In this study, children aged 7-10 years underwent a theoretically motivated 4-week number sense training. Using multivariate neural pattern analysis, we investigated whether short-term learning could modify the relation between cross-format NRS and arithmetic skills. Our results revealed a significant correlation between cross-format NRS and arithmetic fluency in distributed brain regions, including the parietal and prefrontal cortices, prior to training. However, this association was no longer observed after training, and multivariate predictive models confirmed these findings. Our findings provide evidence that intensive STT during early childhood can promote behavioral improvements and neural plasticity that resemble and recapitulate long-term neurodevelopmental changes that occur from childhood to adolescence. More generally, our study contributes to our understanding of the malleability of number sense and highlights the potential for targeted interventions to shape neurodevelopmental trajectories in early childhood. RESEARCH HIGHLIGHTS: We tested the hypothesis that short-term number sense training induces the dissociation of symbolic numbers from non-symbolic representations of quantity in children. We leveraged a theoretically motivated intervention and multivariate pattern analysis to determine training-induced neurocognitive changes in the relation between number sense and arithmetic problem-solving skills. Neural representational similarity between non-symbolic and symbolic quantity representations was correlated with arithmetic skills before training but not after training. Short-term training recapitulates long-term neurodevelopmental changes associated with numerical problem-solving from childhood to adolescence.

Explainable deep-learning framework: decoding brain states and prediction of individual performance in false-belief task at early childhood stage

Decoding of cognitive states aims to identify individuals' brain states and brain fingerprints to predict behavior. Deep learning provides an important platform for analyzing brain signals at different developmental stages to understand brain dynamics. Due to their internal architecture and feature extraction techniques, existing machine-learning and deep-learning approaches are suffering from low classification performance and explainability issues that must be improved. In the current study, we hypothesized that even at the early childhood stage (as early as 3-years), connectivity between brain regions could decode brain states and predict behavioral performance in false-belief tasks. To this end, we proposed an explainable deep learning framework to decode brain states (Theory of Mind and Pain states) and predict individual performance on ToM-related false-belief tasks in a developmental dataset. We proposed an explainable spatiotemporal connectivity-based Graph Convolutional Neural Network (Ex-stGCNN) model for decoding brain states. Here, we consider a developmental dataset, N = 155 (122 children; 3-12 yrs and 33 adults; 18-39 yrs), in which participants watched a short, soundless animated movie, shown to activate Theory-of-Mind (ToM) and pain networs. After scanning, the participants underwent a ToM-related false-belief task, leading to categorization into the pass, fail, and inconsistent groups based on performance. We trained our proposed model using Functional Connectivity (FC) and Inter-Subject Functional Correlations (ISFC) matrices separately. We observed that the stimulus-driven feature set (ISFC) could capture ToM and Pain brain states more accurately with an average accuracy of 94%, whereas it achieved 85% accuracy using FC matrices. We also validated our results using five-fold cross-validation and achieved an average accuracy of 92%. Besides this study, we applied the SHapley Additive exPlanations (SHAP) approach to identify brain fingerprints that contributed the most to predictions. We hypothesized that ToM network brain connectivity could predict individual performance on false-belief tasks. We proposed an Explainable Convolutional Variational Auto-Encoder (Ex-Convolutional VAE) model to predict individual performance on false-belief tasks and trained the model using FC and ISFC matrices separately. ISFC matrices again outperformed the FC matrices in prediction of individual performance. We achieved 93.5% accuracy with an F1-score of 0.94 using ISFC matrices and achieved 90% accuracy with an F1-score of 0.91 using FC matrices.

Integrated number sense tutoring remediates aberrant neural representations in children with mathematical disabilities

Number sense is essential for early mathematical development but it is compromised in children with mathematical disabilities (MD). Here we investigate the impact of a personalized 4-week Integrated Number Sense (INS) tutoring program aimed at improving the connection between nonsymbolic (sets of objects) and symbolic (Arabic numerals) representations in children with MD. Utilizing neural pattern analysis, we found that INS tutoring not only improved cross-format mapping but also significantly boosted arithmetic fluency in children with MD. Critically, the tutoring normalized previously low levels of cross-format neural representations in these children to pre-tutoring levels observed in typically developing, especially in key brain regions associated with numerical cognition. Moreover, we identified distinct, 'inverted U-shaped' neurodevelopmental changes in the MD group, suggesting unique neural plasticity during mathematical skill development. Our findings highlight the effectiveness of targeted INS tutoring for remediating numerical deficits in MD, and offer a foundation for developing evidence-based educational interventions.

Inter-individual, hemispheric and sex variability of brain activations during numerosity processing

Numerosity perception is a fundamental and innate cognitive function shared by both humans and many animal species. Previous research has primarily focused on exploring the spatial and functional consistency of neural activations that were associated with the processing of numerosity information. However, the inter-individual variability of brain activations of numerosity perception remains unclear. In the present study, with a large-sample functional magnetic resonance imaging (fMRI) dataset (n = 460), we aimed to localize the functional regions related to numerosity perceptions and explore the inter-individual, hemispheric, and sex differences within these brain regions. Fifteen subject-specific activated regions, including the anterior intraparietal sulcus (aIPS), posterior intraparietal sulcus (pIPS), insula, inferior frontal gyrus (IFG), inferior temporal gyrus (ITG), premotor area (PM), middle occipital gyrus (MOG) and anterior cingulate cortex (ACC), were delineated in each individual and then used to create a functional probabilistic atlas to quantify individual variability in brain activations of numerosity processing. Though the activation percentages of most regions were higher than 60%, the intersections of most regions across individuals were considerably lower, falling below 50%, indicating substantial variations in brain activations related to numerosity processing among individuals. Furthermore, significant hemispheric and sex differences in activation location, extent, and magnitude were also found in these regions. Most activated regions in the right hemisphere had larger activation volumes and activation magnitudes, and were located more lateral and anterior than their counterparts in the left hemisphere. In addition, in most of these regions, males displayed stronger activations than females. Our findings demonstrate large inter-individual, hemispheric, and sex differences in brain activations related to numerosity processing, and our probabilistic atlas can serve as a robust functional and spatial reference for mapping the numerosity-related neural networks.

