Common and distinct brain regions in both parietal and frontal cortex support symbolic and nonsymbolic number processing in humans: A functional neuroimaging meta-analysis

Origins of numbers: a shared language-of-thought for arithmetic and geometry?

Concepts of exact number are often thought to originate from counting and the successor function, or from a refinement of the approximate number system (ANS). We argue here for a third origin: a shared language-of-thought (LoT) for geometry and arithmetic that involves primitives of repetition, concatenation, and recursive embedding. Applied to sets, those primitives engender concepts of exact integers through recursive applications of additions and multiplications. Links between geometry and arithmetic also explain the emergence of higher-level notions (squares, primes, etc.). Under our hypothesis, understanding a number means having one or several mental expressions for it, and their minimal description length (MDL) determines how easily they can be mentally manipulated. Several historical, developmental, linguistic, and brain imaging phenomena provide preliminary support for our proposal.

The role of the intraparietal sulcus in numeracy: A review of parietal lesion cases

Prominent theories of numeracy link the intraparietal sulcus (IPS) to approximate representations of quantity that undergird basic math abilities. The goal of this review is to better understand the neural basis of mathematical cognition through the lens of acalculia, by identifying numeracy-focused single case studies of patients with parietal lesions and testing for causal relationships between numeracy impairments and the locus of parietal damage. A systematic literature review identified 27 single case studies with left parietal lesions and categorized administered tasks across four numeracy domains: Approximation, Calculation, Ordinality/Cardinality, and Transcoding. We compared published lesion images by drawing a sphere at the inferred center-of-mass and assigning each case to an anatomical group (IPS or Other Parietal damage) based on overlap with left IPS and original anatomical description. We performed Fisher's Exact Test to compare behavioral performance on each numeracy domain between the two groups. As an exploratory follow-up, we used Activation Likelihood Estimation (ALE) to identify sites of damage within parietal cortex preferentially associated with impairments in each domain. We found that Approximation impairments were significantly more frequent in the IPS group (p = .003). The exploratory ALE analysis revealed that only Approximation impairment cases significantly overlapped with the IPS, while impairments in other domains were localized to different regions of the parietal lobe. Based on the pattern of impairments shown across these cases, we conclude that damage to the left IPS is linked to impairments in approximation ability specifically. Our findings support theoretical claims linking IPS to magnitude representation, but do not provide evidence that IPS critically underpins performance across all numeracy tasks. Instead, our findings are more compatible with models of dissociable circuits of numerical processing within the parietal lobe.

Numerical cognition across the lifespan: A selective review of key developmental stages and neural, cognitive, and affective underpinnings

Numerical cognition constitutes a set of hierarchically related skills and abilities that develop-and may subsequently begin to decline-over developmental time. An innate "number sense" has long been argued to provide a foundation for the development of increasingly complex and applied numerical cognition, such as symbolic numerical reference, arithmetic, and financial literacy. However, evidence for a direct link between basic perceptual mechanisms that allow us to determine numerical magnitude (e.g., "how many" objects are in front of us and whether some of these are of a "greater" or "lesser" quantity), and later symbolic applications for counting and mathematics, has recently been challenged. Understanding how one develops an increasingly precise sense of number and which neurocognitive mechanisms support arithmetic development and achievement is crucial for developing successful mathematics curricula, supporting individual financial literacy and decision-making, and designing appropriate intervention and remediation programs for mathematical learning disabilities as well as mathematics anxiety. The purpose of this review is to provide a broad overview of the cognitive, neural, and affective underpinnings of numerical cognition-spanning the earliest hours of infancy to senior adulthood-and highlight gaps in our knowledge that remain to be addressed.

Hierarchical representations of relative numerical magnitudes in the human frontoparietal cortex

The ability to estimate numerical magnitude is essential for decision-making and is thought to underlie arithmetic skills. In humans, neural populations in the frontoparietal regions are tuned to represent numerosity. However, it remains unclear whether their response properties are fixed to a specific numerosity (i.e., absolute code) or dynamically scaled according to the range of numerosities relevant to the context (i.e., relative code). Here, using functional magnetic resonance imaging combined with multivariate pattern analysis, we uncover evidence that representations of relative numerosity coding emerge gradually as visual information processing advances in the frontoparietal regions. In contrast, the early sensory areas predominantly exhibit absolute coding. These findings indicate a hierarchical organization of relative numerosity representations that adapt their response properties according to the context. Our results highlight the existence of a context-dependent optimization mechanism in numerosity representation, enabling the efficient processing of infinite magnitude information with finite neural resources.

Number, size, and space associated in a common system by distinct mechanisms

The spatial numerical association of response codes (SNARC) effect demonstrates that people respond faster to small numbers with their left hand and faster to large numbers with their right hand. The size congruity effect (SCE) refers to the fact that congruent trials between numerical values and physical sizes are faster than incongruent trials. Previous studies have found that the SNARC effect and SCE are independent when magnitudes or sizes are processed explicitly. This study aimed to explore whether number, size, and space are common and distinct mechanisms using an implicit parity judgment task. The results showed that the SNARC effect, SCE, and SNARC-like effect all co-existed. Furthermore, there was a significant interaction between the SNARC effect and SCE, in which the SNARC effect in the SCE-congruent condition was larger than in the SCE-incongruent condition, whereas SCE merely emerged in the SNARC-compatible trials. However, participants responded to small numbers in large size faster than to large numbers in small size with the left hand in SCE-incongruent trials, which reflected that number-space mapping (SNARC effect) was stronger than size-space mapping (SNARC-like effect). These findings provide new evidence for A Theory of Magnitude (ATOM), which suggests that number, size, and space are associated with a common generalized magnitude system through distinct mechanisms.

Investigating the Triple Code Model in numerical cognition using stereotactic electroencephalography

The ability to conceptualize numerical quantities is an essential human trait. According to the "Triple Code Model" in numerical cognition, distinct neural substrates encode the processing of visual, auditory, and non-symbolic numerical representations. While our contemporary understanding of human number cognition has benefited greatly from advances in clinical imaging, limited studies have investigated the intracranial electrophysiological correlates of number processing. In this study, 13 subjects undergoing stereotactic electroencephalography for epilepsy participated in a number recognition task. Drawing upon postulates of the Triple Code Model, we presented subjects with numerical stimuli varying in representation type (symbolic vs. non-symbolic) and mode of stimuli delivery (visual vs. auditory). Time-frequency spectrograms were dimensionally reduced with principal component analysis and passed into a linear support vector machine classification algorithm to identify regions associated with number perception compared to inter-trial periods. Across representation formats, the highest classification accuracy was observed in the bilateral parietal lobes. Auditory (spoken and beeps) and visual (Arabic) number formats preferentially engaged the superior temporal cortices and the frontoparietal regions, respectively. The left parietal cortex was found to have the highest classification for number dots. Notably, the putamen exhibited robust classification accuracies in response to numerical stimuli. Analyses of spectral feature maps revealed that non-gamma frequency, below 30 Hz, had greater-than-chance classification value and could be potentially used to characterize format specific number representations. Taken together, our findings obtained from intracranial recordings provide further support and expand on the Triple Code Model for numerical cognition.

Deficits in or Preservation of Basic Number Processing in Parkinson's Disease? A Registered Report

Neurodegenerative diseases such as Parkinson's disease (PD) have a huge impact on patients, caregivers, and the health care system. Until now, diagnosis of mild cognitive impairments in PD has been established based on domain-general functions such as executive functions, attention, or working memory. However, specific numerical deficits observed in clinical practice have not yet been systematically investigated. PD-immanent deterioration of domain-general functions and domain-specific numerical areas suggests mechanisms of both primary and secondary dyscalculia. The current study systematically investigated basic number processing performance in PD patients for the first time, targeting domain-specific cognitive representations of numerosity and the influence of domain-general factors. The overall sample consisted of patients with a diagnosis of PD, according to consensus guidelines, and healthy controls. PD patients were stratified into patients with normal cognition (PD-NC) or mild cognitive impairment (level I-PD-MCI based on cognitive screening). Basic number processing was assessed using transcoding, number line estimation, and (non-) symbolic number magnitude comparison tasks. Discriminant analysis was employed to assess whether basic number processing tasks can differentiate between a healthy control group and both PD groups. All participants were subjected to a comprehensive numerical and a neuropsychological test battery, as well as sociodemographic and clinical measures. Results indicate a profile of preserved (verbal representation) and impaired (magnitude representation, place × value activation) function in PD-MCI, hinting at basal ganglia dysfunction affecting numerical cognition in PD. Numerical deficits could not be explained by domain-general cognitive impairments, so that future research needs to incorporate domain-specific tasks of sufficient difficulty.

Behavior-related potentials from single-trial interindividual correlation between event related potentials and behavioral performance reveals right lateralized processing of numerosity

Accumulated functional magnetic resonance imaging (fMRI) and electroencephalography evidence indicate that numerosity is first processed in the occipito-parietal cortex. fMRI evidence also indicates right-lateralized processing of numerosity, but there is no consistent evidence from event-related potential (ERP) studies. This study investigated the ERP of numerosity processing in the left, right, and bilateral visual fields. The single-trial ERP-behavioral correlation was applied to show how the ERP was associated with behavioral responses. The results showed a significant early behavioral-ERP correlation on the right N1 component when stimuli were presented in the left visual field rather than in the right visual field. The behavioral ERP correlation was termed BN1. There was bilateral BN1 based on the reaction time or error rate, but the right BN1 was larger than that the left BN1 when the stimulus was present in the bilateral visual field. Therefore, this study provided a new neural marker for individual differences in processing numerosity and suggested that processing numerosity was supported by the right occipito-parietal cortex.

Gradient Organization of Space, Time, and Numbers in the Brain: A Meta-analysis of Neuroimaging Studies

In this study, we ran a meta-analysis of neuroimaging studies to pinpoint the neural regions that are commonly activated across space, time, and numerosity, and we tested the existence of gradient transitions among these magnitude representations in the brain. Following PRISMA guidelines, we included in the meta-analysis 112 experiments (for space domain), 114 experiments (time domain), and 115 experiments (numerosity domain), and we used the activation likelihood estimation method. We found a system of brain regions that was commonly recruited in all the three magnitudes, which included bilateral insula, the supplementary motor area (SMA), the right inferior frontal gyrus, and bilateral intraparietal sulci. Gradiental transitions between different magnitudes were found along all these regions but insulae, with space and numbers leading to gradients mainly over parietal regions (and SMA) whereas time and numbers mainly over frontal regions. These findings provide evidence for the GradiATOM theory (Gradient Theory of Magnitude), suggesting that spatial proximity given by overlapping activations and gradients is a key aspect for efficient interactions and integrations among magnitudes.

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.

Frontoparietal and salience network synchronizations during nonsymbolic magnitude processing predict brain age and mathematical performance in youth

The development and refinement of functional brain circuits crucial to human cognition is a continuous process that spans from childhood to adulthood. Research increasingly focuses on mapping these evolving configurations, with the aim to identify markers for functional impairments and atypical development. Among human cognitive systems, nonsymbolic magnitude representations serve as a foundational building block for future success in mathematical learning and achievement for individuals. Using task-based frontoparietal (FPN) and salience network (SN) features during nonsymbolic magnitude processing alongside machine learning algorithms, we developed a framework to construct brain age prediction models for participants aged 7-30. Our study revealed differential developmental profiles in the synchronization within and between FPN and SN networks. Specifically, we observed a linear increase in FPN connectivity, concomitant with a decline in SN connectivity across the age span. A nonlinear U-shaped trajectory in the connectivity between the FPN and SN was discerned, revealing reduced FPN-SN synchronization among adolescents compared to both pediatric and adult cohorts. Leveraging the Gradient Boosting machine learning algorithm and nested fivefold stratified cross-validation with independent training datasets, we demonstrated that functional connectivity measures of the FPN and SN nodes predict chronological age, with a correlation coefficient of .727 and a mean absolute error of 2.944 between actual and predicted ages. Notably, connectivity within the FPN emerged as the most contributing feature for age prediction. Critically, a more matured brain age estimate is associated with better arithmetic performance. Our findings shed light on the intricate developmental changes occurring in the neural networks supporting magnitude representations. We emphasize brain age estimation as a potent tool for understanding cognitive development and its relationship to mathematical abilities across the critical developmental period of youth. PRACTITIONER POINTS: This study investigated the prolonged changes in the brain's architecture across childhood, adolescence, and adulthood, with a focus on task-state frontoparietal and salience networks. Distinct developmental pathways were identified: frontoparietal synchronization strengthens consistently throughout development, while salience network connectivity diminishes with age. Furthermore, adolescents show a unique dip in connectivity between these networks. Leveraging advanced machine learning methods, we accurately predicted individuals' ages based on these brain circuits, with a more mature estimated brain age correlating with better math skills.