Neurobiology of numerical learning

Numerical abilities are complex cognitive skills essential for dealing with requirements of the modern world. Although the brain structures and functions underlying numerical cognition in different species have long been appreciated, genetic and molecular techniques have more recently expanded the knowledge about the mechanisms underlying numerical learning. In this review, we discuss the status of the research related to the neurobiological bases of numerical abilities. We consider how genetic factors have been associated with mathematical capacities and how these link to the current knowledge of brain regions underlying these capacities in human and non-human animals. We further discuss the extent to which significant variations in the levels of specific neurotransmitters may be used as potential markers of individual performance and learning difficulties and take into consideration the therapeutic potential of brain stimulation methods to modulate learning and improve interventional outcomes. The implications of this research for formulating a more comprehensive view of the neural basis of mathematical learning are discussed.

Distributed attribute representation in the superior parietal lobe during probabilistic decision-making

Several studies have examined the neural substrates of probabilistic decision-making, but few have systematically investigated the neural representations of the two objective attributes of probabilistic rewards, that is, the reward amount and the probability. Specifically, whether there are common or distinct neural activity patterns to represent the objective attributes and their association with the neural representation of the subjective valuation remains largely underexplored. We conducted two studies (nStudy1  = 34, nStudy2  = 41) to uncover distributed neural representations of the objective attributes and subjective value as well as their association with individual probability discounting rates. The amount and probability were independently manipulated to better capture brain signals sensitive to these two attributes and were presented simultaneously in Study 1 and successively in Study 2. Both univariate and multivariate pattern analyses showed that the brain activities in the superior parietal lobule (SPL), including the postcentral gyrus, were modulated by the amount of rewards and probability in both studies. Further, representational similarity analysis revealed a similar neural representation between these two objective attributes and between the attribute and valuation. Moreover, the SPL tracked the subjective value integrated by the hyperbolic function. Probability-related brain activations in the inferior parietal lobule were associated with the variability in individual discounting rates. These findings provide novel insights into a similar neural representation of the two attributes during probabilistic decision-making and perhaps support the common neural coding of stimulus objective properties and subjective value in the field of probabilistic discounting.

The brain lateralization and development of math functions: progress since Sperry, 1974

In 1974, Roger Sperry, based on his seminal studies on the split-brain condition, concluded that math was almost exclusively sustained by the language dominant left hemisphere. The right hemisphere could perform additions up to sums less than 20, the only exception to a complete left hemisphere dominance. Studies on lateralized focal lesions came to a similar conclusion, except for written complex calculation, where spatial abilities are needed to display digits in the right location according to the specific requirements of calculation procedures. Fifty years later, the contribution of new theoretical and instrumental tools lead to a much more complex picture, whereby, while left hemisphere dominance for math in the right-handed is confirmed for most functions, several math related tasks seem to be carried out in the right hemisphere. The developmental trajectory in the lateralization of math functions has also been clarified. This corpus of knowledge is reviewed here. The right hemisphere does not simply offer its support when calculation requires generic space processing, but its role can be very specific. For example, the right parietal lobe seems to store the operation-specific spatial layout required for complex arithmetical procedures and areas like the right insula are necessary in parsing complex numbers containing zero. Evidence is found for a complex orchestration between the two hemispheres even for simple tasks: each hemisphere has its specific role, concurring to the correct result. As for development, data point to right dominance for basic numerical processes. The picture that emerges at school age is a bilateral pattern with a significantly greater involvement of the right-hemisphere, particularly in non-symbolic tasks. The intraparietal sulcus shows a left hemisphere preponderance in response to symbolic stimuli at this age.

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.

Quantitative modelling demonstrates format-invariant representations of mathematical problems in the brain

Mathematical problems can be described in either symbolic form or natural language. Previous studies have reported that activation overlaps exist for these two types of mathematical problems, but it is unclear whether they are based on similar brain representations. Furthermore, quantitative modelling of mathematical problem solving has yet to be attempted. In the present study, subjects underwent 3 h of functional magnetic resonance experiments involving math word and math expression problems, and a read word condition without any calculations was used as a control. To evaluate the brain representations of mathematical problems quantitatively, we constructed voxel-wise encoding models. Both intra- and cross-format encoding modelling significantly predicted brain activity predominantly in the left intraparietal sulcus (IPS), even after subtraction of the control condition. Representational similarity analysis and principal component analysis revealed that mathematical problems with different formats had similar cortical organization in the IPS. These findings support the idea that mathematical problems are represented in the brain in a format-invariant manner.

Cortical representations of numbers and nonsymbolic quantities expand and segregate in children from 5 to 8 years of age

Number symbols, such as Arabic numerals, are cultural inventions that have transformed human mathematical skills. Although their acquisition is at the core of early elementary education in children, it remains unknown how the neural representations of numerals emerge during that period. It is also unclear whether these relate to an ontogenetically earlier sense of approximate quantity. Here, we used multivariate fMRI adaptation coupled with within- and between-format machine learning to probe the cortical representations of Arabic numerals and approximate nonsymbolic quantity in 89 children either at the beginning (age 5) or four years into formal education (age 8). Although the cortical representations of both numerals and nonsymbolic quantities expanded from age 5 to age 8, these representations also segregated with learning and development. Specifically, a format-independent neural representation of quantity was found in the right parietal cortex, but only for 5-year-olds. These results are consistent with the so-called symbolic estrangement hypothesis, which argues that the relation between symbolic and nonsymbolic quantity weakens with exposure to formal mathematics in children.

Does auditory numerosity and non-numerical magnitude affect visual non-symbolic numerical representation?