Arithmetic in two languages: Localizing simple multiplication processing in the adult bilingual brain

Verbally memorized multiplication tables are thought to create language-specific memories. Supporting this idea, bilinguals are typically faster and more accurate in the language in which they learned math (LA+) than in their other language (LA- ) . No study has yet revealed the underlying neurocognitive mechanisms explaining this effect, or the role of problem size in explaining the recruitment of different brain regions in LA+ and LA- . To fill this gap in the literature, 29 Spanish-English early bilingual adults, proficient in both languages, verified simple multiplication problems in each language while functional magnetic resonance imaging (fMRI) was acquired. More specifically, this study aimed to answer two questions: 1) Does LA+ recruit left superior and middle temporal gyri (STG/MTG) to a greater extent than LA- , reflecting more robust verbal representations of multiplication facts in LA+? In contrast, does LA- recruit the inferior frontal gyrus (IFG), reflecting more effortful retrieval, or the intraparietal sulcus (IPS), reflecting reliance on quantity processes? 2) Is there an interaction between language and problem size, where language differences are more pronounced for less practiced, large multiplication problems (e.g., 8 × 9) in comparison to more familiar, small problems (e.g., 2 × 3). Functional localizer tasks were used to identify hypothesis-driven regions of interest in verbal areas associated with verbal representations of arithmetic facts (left STG/MTG) and with the effortful retrieval of these facts (left IFG) and quantity areas engaged when calculation-based strategies are used (bilateral IPS). In planned analyses, no cluster reached significance for the direct comparison of languages (question 1) or for the interaction between language and problem size (question 2). An exploratory analysis found a main effect of problem size, where small problems recruited left STG/MTG and left IFG to a greater extent than large problems, suggesting greater verbal involvement for these problems in both languages. Additionally, large problems recruited right IPS to a greater extent than small problems, suggesting reliance on quantity processes. Our results suggest that proficient early bilingual adults engage similar brain regions in both languages, even for more difficult, large problems.

The inferior fronto-occipital fasciculus correlates with early precursors of mathematics and reading before the start of formal schooling

Diffusion-weighted imaging studies in preschoolers have almost exclusively been done in the field of reading. As a result, virtually nothing is known about white matter tracts associated with individual differences in mathematics at this age. Studying the preschoolers' brain is crucial because it allows us to identify individual differences in brain anatomy without influences of formal mathematics and reading instruction. To fill this gap, we investigated for the first time before the start of formal school entry the associations between white matter tracts and precursors of mathematics and reading simultaneously. We also investigated whether these associations were specific to mathematics and to reading, or not. We focused on four bilateral white matter tracts (arcuate fasciculus (direct, anterior), inferior fronto-occipital fasciculus, inferior longitudinal fasciculus), which have been previously correlated with mathematical performance in older children and with reading performance in children of a similar age as the current study. Participants were 56 5-year-old children (Mage = 67 months; SD = 1.8), none of which received formal instruction. Our results showed an association between the bilateral inferior fronto-occipital fasciculus and precursors of mathematics (numerical ordering, numeral knowledge) and reading (phonological awareness, letter knowledge). Follow-up regression analyses revealed that the associations found with the inferior fronto-occipital fasciculus were neither specific to mathematics nor specific to reading. These findings suggest that, already before the start of formal schooling, the inferior fronto-occipital fasciculus might be related to the neural overlap between mathematics and reading. This overlap potentially reflects one of their many shared mechanisms, such as the reliance on phonological codes or the processing of visual symbols, and these mechanisms should be exploited in future studies.

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.

Probing Our Built-in Calculator: A Systematic Narrative Review of Noninvasive Brain Stimulation Studies on Arithmetic Operation-Related Brain Areas

This systematic review presented a comprehensive survey of studies that applied transcranial magnetic stimulation and transcranial electrical stimulation to parietal and nonparietal areas to examine the neural basis of symbolic arithmetic processing. All findings were compiled with regard to the three assumptions of the triple-code model (TCM) of number processing. Thirty-seven eligible manuscripts were identified for review (33 with healthy participants and 4 with patients). Their results are broadly consistent with the first assumption of the TCM that intraparietal sulcus both hold a magnitude code and engage in operations requiring numerical manipulations such as subtraction. However, largely heterogeneous results conflicted with the second assumption of the TCM that the left angular gyrus subserves arithmetic fact retrieval, such as the retrieval of rote-learned multiplication results. Support is also limited for the third assumption of the TCM, namely, that the posterior superior parietal lobule engages in spatial operations on the mental number line. Furthermore, results from the stimulation of brain areas outside of those postulated by the TCM show that the bilateral supramarginal gyrus is involved in online calculation and retrieval, the left temporal cortex in retrieval, and the bilateral dorsolateral prefrontal cortex and cerebellum in online calculation of cognitively demanding arithmetic problems. The overall results indicate that multiple cortical areas subserve arithmetic skills.

The significance of structural rich club hubs for the processing of hierarchical stimuli

The brain's structural network follows a hierarchy that is described as rich club (RC) organization, with RC hubs forming the well-interconnected top of this hierarchy. In this study, we tested whether RC hubs are involved in the processing of hierarchically higher structures in stimulus sequences. Moreover, we explored the role of previously suggested cortical gradients along anterior-posterior and medial-lateral axes throughout the frontal cortex. To this end, we conducted a functional magnetic resonance imaging (fMRI) experiment and presented participants with blocks of digit sequences that were structured on different hierarchically nested levels. We additionally collected diffusion weighted imaging data of the same subjects to identify RC hubs. This classification then served as the basis for a region of interest analysis of the fMRI data. Moreover, we determined structural network centrality measures in areas that were found as activation clusters in the whole-brain fMRI analysis. Our findings support the previously found anterior and medial shift for processing hierarchically higher structures of stimuli. Additionally, we found that the processing of hierarchically higher structures of the stimulus structure engages RC hubs more than for lower levels. Areas involved in the functional processing of hierarchically higher structures were also more likely to be part of the structural RC and were furthermore more central to the structural network. In summary, our results highlight the potential role of the structural RC organization in shaping the cortical processing hierarchy.

Perceptual addition of continuous magnitudes in an 'artificial algebra'

Although there is substantial evidence for an innate 'number sense' that scaffolds learning about mathematics, whether the underlying representations are based on discrete or continuous perceptual magnitudes has been controversial. Yet the nature of the computations supported by these representations has been neglected in this debate. While basic computation of discrete non-symbolic quantities has been reliably demonstrated in adults, infants, and non-humans, far less consideration has been given to the capacity for computation of continuous perceptual magnitudes. Here we used a novel experimental task to ask if humans can learn to add non-symbolic, continuous magnitudes in accord with the properties of an algebraic group, by feedback and without explicit instruction. Three pairs of experiments tested perceptual addition under the group properties of commutativity (Experiments 1a-b), identity and inverses (Experiments 2a-b) and associativity (Experiments 3a-b), with both line length and brightness modalities. Transfer designs were used in which participants responded on trials with feedback based on sums of magnitudes and later were tested with novel stimulus configurations. In all experiments, correlations of average responses with magnitude sums were high on trials with feedback. Responding on transfer trials was accurate and provided strong support for addition under all of the group axioms with line length, and for all except associativity with brightness. Our results confirm that adult human subjects can implicitly add continuous quantities in a manner consistent with symbolic addition over the integers, and that an 'artificial algebra' task can be used to study implicit computation.

Regional specificity of cathodal transcranial direct current stimulation effects on spatial-numerical associations: Comparison of four stimulation sites

Neuromodulation with transcranial direct current stimulation (tDCS) is an increasingly popular research tool to experimentally manipulate cortical areas and probe their causal involvements in behavior, but its replicability and regional specificity are not clear. This registered report investigated cathodal tDCS effects on spatial-numerical associations (i.e., the SNARC effect), the numerical distance effect (NDE), and inhibitory control (i.e., stop-signal reaction time; SSRT). Healthy adults (N = 160) were randomly assigned to one of five groups to receive sham tDCS or 1 mA cathodal tDCS to one of four stimulation sites (left/right prefrontal cortex [PFC], left/right posterior parietal cortex) with extracephalic return. We replicated that cathodal tDCS over the left PFC reduced the SNARC effect compared to sham tDCS and to tDCS over the left parietal cortex. However, neither NDE nor SSRT were modulated in the main analyses. Post hoc contrasts and exploratory analyses showed that cathodal tDCS over the right PFC had a time-dependent effect by delayed practice-related improvements in SSRT. Math anxiety moderated changes in the NDE in the groups receiving tDCS to the right parietal cortex. With few exceptions, the replicability and regional specificity of tDCS effects on behavior were weak and partially moderated by individual differences. Future research needs to characterize the parameter settings for effective neuromodulation.

Math on cortex-enhanced delta phase synchrony in math experts during long and complex math demonstrations

Neural oscillations are important for working memory and reasoning and they are modulated during cognitively challenging tasks, like mathematics. Previous work has examined local cortical synchrony on theta (4-8 Hz) and alpha (8-13 Hz) bands over frontal and parietal electrodes during short mathematical tasks when sitting. However, it is unknown whether processing of long and complex math stimuli evokes inter-regional functional connectivity. We recorded cortical activity with EEG while math experts and novices watched long (13-68 seconds) and complex (bachelor-level) math demonstrations when sitting and standing. Fronto-parietal connectivity over the left hemisphere was stronger in math experts than novices reflected by enhanced delta (0.5-4 Hz) phase synchrony in experts. Processing of complex math tasks when standing extended the difference to right hemisphere, suggesting that other cognitive processes, such as maintenance of body balance when standing, may interfere with novice's internal concentration required during complex math tasks more than in experts. There were no groups differences in phase synchrony over theta or alpha frequencies. These results suggest that low-frequency oscillations modulate inter-regional connectivity during long and complex mathematical cognition and demonstrate one way in which the brain functions of math experts differ from those of novices: through enhanced fronto-parietal functional connectivity.

Brain connectivity and academic skills in English learners

English learners (ELs) are a rapidly growing population in schools in the United States with limited experience and proficiency in English. To better understand the path for EL's academic success in school, it is important to understand how EL's brain systems are used for academic learning in English. We studied, in a cohort of Hispanic middle-schoolers (n = 45, 22F) with limited English proficiency and a wide range of reading and math abilities, brain network properties related to academic abilities. We applied a method for localizing brain regions of interest (ROIs) that are group-constrained, yet individually specific, to test how resting state functional connectivity between regions that are important for academic learning (reading, math, and cognitive control regions) are related to academic abilities. ROIs were selected from task localizers probing reading and math skills in the same participants. We found that connectivity across all ROIs, as well as connectivity of just the cognitive control ROIs, were positively related to measures of reading skills but not math skills. This work suggests that cognitive control brain systems have a central role for reading in ELs. Our results also indicate that an individualized approach for localizing brain function may clarify brain-behavior relationships.

tDCS effects in basic symbolic number magnitude processing are not significantly lateralized

Functional lateralization was previously established for various cognitive domains-but not for number processing. Although numbers are considered to be bilaterally represented in the intraparietal sulcus (IPS), there are some indications of different functional roles of the left vs. right IPS in processing number pairs with small vs. large distance, respectively. This raises the question whether number size plays a distinct role in the lateralization within the IPS. In our preregistered study, we applied anodal transcranial direct current stimulation (tDCS) over the left vs. right IPS to investigate the effect of stimulation as compared to sham on small vs. large distance, in both single-digit and two-digit number comparison. We expected that anodal tDCS over the left IPS facilitates number comparison with small distance, while anodal tDCS over the right IPS facilitates number comparison with large distance. Results indicated no effect of stimulation; however, exploratory analyses revealed that tDCS over the right IPS slowed down single-digit number processing after controlling for the training effect. In conclusion, number magnitude processing might be bilaterally represented in the IPS, however, our exploratory analyses emphasise the need for further investigation on functional lateralization of number processing.

Competing numerical magnitude codes in decimal comparison: Whole number and rational number distance both impact performance

A critical difference between decimal and whole numbers is that among whole numbers the number of digits provides reliable information about the size of the number, e.g., double-digit numbers are larger than single-digit numbers. However, for decimals, fewer digits can sometimes denote a larger number (i.e., 0.8 > 0.27). Accordingly, children and adults perform worse when comparing such Inconsistent decimal pairs relative to Consistent pairs, where the larger number also has more digits (i.e., 0.87 > 0.2). Two explanations have been posited for this effect. The string length congruity account proposes that participants compare each position in the place value system, and they additionally compare the number of digits. The semantic interference account suggests that participants additionally activate the whole number referents of numbers - the numbers unadorned with decimal points (e.g., 8 < 27) - and compare these. The semantic interference account uniquely predicts that for Inconsistent problems with the same actual rational distance, those with larger whole number distances should be harder, e.g., 0.9 vs. 0.81 should be harder than 0.3 vs. 0.21 because 9 < < 81 whereas 3 < 21. Here we test this prediction in two experiments with college students (Study 1: n = 58 participants, Study 2: n = 78). Across both, we find a main effect of consistency, demonstrating string length effects, and also that whole number distance interferes with processing conflicting decimals, demonstrating semantic interference effects. Evidence for both effects supports the semantic interference account, highlighting that decimal comparison difficulties arise from multiple competing numerical codes. Finally, for accuracy we found no relationship between whole number distance sensitivity and math achievement, indicating that whole number magnitude interference affects participants similarly across the spectrum of math achievement.

The Interaction between Congruency and Numerical Ratio Effects in the Nonsymbolic Comparison Test

The nonsymbolic comparison task is used to investigate the precision of the Approximate Number Sense, the ability to process discrete numerosity without counting and symbols. There is an ongoing debate regarding the extent to which the ANS is influenced by the processing of non-numerical visual cues. To address this question, we assessed the congruency effect in a nonsymbolic comparison task, examining its variability across different stimulus presentation formats and numerical proportions. Additionally, we examined the variability of the numerical ratio effect with the format and congruency. Utilizing generalized linear mixed-effects models with a sample of 290 students (89% female, mean age 19.33 years), we estimated the congruency effect and numerical ratio effect for separated and intermixed formats of stimulus presentation, and for small and large numerical proportions. The findings indicated that the congruency effect increased in large numerical proportion conditions, but this pattern was observed only in the separated format. In the intermixed format, the congruency effect was insignificant for both types of numerical proportion. Notably, the numerical ratio effect varied for congruent and incongruent trials in different formats. The results may suggest that the processing of visual non-numerical parameters may be crucial when numerosity processing becomes noisier, specifically when numerical proportion becomes larger. The implications of these findings for refining the ANS theory are discussed.