In the present study, we investigated the effects of auditory numerosity and magnitude (loudness) on visual numerosity processing. Participants compared numerosities of two sequential dot arrays. The second dot array was paired with a tone array that was independent of visual comparison. The numerosity (One-tone vs. Multiple-tone) and the non-numerical magnitude of tones (loudness) were manipulated in Experiments 1 and 2, respectively. In Experiment 1, participants' inverse efficiency score (IES), that is, the quotient between response time and accuracy, was significantly smaller in the One-tone and Multiple-tone conditions than that in the No-tone condition, and linear trend analyses showed that the IES decreased with the number of tones. In Experiment 2, the IES in the Loud-tone condition was significantly smaller than that in the No-tone condition, and the IES decreased as the loudness of the tones increased. In Experiment 3, both auditory numerosity and magnitude were manipulated. For soft tones, the IES was smaller in the Multiple-tone condition than in the One-tone condition, whereas no significant difference was found between two conditions in loud tones. In sum, these findings suggest that the visual numerical representation can be spontaneously affected by the numerosity and non-numerical magnitude of stimuli from another modality.

Structural and functional connectivity of the inferior temporal numeral area

A growing body of evidence suggests that in adults, there is a spatially consistent "inferior temporal numeral area" (ITNA) in the occipitotemporal cortex that appears to preferentially process Arabic digits relative to non-numerical symbols and objects. However, very little is known about why the ITNA is spatially segregated from regions that process other orthographic stimuli such as letters, and why it is spatially consistent across individuals. In the present study, we used diffusion-weighted imaging and functional magnetic resonance imaging to contrast structural and functional connectivity between left and right hemisphere ITNAs and a left hemisphere letter-preferring region. We found that the left ITNA had stronger structural and functional connectivity than the letter region to inferior parietal regions involved in numerical magnitude representation and arithmetic. Between hemispheres, the left ITNA showed stronger structural connectivity with the left inferior frontal gyrus (Broca's area), while the right ITNA showed stronger structural connectivity to the ipsilateral inferior parietal cortex and stronger functional coupling with the bilateral IPS. Based on their relative connectivity, our results suggest that the left ITNA may be more readily involved in mapping digits to verbal number representations, while the right ITNA may support the mapping of digits to quantity representations.

Visual P2p component responds to perceived numerosity

Numerosity perception is a key ability for human and non-human species, probably mediated by dedicated brain mechanisms. Electrophysiological studies revealed the existence of both early and mid-latency components of the Electrophysiological (EEG) signal sensitive to numerosity changes. However, it is still unknown whether these components respond to physical or perceived variation in numerical attributes. We here tackled this point by recording electrophysiological signal while participants performed a numerosity adaptation task, a robust psychophysical method yielding changes in perceived numerosity judgments despite physical numerosity invariance. Behavioral measures confirmed that the test stimulus was consistently underestimated when presented after a high numerous adaptor while perceived as veridical when presented after a neutral adaptor. Congruently, EEG results revealed a potential at around 200 ms (P2p) which was reduced when the test stimulus was presented after the high numerous adaptor. This result was much prominent over the left posterior cluster of electrodes and correlated significantly with the amount of adaptation. No earlier modulations were retrievable when changes in numerosity were illusory while both early and mid-latency modulations occurred for physical changes. Taken together, our results reveal that mid-latency P2p mainly reflects perceived changes in numerical attributes, while earlier components are likely to be bounded to the physical characteristics of the stimuli. These results suggest that short-term plastic mechanisms induced by numerosity adaptation may involve a relatively late processing stage of the visual hierarchy likely engaging cortical areas beyond the primary visual cortex. Furthermore, these results also indicate mid-latency electrophysiological correlates as a signature of the internal representation of numerical information.

Mental arithmetic modulates temporal variabilities of finger-tapping tasks in a tempo-dependent manner

Background

Several psychiatric diseases impair temporal processing. Temporal processing is thought to be based on two domains: supra-second intervals and sub-second intervals. Studies show that temporal processing in sub-second intervals is mainly an automated process. However, the brain functions involved in temporal processing at each time scale remain unclear. We hypothesized that temporal processing in supra-second intervals requires several brain areas, such as the ventrolateral prefrontal cortex, intraparietal sulcus (IPS), and inferior parietal lobe, corresponding to various cognitions in a time scale-dependent manner. We focused on a dual-task paradigm (DTP) involving simultaneous performance of cognitive and motor tasks, which is an effective method for screening psychomotor functions; we then designed a DTP comprising finger tapping at various tempi as the temporal processing task and two cognitive tasks (mental arithmetic and reading) that might affect temporal processing. We hoped to determine whether task-dependent interferences on temporal processing in supra-second intervals differed depending on the cognitive tasks involved.

Methods

The study included 30 participants with no history of neuromuscular disorders. Participants were asked to perform a DTP involving right index finger tapping at varying tempi (0.33, 0.5, 1, 2, 3, and 4 s inter-tapping intervals). Cognitive tasks comprised mental arithmetic (MA) involving three-digit addition, mental reading (MR) of three- to four-digit numbers, and a control (CTL) task without any cognitive loading. For comparison between tasks, we calculated the SDs of the inter-tapping intervals. Participants' MA abilities in the three-digit addition task were evaluated.

Results

The MA and MR tasks significantly increased the SDs of the inter-tapping intervals compared to those of the CTL task in 2-3 s and 3-4 s for the MA and MR tasks, respectively. Furthermore, SD peaks in the finger-tapping tasks involving MA were normalized by those in the CTL task, which were moderately correlated with the participants' MA ability (r = 0.462, P = 0.010).

Discussion

Our results established that DTP involving the temporal coordination of finger-tapping and cognitive tasks increased temporal variability in a task- and tempo-dependent manner. Based on the behavioral aspects, we believe that these modulations of temporal variability might result from the interaction between finger function, arithmetic processing, and temporal processing, especially during the "pre-semantic period". Our findings may help in understanding the temporal processing deficits in various disorders such as dementia, Parkinson's disease, and autism.

Common Neural Functions during Children's Learning from Naturalistic and Controlled Mathematics Paradigms

Two major goals of human neuroscience are to understand how the brain functions in the real world and to measure neural processes under conditions that are ecologically valid. A critical step toward these goals is understanding how brain activity during naturalistic tasks that mimic the real world relates to brain activity in more traditional laboratory tasks. In this study, we used intersubject correlations to locate reliable stimulus-driven cerebral processes among children and adults in a naturalistic video lesson and a laboratory forced-choice task that shared the same arithmetic concept. We show that relative to a control condition with grammatical content, naturalistic and laboratory arithmetic tasks evoked overlapping activation within brain regions previously associated with math semantics. The regions of specific functional overlap between the naturalistic mathematics lesson and laboratory mathematics task included bilateral intraparietal cortex, which confirms that this region processes mathematical content independently of differences in task mode. These findings suggest that regions of the intraparietal cortex process mathematical content when children are learning about mathematics in a naturalistic setting.