Effects of prefrontal and parietal neuromodulation on magnitude processing and integration

Numerical cognition is an essential skill for survival, which includes the processing of discrete and continuous quantities, involving a mainly right fronto-parietal network. However, the neurocognitive systems underlying the processing and integration of discrete and continuous quantities are currently under debate. Noninvasive brain stimulation techniques have been used in the study of the neural basis of numerical cognition with a spatial, temporal and functional resolution superior to other neuroimaging techniques. The present randomized sham-controlled single-blinded trial addresses the involvement of the right dorsolateral prefrontal cortex and the right intraparietal sulcus in magnitude processing and integration. Multifocal anodal transcranial direct current stimulation was applied online during the execution of magnitude comparison tasks in three conditions: right prefrontal, right parietal and sham stimulation. The results show that prefrontal stimulation produced a moderated decrease in response times in all magnitude processing and integration tasks compared to sham condition. While parietal stimulation had no significant effect on any of the tasks. The effect found is interpreted as a generalized improvement in processing speed and magnitude integration due to right prefrontal neuromodulation, which may be attributable to domain-general or domain-specific factors.

The Brain's Control Networks in Reading: Insights From Cross-Task Studies of Youth

Humans engage multiple brain systems to read successfully, including using regions important for vision, language, and control. Control refers to the set of executive processes in the brain that guide moment-to-moment behavior in service of our goals. There is a growing appreciation for the role of the brain's control system in reading comprehension, in reading skill change over time, and in those who have difficulty with the reading process. One way to understand the brain's control engagement in reading may be to study control engagement across multiple tasks in order to study consistencies, or cross-task similarities, relative to reading-specific variations. In this commentary, I briefly summarize some of our recent work studying the brain's control networks across different tasks (e.g., when reading, or doing different executive function tasks). I then review our findings of when control activation does or does not relate to measures of reading ability, and reading growth over time. The utility of cross-task comparisons in neuroimaging is noted, as well as the need to better understand multiple sources of heterogeneity in our developmental samples. I end by discussing a few of the many future directions for further study of the brain with regard to the brain's control processing and academic achievement.

Questions About Quantifiers: Symbolic and Nonsymbolic Quantity Processing by the Brain

One approach to understanding how the human cognitive system stores and operates with quantifiers such as "some," "many," and "all" is to investigate their interaction with the cognitive mechanisms for estimating and comparing quantities from perceptual input (i.e., nonsymbolic quantities). While a potential link between quantifier processing and nonsymbolic quantity processing has been considered in the past, it has never been discussed extensively. Simultaneously, there is a long line of research within the field of numerical cognition on the relationship between processing exact number symbols (such as "3" or "three") and nonsymbolic quantity. This accumulated knowledge can potentially be harvested for research on quantifiers since quantifiers and number symbols are two different ways of referring to quantity information symbolically. The goal of the present review is to survey the research on the relationship between quantifiers and nonsymbolic quantity processing mechanisms and provide a set of research directions and specific questions for the investigation of quantifier processing.

Engaging learners with games-Insights from functional near-infrared spectroscopy

The use of game elements in learning tasks is thought to facilitate emotional and behavioral responses as well as learner engagement. So far, however, little is known about the underlying neural mechanisms of game-based learning. In the current study, we added game elements to a number line estimation task assessing fraction understanding and compared brain activation patterns to a non-game-based task version. Forty-one participants performed both task versions in counterbalanced order while frontal brain activation patterns were assessed using near-infrared spectroscopy (within-subject, cross-sectional study design). Additionally, heart rate, subjective user experience, and task performance were recorded. Task performance, mood, flow experience, as well as heart rate did not differ between task versions. However, the game-based task-version was rated as more attractive, stimulating and novel compared to the non-game-based task version. Additionally, completing the game-based task version was associated with stronger activation in frontal brain areas generally involved in emotional and reward processing as well as attentional processes. These results provide new neurofunctional evidence substantiating that game elements in learning tasks seem to facilitate learning through emotional and cognitive engagement.

Functional reconfiguration of task-active frontoparietal control network facilitates abstract reasoning

While the brain's functional network architecture is largely conserved between resting and task states, small but significant changes in functional connectivity support complex cognition. In this study, we used a modified Raven's Progressive Matrices Task to examine symbolic and perceptual reasoning in human participants undergoing fMRI scanning. Previously, studies have focused predominantly on discrete symbolic versions of matrix reasoning, even though the first few trials of the Raven's Advanced Progressive Matrices task consist of continuous perceptual stimuli. Our analysis examined the activation patterns and functional reconfiguration of brain networks associated with resting state and both symbolic and perceptual reasoning. We found that frontoparietal networks, including the cognitive control and dorsal attention networks, were significantly activated during abstract reasoning. We determined that these same task-active regions exhibited flexibly-reconfigured functional connectivity when transitioning from resting state to the abstract reasoning task. Conversely, we showed that a stable network core of regions in default and somatomotor networks was maintained across both resting and task states. We propose that these regionally-specific changes in the functional connectivity of frontoparietal networks puts the brain in a "task-ready" state, facilitating efficient task-based activation.

Overlapping but separate number representations in the intraparietal sulcus-Probing format- and modality-independence in sighted Braille readers

The Triple-Code Model stipulates that numerical information from different formats and modalities converges on a common magnitude representation in the Intraparietal Sulcus (IPS). To what extent the representations of all numerosity forms overlap remains unsolved. It has been postulated that the representation of symbolic numerosities (for example, Arabic digits) is sparser and grounded in an existing representation that codes for non-symbolic numerosity information (i.e., sets of objects). Other theories argue that numerical symbols represent a separate number category that emerges only during education. Here, we tested a unique group of sighted tactile Braille readers with numerosities 2, 4, 6 and 8 in three number notations: Arabic digits, sets of dots, tactile Braille numbers. Using univariate methods, we showed a consistent overlap in activations evoked by these three number notations. This result shows that all three used notations are represented in the IPS, which may suggest at least a partial overlap between the representations of the three notations used in this experiment. Using MVPA, we found that only non-automatized number information (Braille and sets of dots) allowed successful number classification. However, the numerosity of one notation could not be predicted above chance from the brain activation patterns evoked by another notation (no cross-classification). These results show that the IPS may host independent number codes in overlapping cortical circuits. In addition, they suggest that the level of training in encoding a given type of number information is an important factor that determines the amount of exploitable information and needs to be controlled for in order to identify the neural code underlying numerical information per se.

Brain Engagement During a Cognitive Flexibility Task Relates to Academic Performance in English Learners

English Learners (ELs), students from non-English-speaking backgrounds, are a fast-growing, understudied, group of students in the U.S. with unique learning challenges. Cognitive flexibility-the ability to switch between task demands with ease-may be an important factor in learning for ELs as they have to manage learning in their non-dominant language and access knowledge in multiple languages. We used functional MRI to measure cognitive flexibility brain activity in a group of Hispanic middle school ELs (N = 63) and related it to their academic skills. We found that brain engagement during the cognitive flexibility task was related to both out-of-scanner reading and math measures. These relationships were observed across the brain, including in cognitive control, attention, and default mode networks. This work suggests the real-world importance of cognitive flexibility for adolescent ELs, where individual differences in brain engagement were associated with educational outcomes.

Dysfunctions associated with the intraparietal sulcus and a distributed network in individuals with math learning difficulties: An ALE meta-analysis

Math learning difficulty (MLD) is a learning disorder characterized by persistent impairments in the understanding and application of numbers independent of intelligence or schooling. The current study aims to review existing neuroimaging studies to characterize the neurobiological basis in MLD for their quantity and arithmetic dysfunctions. We identified a total of 24 studies with 728 participants through the literature. Using the activation likelihood estimate (ALE) method, we found that the most consistent neurobiological dysfunction in MLD was observed in the right intraparietal sulcus (IPS) with distinct patterns of the anterior and posterior aspects. Meanwhile, neurobiological dysfunctions were also observed in a distributed network including the fusiform gyrus, inferior temporal gyrus, insula, prefrontal cortex, anterior cingulate cortex, and claustrum. Our results suggest a core dysfunction in the right anterior IPS and left fusiform gyrus with atypically upregulated functions in brain regions for attention, working memory, visual processing, and motivation, serving as the neurobiological basis of MLD.

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.

Arithmetic in the signing brain: Differences and similarities in arithmetic processing between deaf signers and hearing non-signers

Deaf signers and hearing non-signers have previously been shown to recruit partially different brain regions during simple arithmetic. In light of the triple code model, the differences were interpreted as relating to stronger recruitment of the verbal system of numerical processing, that is, left angular and inferior frontal gyrus, in hearing non-signers, and of the quantity system of numerical processing, that is, right horizontal intraparietal sulcus, for deaf signers. The main aim of the present study was to better understand similarities and differences in the neural correlates supporting arithmetic in deaf compared to hearing individuals. Twenty-nine adult deaf signers and 29 hearing non-signers were enrolled in an functional magnetic resonance imaging study of simple and difficult subtraction and multiplication. Brain imaging data were analyzed using whole-brain analysis, region of interest analysis, and functional connectivity analysis. Although the groups were matched on age, gender, and nonverbal intelligence, the deaf group performed generally poorer than the hearing group in arithmetic. Nevertheless, we found generally similar networks to be involved for both groups, the only exception being the involvement of the left inferior frontal gyrus. This region was activated significantly stronger for the hearing compared to the deaf group but showed stronger functional connectivity with the left superior temporal gyrus in the deaf, compared to the hearing, group. These results lend no support to increased recruitment of the quantity system in deaf signers. Perhaps the reason for performance differences is to be found in other brain regions not included in the original triple code model.

Estimation Strategy Utilization Is Modulated by Implicit Emotion Regulation: Evidence from Behavioral and Event-Related Potentials Studies

A large number of studies have studied the influence of emotional experience on an individual's estimation performance, but the influence of implicit emotion regulation is still unknown. Participants were asked to complete the following tasks in order: idiom matching task, multiplication computational estimation task (MCE task), gender judgment task (GJ task), and emotional experience intensity assessment task. The words matching task was adopted to achieve the purpose of implicit emotion regulation (implicit reappraisal and implicit suppression). Behavioral results showed that implicit reappraisal and implicit suppression equally contributed to improving an individual's estimation speed (but not ACC (accuracy)). The MCE task related ERP (event-related potential) results showed that the influence of implicit emotion regulation on estimation consisted of two phases. In the first phase (encoding phase), implicit reappraisal both enhanced (larger P1 amplitudes) and weakened (smaller N170 amplitudes) an individual's encoding sensitivity, while implicit suppression enhanced an individual's encoding sensitivity (larger P1 amplitudes). In the second phase (estimation strategies retrieval phase), implicit reappraisal (but not implicit suppression) cost more attention resources (larger LPC2 and LPC3 amplitudes). The present study suggested that both implicit reappraisal and implicit suppression contributed to improving an individual's estimation performance, and the regulation effect of implicit suppression (vs. implicit reappraisal) was better.

Common neural substrates of diverse neurodevelopmental disorders

Neurodevelopmental disorders are categorized and studied according to their manifestations as distinct syndromes. For instance, congenital prosopagnosia and dyslexia have largely non-overlapping research literatures and clinical pathways for diagnosis and intervention. On the other hand, the high incidence of neurodevelopmental comorbidities or co-existing extreme strengths and weaknesses suggest that transdiagnostic commonalities may be greater than currently appreciated. The core-periphery model holds that brain regions within the stable core perceptual and motor regions are more densely connected to one another compared to regions in the flexible periphery comprising multimodal association regions. This model provides a framework for the interpretation of neural data in normal development and clinical disorders. Considering network-level commonalities reported in studies of neurodevelopmental disorders, variability in multimodal association cortex connectivity may reflect a shared origin of seemingly distinct neurodevelopmental disorders. This framework helps to explain both comorbidities in neurodevelopmental disorders and profiles of strengths and weaknesses attributable to competitive processing between cognitive systems within an individual.

The neural correlates of retrieval and procedural strategies in mental arithmetic: A functional neuroimaging meta-analysis

Mental arithmetic is a complex skill of great importance for later academic and life success. Many neuroimaging studies and several meta-analyses have aimed to identify the neural correlates of mental arithmetic. Previous meta-analyses of arithmetic grouped all problem types into a single meta-analytic map, despite evidence suggesting that different types of arithmetic problems are solved using different strategies. We used activation likelihood estimation (ALE) to conduct quantitative meta-analyses of mental arithmetic neuroimaging (n = 31) studies, and subsequently grouped contrasts from the 31 studies into problems that are typically solved using retrieval strategies (retrieval problems) (n = 18) and problems that are typically solved using procedural strategies (procedural problems) (n = 19). Foci were compiled to generate probabilistic maps of activation for mental arithmetic (i.e., all problem types), retrieval problems, and procedural problems. Conjunction and contrast analyses were conducted to examine overlapping and distinct activation for retrieval and procedural problems. The conjunction analysis revealed overlapping activation for retrieval and procedural problems in the bilateral inferior parietal lobules, regions typically associated with magnitude processing. Contrast analyses revealed specific activation in the left angular gyrus for retrieval problems and specific activation in the inferior frontal gyrus and cingulate gyrus for procedural problems. These findings indicate that the neural bases of arithmetic systematically differs according to problem type, providing new insights into the dynamic and task-dependent neural underpinnings of the calculating brain.