Bilateral intraparietal activation for number tasks in studies using an adaptation paradigm: A meta-analysis

Mathematical processing is important for professional successes. The Adaptation Paradigm has been widely used to study the brain underpinnings of mathematical processing. In this study, we aim at shedding light on an important component of mathematical processing, namely numerical cognition. To do so, we performed a meta-analysis using the Activation Likelihood Estimation method on studies that have employed the Adaptation Paradigm for examining numerical cognition. We found a bilateral Intraparietal Sulcus (IPS) activation in studies using both symbolic and non-symbolic stimuli formats. We also found a right lateralized brain activation for the non-symbolic condition and a left lateralized brain activation for the symbolic condition. These results imply that the Adaptation Paradigm likely targets numeric magnitude processing and confirms the potency of this paradigm to activate the Intraparietal Sulcus.

Neural Correlates of Numerical Estimation: The Role of Strategy Use

Introduction: Computation estimation is the ability to provide an approximate answer to a complex arithmetic problem without calculating it exactly. Despite its importance in daily life, the neuronal network underlying computation estimation is largely unknown. Methods: We looked at the neuronal correlates of two computational estimation strategies: approximated calculation and sense of magnitude (SOM)–intuitive representation of magnitude, without calculation. During an fMRI scan, thirty-one college students judged whether the result of a two-digit multiplication problem was larger or smaller than a given reference number. In two different blocks, they were asked to use a specific strategy (AC or SOM). Results: The two strategies activated brain regions related to calculation, numerical cognition, decision-making, and working memory. AC more than SOM elicited activations in multiple, domain-specific brain regions in the parietal lobule, including the left SMG (BA 40), the bilateral superior parietal lobule (BA 7), and the right inferior parietal lobule (BA 7). The activation level of the IFG was positively correlated to individual accuracy, indicating that the IFG has an essential role in both strategies. Conclusions: These finding suggest that the analogic code of magnitude is more involved in the AC than the SOM strategy.

The link between number and action in human infants

Humans' inborn ability to represent and manipulate numerical quantities is supported by the parietal cortex, which is also involved in a variety of spatial and motor abilities. While the behavioral links between numerical and spatial information have been extensively studied, little is known about the connection between number and action. Some studies in adults have shown a series of interference effects when simultaneously processing numerical and action information. We investigated the origins of this link by testing forty infants (7- to 9-month-old) in one of two experimental conditions: one group was habituated to congruent number-hand pairings, where the larger the number, the more open the hand-shape associated; the second group was habituated to incongruent number-hand pairings, where the larger the number, the more close the hand-shape associated. In test trials, both groups of infants were presented with congruent and incongruent pairings. We found that only infants habituated to congruency showed a significantly higher looking time to the test trial depicting incongruent pairings. These findings show for the first time that infants spontaneously associate magnitude-related changes across the dimensions of number and action-related information, thus offering support to the existence of an early, preverbal number-action link in the human mind.

Politics of Plasticity: Implications of the New Science of the "Teen Brain" for Education

In recent years, claims that developmental brain science should inform pedagogical approaches have begun to influence educational policies. This article investigates the promise, pitfalls, processes, and implications of these claims. We explore how research on neuroplasticity has led to enormous interest in harnessing mechanistic models of development for applications in the classroom. Synthesizing analysis from the scientific literature on "neuroeducation" and interviews with key actors in the field, we analyze how neural and cognitive processes are mapped onto pedagogical constructs, and how psychological and social-structural factors are (or are not) integrated into explanations. First, we describe the historical trajectory of educational neuroscience and identify how tensions between antagonist groups struggling for authority over brain-based educational claims shaped the field. Second, we focus on the pervasive use of the concept of "neuroplasticity" in the literature. We argue that it is used as a rhetorical device to create hope and empower children, teachers, and parents through educational exercises that promote neurobiological reflexivity. Third, we turn to the notion of "self-regulation" in the neuroeducational programs. We argue that the rationale of these programs emphasizes the young person's responsibility in navigating their social worlds through the imperative to enhance their executive functions while failing to adequately account for the role of the social environment in the development of self-regulation.

The evolution of quantitative sensitivity

The ability to represent approximate quantities appears to be phylogenetically widespread, but the selective pressures and proximate mechanisms favouring this ability remain unknown. We analysed quantity discrimination data from 672 subjects across 33 bird and mammal species, using a novel Bayesian model that combined phylogenetic regression with a model of number psychophysics and random effect components. This allowed us to combine data from 49 studies and calculate the Weber fraction (a measure of quantity representation precision) for each species. We then examined which cognitive, socioecological and biological factors were related to variance in Weber fraction. We found contributions of phylogeny to quantity discrimination performance across taxa. Of the neural, socioecological and general cognitive factors we tested, cortical neuron density and domain-general cognition were the strongest predictors of Weber fraction, controlling for phylogeny. Our study is a new demonstration of evolutionary constraints on cognition, as well as of a relation between species-specific neuron density and a particular cognitive ability.

This article is part of the theme issue ‘Systems neuroscience through the lens of evolutionary theory’.

Relating mathematical abilities to numerical skills and executive functions in informal and formal schooling

Background

The current evidence on an integrative role of the domain-specific early mathematical skills and number-specific executive functions (EFs) from informal to formal schooling and their effect on mathematical abilities is so far unclear. The main objectives of this study were to (i) compare the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities between preschool and primary school children, and (ii) examine the relationship among the domain-specific early mathematics, the number-specific EFs, and the mathematical abilities among preschool and primary school children.

Methods

The current study recruited 6- and 7-year-old children (N_total = 505, n_6yrs = 238, and n_7yrs = 267). The domain-specific early mathematics as measured by symbolic and nonsymbolic tasks, number-specific EFs tasks, and mathematics tasks between these preschool and primary school children were compared. The relationship among domain-specific early mathematics, number-specific EFs, and mathematical abilities among preschool and primary school children was examined. MANOVA and structural equation modeling (SEM) were used to test research hypotheses.

Results

The current results showed using MANOVA that primary school children were superior to preschool children over more complex tests of the domain-specific early mathematics; number-specific EFs; mathematical abilities, particularly for more sophisticated numerical knowledge; and number-specific EF components. The SEM revealed that both the domain-specific early numerical and the number-specific EFs significantly related to the mathematical abilities across age groups. Nevertheless, the number comparison test and mental number line of the domain-specific early mathematics significantly correlated with the mathematical abilities of formal school children. These results show the benefits of both the domain-specific early mathematics and the number-specific EFs in mathematical development, especially at the key stages of formal schooling. Understanding the relationship between EFs and early mathematics in improving mathematical achievements could allow a more powerful approach in improving mathematical education at this developmental stage.

Understanding Estimations of Magnitudes: An fMRI Investigation

The current study examined whether discrete numerical estimation is based on the same cognitive process as estimation of continuous magnitudes such as weight and time. While the verbal estimation of numerical quantities has a contingent unit of measurement (e.g., how many cookies fit in a cookie jar? _X_ cookies), estimation of time and weight does not (e.g., how much time does it take to fill a bath with water? _X_ minutes/hours/seconds). Therefore, estimation of the latter categories has another level of difficulty, requiring extensive involvement of cognitive control. During a functional magnetic resonance imaging (fMRI) scan, 18 students performed estimations with three estimation categories: number, time, and weight. Estimations elicited activity in multiple brain regions, mainly: (1) visual regions including bilateral lingual gyrus), (2) parietal regions including the left angular gyrus and right supramarginal gyrus, and (3) the frontal regions (cingulate gyrus and the inferior frontal cortex). Continuous magnitude estimations (mostly time) produced different frontal activity than discrete numerical estimations did, demonstrating different profiles of brain activations between discrete numerical estimations and estimations of continuous magnitudes. The activity level in the right middle and inferior frontal gyrus correlated with the tendency to give extreme responses, signifying the importance of the right prefrontal lobe in estimations.

Distinct Mechanisms in Number Comparison of Random and Regular Dots: An ERP Study

Numerosity comparison for regular patterns shows different features compared with that for random ones in previous studies, suggesting an underlying mechanism distinct from numerosity. In this study, we went further to compare the event-related potentials (ERP) components in numerosity processing of random and regular patterns, which are identical in all aspects of texture features except for the distribution. ERP components were recorded and analyzed while participants compared which of the two successively presented sets was more numerous. P2p amplitude was revealed to be significantly weaker for regular patterns compared with that for random patterns over right occipital-parietal cites, whereas no difference was found for P1 or N1 components. The difference in P2p amplitude, which is consistent with the behavior dissociation revealed in our previous studies, suggests that regular distribution can trigger distinct processing in numeral comparison tasks. Processing of continuous magnitudes or configuration cannot explain the decrease in P2p amplitude for regular distributed patterns. Therefore, this study further supports that P2p is mediated by numerosity processing.

Developmental changes in neural lateralization for visual-spatial function: Evidence from a line-bisection task

Studies of hemispheric specialization have traditionally cast the left hemisphere as specialized for language and the right hemisphere for spatial function. Much of the supporting evidence for this separation of function comes from studies of healthy adults and those who have sustained lesions to the right or left hemisphere. However, we know little about the developmental origins of lateralization. Recent evidence suggests that the young brain represents language bilaterally, with 4-6-year-olds activating the left-hemisphere regions known to support language in adults as well as homotopic regions in the right hemisphere. This bilateral pattern changes over development, converging on left-hemispheric activation in late childhood. In the present study, we ask whether this same developmental trajectory is observed in a spatial task that is strongly right-lateralized in adults-the line bisection (or "Landmark") task. We examined fMRI activation among children ages 5-11 years as they were asked to judge which end of a bisected vertical line was longer. We found that young children showed bilateral activation, with activation in the same areas of the right hemisphere as has been shown among adults, as well as in the left hemisphere homotopic regions. By age 10, activation was right-lateralized. This strongly resembles the developmental trajectory for language, moving from bilateral to lateralized activation. We discuss potential underlying mechanisms and suggest that understanding the development of lateralization for a range of cognitive functions can play a crucial role in understanding general principles of how and why the brain comes to lateralize certain functions.

Homogenization of face neural representation during development

Extensive studies have demonstrated that face processing ability develops gradually during development until adolescence. However, the underlying mechanism is unclear. One hypothesis is that children and adults represent faces in qualitatively different fashions with different group templates. An alternative hypothesis emphasizes the development as a quantitative change with a decrease of variation in representations. To test these hypotheses, we used between-participant correlation to measure activation pattern similarity both within and between late-childhood children and adults. We found that activation patterns for faces in the fusiform face area and occipital face area were less similar within the children group than within the adults group, indicating children had a greater variation in representing faces. Interestingly, the activation pattern similarity of children to their own group template was not significantly larger than that to adults' template, suggesting children and adults shared a template in representing faces. Further, the decrease in representation variance was likely a general principle in the ventral visual cortex, as a similar result was observed in a scene-selective region when perceiving scenes. Taken together, our study provides evidence that development of object representation may result from a homogenization process that shifts from greater variance in late-childhood to homogeneity in adults.

Opportunities and Limitations of Mobile Neuroimaging Technologies in Educational Neuroscience

As the field of educational neuroscience continues to grow, questions have emerged regarding the ecological validity and applicability of this research to educational practice. Recent advances in mobile neuroimaging technologies have made it possible to conduct neuroscientific studies directly in naturalistic learning environments. We propose that embedding mobile neuroimaging research in a cycle (Matusz, Dikker, Huth, & Perrodin, 2019), involving lab-based, seminaturalistic, and fully naturalistic experiments, is well suited for addressing educational questions. With this review, we take a cautious approach, by discussing the valuable insights that can be gained from mobile neuroimaging technology, including electroencephalography and functional near-infrared spectroscopy, as well as the challenges posed by bringing neuroscientific methods into the classroom. Research paradigms used alongside mobile neuroimaging technology vary considerably. To illustrate this point, studies are discussed with increasingly naturalistic designs. We conclude with several ethical considerations that should be taken into account in this unique area of research.