Visual Occipito-Temporal N1 Sensitivity to Digits Across Elementary School

Number processing abilities are important for academic and personal development. The course of initial specialization of ventral occipito-temporal cortex (vOTC) sensitivity to visual number processing is crucial for the acquisition of numeric and arithmetic skills. We examined the visual N1, the electrophysiological correlate of vOTC activation across five time points in kindergarten (T1, mean age 6.60 years), middle and end of first grade (T2, 7.38 years; T3, 7.68 years), second grade (T4, 8.28 years), and fifth grade (T5, 11.40 years). A combination of cross-sectional and longitudinal EEG data of a total of 62 children (35 female) at varying familial risk for dyslexia were available to form groups of 23, 22, 27, 27, and 42 participants for each of the five time points. The children performed a target detection task which included visual presentation of single digits (DIG), false fonts (FF), and letters (LET) to derive measures for coarse (DIG vs. FF) and fine (DIG vs. LET) digit sensitive processing across development. The N1 amplitude analyses indicated coarse and fine sensitivity characterized by a stronger N1 to digits than false fonts across all five time points, and stronger N1 to digits than letters at all but the second (T2) time point. In addition, lower arithmetic skills were associated with stronger coarse N1 digit sensitivity over the left hemisphere in second grade (T4), possibly reflecting allocation of more attentional resources or stronger reliance on the verbal system in children with poorer arithmetic skills. To summarize, our results show persistent visual N1 sensitivity to digits that is already present early on in pre-school and remains stable until fifth grade. This pattern of digit sensitivity development clearly differs from the relatively sharp rise and fall of the visual N1 sensitivity to words or letters between kindergarten and middle of elementary school and suggests unique developmental trajectories for visual processing of written characters that are relevant to numeracy and literacy.

The effect of parietal glutamate/GABA balance on test anxiety levels in early childhood in a cross-sectional and longitudinal study

The increased prevalence of test anxiety in our competitive society makes it a health issue of public concern. However, its neurobiological basis, especially during the years of formal education, is currently scant. Previous research has highlighted the association between neural excitation/inhibition balance and psychopathology and disease. We examined whether the glutamate/GABA profile tracks test anxiety levels in development, using a cross-sectional and longitudinal design in a cohort spanning from early childhood to early adulthood (N = 289), reassessed approximately 21 months later (N = 194). We used magnetic resonance spectroscopy to noninvasively quantify glutamate and gamma-Aminobutyric acid (GABA) levels in the intraparietal sulcus (IPS) and the middle frontal gyrus. We show that the glutamate/GABA balance within the IPS relates to current individual variation in test anxiety levels and predict future test anxiety approximately 21 months later. Critically, this relationship was observed during early childhood but not during the later developmental stages. Our results extend the use of the excitation/inhibition balance framework to characterize the psychopathology mechanisms of test anxiety, an underexplored yet widespread and debilitating condition that can impact early child development. Our findings provide a better understanding of the neurotransmitter basis underlying the emergence of anxiety disorders during development.

Investigating the association between variability in sulcal pattern and academic achievement

Investigating how the brain may constrain academic achievement is not only relevant to understanding brain structure but also to providing insight into the origins of individual differences in these academic abilities. In this pre-registered study, we investigated whether the variability of sulcal patterns, a qualitative feature of the brain determined in-utero and not affected by brain maturation and learning, accounted for individual differences in reading and mathematics. Participants were 97 typically developing 10-year-olds. We examined (a) the association between the sulcal pattern of the IntraParietal Sulcus (IPS) and mathematical ability; (b) the association between the sulcal pattern of the Occipito Temporal Sulcus (OTS) and reading ability; and (c) the overlap and specificity of sulcal morphology of IPS and OTS and their associations with mathematics and reading. Despite its large sample, the present study was unable to replicate a previously observed relationship between the IPS sulcal pattern and mathematical ability and a previously observed association between the left posterior OTS sulcal pattern and reading. We found a weak association between right IPS sulcal morphology and symbolic number abilities and a weak association between left posterior OTS and reading. However, both these associations were the opposite of previous reports. We found no evidence for a possible overlap or specificity in the effect of sulcal morphology on mathematics and reading. Possible explanations for this weak association between sulcal morphology and academic achievement and suggestions for future research are discussed.

Number symbols are processed more automatically than nonsymbolic numerical magnitudes: Findings from a Symbolic-Nonsymbolic Stroop task

Are number symbols (e.g., 3) and numerically equivalent quantities (e.g., •••) processed similarly or distinctly? If symbols and quantities are processed similarly then processing one format should activate the processing of the other. To experimentally probe this prediction, we assessed the processing of symbols and quantities using a Stroop-like paradigm. Participants (N_Study1 = 80, N_Study2 = 63) compared adjacent arrays of symbols (e.g., 4444 vs 333) and were instructed to indicate the side containing either the greater quantity of symbols (nonsymbolic task) or the numerically larger symbol (symbolic task). The tasks included congruent trials, where the greater symbol and quantity appeared on the same side (e.g. 333 vs. 4444), incongruent trials, where the greater symbol and quantity appeared on opposite sides (e.g. 3333 vs. 444), and neutral trials, where the irrelevant dimension was the same across both sides (e.g. 3333 vs. 333 for nonsymbolic; 333 vs. 444 for symbolic). The numerical distance between stimuli was systematically varied, and quantities in the subitizing and counting range were analyzed together and independently. Participants were more efficient comparing symbols and ignoring quantities, than comparing quantities and ignoring symbols. Similarly, while both symbols and quantities influenced each other as the irrelevant dimension, symbols influenced the processing of quantities more than quantities influenced the processing of symbols, especially for quantities in the counting rage. Additionally, symbols were less influenced by numerical distance than quantities, when acting as the relevant and irrelevant dimension. These findings suggest that symbols are processed differently and more automatically than quantities.

Magnitude comparison and automaticity in number processing in adolescents with prenatal alcohol exposure: An event-related potentials study

BACKGROUND

Individuals with fetal alcohol spectrum disorders may exhibit a distinct pattern of dysmorphic facial features, growth restriction, and cognitive deficits, particularly in arithmetic. Magnitude comparison, a fundamental element of numerical cognition, is modulated by the numerical distance effect, with numbers closer in value more difficult to compare than those further apart, and by the automaticity of the association of numerical values with their symbolic representations (Arabic numerals).

METHODS

We examined event-related potentials acquired during the Numerical Stroop numerical and physical tasks administered to 24 alcohol-exposed adolescents (eight fetal alcohol syndrome (FAS), eight partial FAS (PFAS), eight heavily exposed (HE) nonsyndromal) and 23 typically developing (TD), same- age controls. The distance effect was assessed on the numerical task to examine differences in reaction time (RT) and accuracy when two numbers are close in value (e.g., 1 vs. 2) compared to when the numbers are less close (e.g., 1 vs. 6). Automaticity was assessed in the physical task by examining the degree to which RT and accuracy are reduced when the relative physical size of two numerals is incongruent with their numerical values (e.g., 1 vs. 6).

RESULTS

Adolescents in all four groups performed behaviorally as expected on these relatively simple magnitude comparison tasks, but accuracy was poorer and RT was slower on both tasks in the FAS and PFAS than the HE and TD groups. At the neurophysiological level, in the numerical task, a higher level of prenatal alcohol exposure was associated with smaller P2p amplitude. In the physical task, only the TD and nonsyndromal HE groups exhibited the expected smaller P300 amplitude in the incongruent than the congruent condition.

CONCLUSIONS

These findings suggest that magnitude comparison in alcohol-exposed individuals may be mediated by recruitment of alternative neural pathways that are likely to be inefficient when number processing becomes more challenging.

Foundational Number Sense Training Gains Are Predicted by Hippocampal-Parietal Circuits

The development of mathematical skills in early childhood relies on number sense, the foundational ability to discriminate among quantities. Number sense in early childhood is predictive of academic and professional success, and deficits in number sense are thought to underlie lifelong impairments in mathematical abilities. Despite its importance, the brain circuit mechanisms that support number sense learning remain poorly understood. Here, we designed a theoretically motivated training program to determine brain circuit mechanisms underlying foundational number sense learning in female and male elementary school-age children (7-10 years). Our 4 week integrative number sense training program gradually strengthened the understanding of the relations between symbolic (Arabic numerals) and nonsymbolic (sets of items) representations of quantity. We found that our number sense training program improved symbolic quantity discrimination ability in children across a wide range of math abilities including children with learning difficulties. Crucially, the strength of pretraining functional connectivity between the hippocampus and intraparietal sulcus, brain regions implicated in associative learning and quantity discrimination, respectively, predicted individual differences in number sense learning across typically developing children and children with learning difficulties. Reverse meta-analysis of interregional coactivations across 14,371 fMRI studies and 89 cognitive functions confirmed a reliable role for hippocampal-intraparietal sulcus circuits in learning. Our study identifies a canonical hippocampal-parietal circuit for learning that plays a foundational role in children's cognitive skill acquisition. Findings provide important insights into neurobiological circuit markers of individual differences in children's learning and delineate a robust target for effective cognitive interventions.SIGNIFICANCE STATEMENT Mathematical skill development relies on number sense, the ability to discriminate among quantities. Here, we develop a theoretically motivated training program and investigate brain circuits that predict number sense learning in children during a period important for acquisition of foundational cognitive skills. Our integrated number sense training program was effective in children across a wide a range of math abilities, including children with learning difficulties. We identify hippocampal-parietal circuits that predict individual differences in learning gains. Our study identifies a brain circuit critical for the acquisition of foundational cognitive skills, which will be useful for developing effective interventions to remediate learning disabilities.

The impact of musical training in symbolic and non-symbolic audiovisual judgements of magnitude

Quantity estimation can be represented in either an analog or symbolic manner and recent evidence now suggests that analog and symbolic representation of quantities interact. Nonetheless, those two representational forms of quantities may be enhanced by convergent multisensory information. Here, we elucidate those interactions using high-density electroencephalography (EEG) and an audiovisual oddball paradigm. Participants were presented simultaneous audiovisual tokens in which the co-varying pitch of tones was combined with the embedded cardinality of dot patterns. Incongruencies were elicited independently from symbolic and non-symbolic modality within the audio-visual percept, violating the newly acquired rule that “the higher the pitch of the tone, the larger the cardinality of the figure.” The effect of neural plasticity in symbolic and non-symbolic numerical representations of quantities was investigated through a cross-sectional design, comparing musicians to musically naïve controls. Individual’s cortical activity was reconstructed and statistically modeled for a predefined time-window of the evoked response (130–170 ms). To summarize, we show that symbolic and non-symbolic processing of magnitudes is re-organized in cortical space, with professional musicians showing altered activity in motor and temporal areas. Thus, we argue that the symbolic representation of quantities is altered through musical training.

The longitudinal development of large-scale functional brain networks for arithmetic ability from childhood to adolescence

Arithmetic ability is an important high-level cognitive function that requires interaction among multiple brain regions. Previous studies on arithmetic development have focused on task-induced activation in isolated brain regions or functional connectivity among particular seed regions. However, it remains largely unknown whether and how functional connectivity among large-scale brain modules contributes to arithmetic development. In the present study, we used a longitudinal sample of task-based functional magnetic resonance imaging (fMRI) data comprising 63 typically developing children, with two testing points being about two years apart. With graph theory, we examined the longitudinal development of large-scale brain modules for a multiplication task in younger (mean age 9.88 at time 1) and older children (mean age 12.34 at time 1), respectively. The results showed that the default-mode (DMN) and frontal-parietal networks (FPN) became increasingly segregated over time. Specifically, intra-connectivity within the DMN and FPN increased significantly with age, and inter-connectivity between the DMN and visual network decreased significantly with age. Such developmental changes were mainly observed in the younger children, but not in the older children. Moreover, the change in network segregation of the DMN was positively correlated with longitudinal gain in arithmetic performance in the younger children, and individual difference in network segregation of the FPN was positively correlated with arithmetic performance at time 2 in the older children. Taken together, the present results highlight the development of the functional architecture in large-scale brain networks from childhood to adolescence, which may provide insights into potential neural mechanisms underlying arithmetic development.

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.

Brain network dysfunctions in addiction: a meta-analysis of resting-state functional connectivity

Resting-state functional connectivity (rsFC) provides novel insights into variabilities in neural networks associated with the use of addictive drugs or with addictive behavioral repertoire. However, given the broad mix of inconsistent findings across studies, identifying specific consistent patterns of network abnormalities is warranted. Here we aimed at integrating rsFC abnormalities and systematically searching for large-scale functional brain networks in substance use disorder (SUD) and behavioral addictions (BA), through a coordinate-based meta-analysis of seed-based rsFC studies. A total of fifty-two studies are eligible in the meta-analysis, including 1911 SUD and BA patients and 1580 healthy controls. In addition, we performed multilevel kernel density analysis (MKDA) for the brain regions reliably involved in hyperconnectivity and hypoconnectivity in SUD and BA. Data from fifty-two studies showed that SUD was associated with putamen, caudate and middle frontal gyrus hyperconnectivity relative to healthy controls. Eight BA studies showed hyperconnectivity clusters within the putamen and medio-temporal lobe relative to healthy controls. Altered connectivity in salience or emotion-processing areas may be related to dysregulated affective and cognitive control-related networks, such as deficits in regulating elevated sensitivity to drug-related stimuli. These findings confirm that SUD and BA might be characterized by dysfunctions in specific brain networks, particularly those implicated in the core cognitive and affective functions. These findings might provide insight into the development of neural mechanistic biomarkers for SUD and BA.