Mathematical learning deficits originate in early childhood from atypical development of a frontoparietal brain network

Mathematical learning deficits are defined as a neurodevelopmental disorder (dyscalculia) in the International Classification of Diseases. It is not known, however, how such deficits emerge in the course of early brain development. Here, we conducted functional and structural magnetic resonance imaging (MRI) experiments in 3- to 6-year-old children without formal mathematical learning experience. We followed this sample until the age of 7 to 9 years, identified individuals who developed deficits, and matched them to a typically developing control group using comprehensive behavioral assessments. Multivariate pattern classification distinguished future cases from controls with up to 87% accuracy based on the regional functional activity of the right posterior parietal cortex (PPC), the network-level functional activity of the right dorsolateral prefrontal cortex (DLPFC), and the effective functional and structural connectivity of these regions. Our results indicate that mathematical learning deficits originate from atypical development of a frontoparietal network that is already detectable in early childhood.

The neural basis of number word processing in children and adults

The ability to map number words to their corresponding quantity representations is a gatekeeper for children's future math success (Spaepen et al., 2018). Without number word knowledge at school entry, children are at greater risk for developing math learning difficulties (Chu et al., 2019). In the present study, we used functional magnetic resonance imaging (fMRI) to examine the neural basis for processing the meaning of spoken number words and its developmental trajectory in 4- to 10-year-old children, and in adults. In a number word-quantity mapping paradigm, participants listened to number words while simultaneously viewing quantities that were congruent or incongruent to the number word they heard. Whole brain analyses revealed that adults showed a neural congruity effect with greater neural activation for incongruent relative to congruent trials in anterior cingulate cortex (ACC) and left intraparietal sulcus (LIPS). In contrast, children did not show a significant neural congruity effect. However, a region of interest analysis in the child sample demonstrated age-related increases in the neural congruity effect, specifically in the LIPS. The positive correlation between neural congruity in LIPS and age was stronger in children who were already attending school, suggesting that developmental changes in LIPS function are experience-dependent.

Symbols Are Special: An fMRI Adaptation Study of Symbolic, Nonsymbolic, and Non-Numerical Magnitude Processing in the Human Brain

How are different formats of magnitudes represented in the human brain? We used functional magnetic resonance imaging adaptation to isolate representations of symbols, quantities, and physical size in 45 adults. Results indicate that the neural correlates supporting the passive processing of number symbols are largely dissociable from those supporting quantities and physical size, anatomically and representationally. Anatomically, passive processing of quantities and size correlate with activation in the right intraparietal sulcus, whereas symbolic number processing, compared with quantity processing, correlates with activation in the left inferior parietal lobule. Representationally, neural patterns of activation supporting symbols are dissimilar from neural activation patterns supporting quantity and size in the bilateral parietal lobes. These findings challenge the longstanding notion that the culturally acquired ability to conceptualize symbolic numbers is represented using entirely the same brain systems that support the evolutionarily ancient system used to process quantities. Moreover, these data reveal that regions that support numerical magnitude processing are also important for the processing of non-numerical magnitudes. This discovery compels future investigations of the neural consequences of acquiring knowledge of symbolic numbers.

Magnitude integration in the Archerfish

We make magnitude-related decisions every day, for example, to choose the shortest queue at the grocery store. When making such decisions, which magnitudes do we consider? The dominant theory suggests that our focus is on numerical quantity, i.e., the number of items in a set. This theory leads to quantity-focused research suggesting that discriminating quantities is automatic, innate, and is the basis for mathematical abilities in humans. Another theory suggests, instead, that non-numerical magnitudes, such as the total area of the compared items, are usually what humans rely on, and numerical quantity is used only when required. Since wild animals must make quick magnitude-related decisions to eat, seek shelter, survive, and procreate, studying which magnitudes animals spontaneously use in magnitude-related decisions is a good way to study the relative primacy of numerical quantity versus non-numerical magnitudes. We asked whether, in an animal model, the influence of non-numerical magnitudes on performance in a spontaneous magnitude comparison task is modulated by the number of non-numerical magnitudes that positively correlate with numerical quantity. Our animal model was the Archerfish, a fish that, in the wild, hunts insects by shooting a jet of water at them. These fish were trained to shoot water at artificial targets presented on a computer screen above the water tank. We tested the Archerfish's performance in spontaneous, untrained two-choice magnitude decisions. We found that the fish tended to select the group containing larger non-numerical magnitudes and smaller quantities of dots. The fish selected the group containing more dots mostly when the quantity of the dots was positively correlated with all five different non-numerical magnitudes. The current study adds to the body of studies providing direct evidence that in some cases animals' magnitude-related decisions are more affected by non-numerical magnitudes than by numerical quantity, putting doubt on the claims that numerical quantity perception is the most basic building block of mathematical abilities.

Developmental brain dynamics of numerical and arithmetic abilities

The development of numerical and arithmetic abilities constitutes a crucial cornerstone in our modern and educated societies. Difficulties to acquire these central skills can lead to severe consequences for an individual's well-being and nation's economy. In the present review, we describe our current broad understanding of the functional and structural brain organization that supports the development of numbers and arithmetic. The existing evidence points towards a complex interaction among multiple domain-specific (e.g., representation of quantities and number symbols) and domain-general (e.g., working memory, visual-spatial abilities) cognitive processes, as well as a dynamic integration of several brain regions into functional networks that support these processes. These networks are mainly, but not exclusively, located in regions of the frontal and parietal cortex, and the functional and structural dynamics of these networks differ as a function of age and performance level. Distinctive brain activation patterns have also been shown for children with dyscalculia, a specific learning disability in the domain of mathematics. Although our knowledge about the developmental brain dynamics of number and arithmetic has greatly improved over the past years, many questions about the interaction and the causal involvement of the abovementioned functional brain networks remain. This review provides a broad and critical overview of the known developmental processes and what is yet to be discovered.

Children With Dyscalculia Show Hippocampal Hyperactivity During Symbolic Number Perception

Dyscalculia is a learning disability affecting the acquisition of arithmetical skills in children with normal intelligence and age-appropriate education. Two hypotheses attempt to explain the main cause of dyscalculia. The first hypothesis suggests that a problem with the core mechanisms of perceiving (non-symbolic) quantities is the cause of dyscalculia (core deficit hypothesis), while the alternative hypothesis suggests that dyscalculics have problems only with the processing of numerical symbols (access deficit hypothesis). In the present study, the symbolic and non-symbolic numerosity processing of typically developing children and children with dyscalculia were examined with functional magnetic resonance imaging (fMRI). Control (n = 15, mean age: 11.26) and dyscalculia (n = 12, mean age: 11.25) groups were determined using a wide-scale screening process. Participants performed a quantity comparison paradigm in the fMRI with two number conditions (dot and symbol comparison) and two difficulty levels (0.5 and 0.7 ratio). The results showed that the bilateral intraparietal sulcus (IPS), left dorsolateral prefrontal cortex (DLPFC) and left fusiform gyrus (so-called “number form area”) were activated for number perception as well as bilateral occipital and supplementary motor areas. The task difficulty engaged bilateral insular cortex, anterior cingulate cortex, IPS, and DLPFC activation. The dyscalculia group showed more activation in the left orbitofrontal cortex, left medial prefrontal cortex, and right anterior cingulate cortex than the control group. The dyscalculia group showed left hippocampus activation specifically for the symbolic condition. Increased left hippocampal and left-lateralized frontal network activation suggest increased executive and memory-based compensation mechanisms during symbolic processing for dyscalculics. Overall, our findings support the access deficit hypothesis as a neural basis for dyscalculia.

Processing symbolic magnitude information conveyed by number words and by scalar adjectives

Humans not only process and compare magnitude information such as size, duration, and number perceptually, but they also communicate about these properties using language. In this respect, a relevant class of lexical items are so-called scalar adjectives like “big,” “long,” “loud,” and so on which refer to magnitude information. It has been proposed that humans use an amodal and abstract representation format shared by different dimensions, called the generalised magnitude system (GMS). In this paper, we test the hypothesis that scalar adjectives are symbolic references to GMS representations, and, therefore, GMS gets involved in processing their meaning. Previously, a parallel hypothesis on the relation between number symbols and GMS representations has been tested with the size congruity paradigm. The results of these experiments showed interference between the processing of number symbols and the processing of physical (font-) size. In the first three experiments of the present study (total N = 150), we used the size congruity paradigm and the same/different task to look at the potential interaction between physical size magnitude and numerical magnitude expressed by number words. In the subsequent three experiments (total N = 149), we looked at a parallel potential interaction between physical size magnitude and scalar adjective meaning. In the size congruity paradigm, we observed interference between the processing of the numerical value of number words and the meaning of scalar adjectives, on the one hand, and physical (font-) size, on the other hand, when participants had to judge the number words or the adjectives (while ignoring physical size). No interference was obtained for the reverse situation, i.e., when participants judged the physical font size (while ignoring numerical value or meaning). The results of the same/different task for both number words and scalar adjectives strongly suggested that the interference that was observed in the size congruity paradigm was likely due to a response conflict at the decision stage of processing rather than due to the recruitment of GMS representations. Taken together, it can be concluded that the size congruity paradigm does not provide evidence in support the hypothesis that GMS representations are used in the processing of number words or scalar adjectives. Nonetheless, the hypothesis we put forward about scalar adjectives is still is a promising potential line of research. We make a number of suggestions for how this hypothesis can be explored in future studies.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms.

Predicting learning and achievement using GABA and glutamate concentrations in human development

Previous research has highlighted the role of glutamate and gamma-aminobutyric acid (GABA) in learning and plasticity. What is currently unknown is how this knowledge translates to real-life complex cognitive abilities that emerge slowly and how the link between these neurotransmitters and human learning and plasticity is shaped by development. While some have suggested a generic role of glutamate and GABA in learning and plasticity, others have hypothesized that their involvement shapes sensitive periods during development. Here we used a cross-sectional longitudinal design with 255 individuals (spanning primary school to university) to show that glutamate and GABA in the intraparietal sulcus explain unique variance both in current and future mathematical achievement (approximately 1.5 years). Furthermore, our findings reveal a dynamic and dissociable role of GABA and glutamate in predicting learning, which is reversed during development, and therefore provide novel implications for models of learning and plasticity during childhood and adulthood.

Neural basis of approximate number in congenital blindness

Although humans are unique among animals in their ability to manipulate symbolic numbers, we share with other species an approximate number sense that allows us to estimate and compare the number of objects or events in a set, such as the number of apples in a tree. Our ability to discriminate the numerosity of two sets decreases as the ratio between them becomes smaller (e.g., 8 vs 16 items is harder to discriminate than 8 vs 32 items). The intraparietal sulcus (IPS) plays a key role in this numerical approximation. Neuronal populations within the IPS code for numerosity, with stimuli of different numerosities eliciting discriminable spatial patterns of activity. The developmental origins of these IPS number representations are not known. Here, we tested the hypothesis that representations of number in the IPS require visual experience with object sets, by working with individuals blind from birth. While undergoing fMRI, congenitally blind (n = 17) and blindfolded sighted (n = 25) participants judged which of two sequences of beeps was more numerous. In both sighted and blind individuals, patterns of activity in the IPS discriminated among different numerosities (4, 8, 16 vs 32), with better discrimination in the IPS of the blind group. In both groups, decoding performance decreased as the ratio between numerosities decreased (e.g., 8 vs 16 was less discriminable than 8 vs 32). These findings suggest that number representations in the IPS either have innate precursors, or that auditory or tactile experience with sets is sufficient for typical development.

The neural basis of counting sequences

Sequence processing is critical for complex behavior, and counting sequences hold a unique place underlying human numerical development. Despite this, the neural bases of counting sequences remain unstudied. We hypothesized that counting sequences in adults would involve representations in sensory, order, magnitude, and linguistic codes that implicate regions in auditory, supplementary motor, posterior parietal, and inferior frontal areas, respectively. In an fMRI scanner, participants heard four-number sequences in a 2 × 2 × 2 design. The sequences were adjacent or not (e.g., 5, 6, 7, 8 vs. 5, 6, 7, 9), ordered or not (e.g., 5, 6, 7, 8 vs. 8, 5, 7, 6), and were spoken by a voice of consistent or variable identity. Then, neural substrates of counting sequences were identified by testing for the effect of consecutiveness (ordered nonadjacent versus ordered adjacent, e.g., 5, 6, 7, 9 > 5, 6, 7, 8) in the hypothesized brain regions. Violations to consecutiveness elicited brain activity in the right inferior frontal gyrus (IFG) and the supplementary motor area (SMA). In contrast, no such activation was observed in the auditory cortex, despite violations in voice identity recruiting strong activity in that region. Also, no activation was observed in the inferior parietal lobule, despite a robust effect of orderedness observed in that brain region. These findings indicate that listening to counting sequences do not automatically elicit sensory or magnitude codes but suggest that the precise increments in the sequence are tracked by the mechanism for processing ordered associations in the SMA and by the mechanism for binding individual lexical items into a cohesive whole in the IFG.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

Neurocognitive modeling of latent memory processes reveals reorganization of hippocampal-cortical circuits underlying learning and efficient strategies

Efficient memory-based problem-solving strategies are a cardinal feature of expertise across a wide range of cognitive domains in childhood. However, little is known about the neurocognitive mechanisms that underlie the acquisition of efficient memory-based problem-solving strategies. Here we develop, to the best of our knowledge, a novel neurocognitive process model of latent memory processes to investigate how cognitive training designed to improve children's problem-solving skills alters brain network organization and leads to increased use and efficiency of memory retrieval-based strategies. We found that training increased both the use and efficiency of memory retrieval. Functional brain network analysis revealed training-induced changes in modular network organization, characterized by increase in network modules and reorganization of hippocampal-cortical circuits. Critically, training-related changes in modular network organization predicted performance gains, with emergent hippocampal, rather than parietal cortex, circuitry driving gains in efficiency of memory retrieval. Our findings elucidate a neurocognitive process model of brain network mechanisms that drive learning and gains in children's efficient problem-solving strategies.

Neurodevelopmental differences in child and adult number processing: An fMRI-based validation of the triple code model

The triple code model of numerical cognition (TCM) details the neurocognitive mechanisms associated with perceiving and manipulating numerical information in exact symbolic (Arabic digits and number words) and approximate nonsymbolic numerical magnitude (e.g., dot arrays) representation codes. The current study provides a first empirical fMRI-based investigation into neurodevelopmental differences in 30 healthy children's and 44 healthy adults' recruitment of neural correlates associated with the Arabic digit, number word, and nonsymbolic magnitude codes. Differences between the two groups were found in cingulate regions commonly associated with domain-general aspects of cognitive control, as opposed to neural correlates of number processing per se. A primary developmental difference was identified in verbal number discrimination, where only adults recruited left-lateralized perisylvian language areas in accordance with the TCM. We therefore call for a revision of the verbal code and a formulation of separate child and adult-specific neurocognitive mechanisms associated with the discrimination of number words. Although further research is necessary, results indicate that numerical discrimination abilities in middle-school-aged children operate close to adult-level maturity. Neurodevelopmental differences may be more apparent in younger children, or on the level of functional network dynamics as opposed to a shift in recruited neural substrates.

Adaptation to visual numerosity changes neural numerosity selectivity

Perceiving numerosity, i.e. the set size of a group of items, is an evolutionarily preserved ability found in humans and animals. A useful method to infer the neural underpinnings of a given perceptual property is sensory adaptation. Like other primary perceptual attributes, numerosity is susceptible to adaptation. Recently, we have shown numerosity-selective neural populations with a topographic organization in the human brain. Here, we investigated whether numerosity adaptation can affect the numerosity selectivity of these populations using ultra-high field (7 Tesla) functional magnetic resonance imaging (fMRI). Participants viewed stimuli of changing numerosity (1 to 7 dots), which allowed the mapping of numerosity selectivity. We interleaved a low or high numerosity adapter stimulus with these mapping stimuli, repeatedly presenting 1 or 20 dots respectively to adapt the numerosity-selective neural populations. We analyzed the responses using custom-build population receptive field neural models of numerosity encoding and compared estimated numerosity preferences between adaptation conditions. We replicated our previous studies where we found several topographic maps of numerosity-selective responses. We found that overall, numerosity adaptation altered the preferred numerosities within the numerosity maps, resulting in predominantly attractive biases towards the numerosity of the adapter. The differential biases could be explained by the difference between the unadapted preferred numerosity and the numerosity of the adapter, with attractive biases being observed with higher difference. The results could link perceptual numerosity adaptation effects to changes in neural numerosity selectivity.

Tactile to visual number priming in the left intraparietal cortex of sighted Braille readers

Numbers can be presented in different notations and sensory modalities. It is currently debated to what extent these formats overlap onto a single representation. We asked whether such an overlap exists between symbolic numbers represented in two sensory modalities: Arabic digits and Braille numbers. A unique group of sighted Braille readers underwent extensive Braille reading training and was tested in an fMRI repetition-suppression paradigm with tactile Braille digit primes and visual Arabic digit targets. Our results reveal cross-modal priming: compared to repetition of two different quantities (e.g., Braille “5” and Arabic “2”), repetition of the same quantity presented in two modalities (e.g., Braille “5” and Arabic “5”) led to a reduction of activation in several sub-regions of the Intraparietal Sulcus (IPS), a key cortical region for magnitude processing. Thus, in sighted Braille readers, the representations of numbers read by sight and by touch overlap to a degree sufficient to cause repetition suppression. This effect was modulated by the numerical prime-probe distance. Altogether this indicates that the left parietal cortex hosts neural assemblies that are sensitive to numerical information from different notations (number words or Arabic digits) and modalities (tactile and visual).