Prospective relations between resting-state connectivity of parietal subdivisions and arithmetic competence

Alterations in functional brain connectivity associated with developmental dyscalculia

BACKGROUND AND PURPOSE

In recent years, there has been a growing interest in the study of resting neural networks in different neurological and mental disorders. While previous studies suggest that the default mode network (DMN) may be altered in dyscalculia, the study of resting-state networks in the development of numerical skills, especially in children with developmental dyscalculia (DD), is scarce and relatively recent. Based on this, this study examines differences in resting-state functional connectivity (rs-FC) data of children with DD using functional connectivity multivariate pattern analysis (fc-MVPA), a data-driven methodology that summarizes properties of the entire connectome.

METHODS

We performed fc-MVPA on resting-state images of a sample composed of a group of children with DD (n = 19, 8.06 ± 0.87 years) and an age- and sex-matched control group of typically developing children (n = 23, 7.76 ± 0.46 years).

RESULTS

Analysis of fc-MVPA showed significant differences between group connectivity profiles in two clusters allocated in both the right and left medial temporal gyrus. Post hoc effect size results revealed a decreased rs-FC between each temporal pole and the DMN in children with DD and an increased rs-FC between each temporal pole and the sensorimotor network.

CONCLUSIONS

Our results suggest an aberrant information flow between resting-state networks in children with DD, demonstrating the importance of these networks for arithmetic development.

Brain markers of subtraction and multiplication skills in childhood: task-based functional connectivity and individualized structural similarity

Arithmetic, a high-order cognitive ability, show marked individual difference over development. Despite recent advancements in neuroimaging techniques have enabled the identification of brain markers for individual differences in high-order cognitive abilities, it remains largely unknown about the brain markers for arithmetic. This study used a data-driven connectome-based prediction model to identify brain markers of arithmetic skills from arithmetic-state functional connectivity and individualized structural similarity in 132 children aged 8 to 15 years. We found that both subtraction-state functional connectivity and individualized SS successfully predicted subtraction and multiplication skills but multiplication-state functional connectivity failed to predict either skill. Among the four successful prediction models, most predictive connections were located in frontal-parietal, default-mode, and secondary visual networks. Further computational lesion analyses revealed the essential structural role of frontal-parietal network in predicting subtraction and the essential functional roles of secondary visual, language, and ventral multimodal networks in predicting multiplication. Finally, a few shared nodes but largely nonoverlapping functional and structural connections were found to predict subtraction and multiplication skills. Altogether, our findings provide new insights into the brain markers of arithmetic skills in children and highlight the importance of studying different connectivity modalities and different arithmetic domains to advance our understanding of children's arithmetic skills.

Single-trial interindividual correlation shows semantic and visuospatial networks are fundamental for advanced mathematical learning

Mathematical learning and ability are crucial for individual and national economic and technological development, but the neural mechanisms underlying advanced mathematical learning remain unclear. The current study used functional magnetic resonance imaging (fMRI) to investigate how brain networks were involved in advanced mathematical learning and transfer. We recorded fMRI data from 24 undergraduate students as they learned the advanced mathematical concept of a commutative mathematical group. After learning, participants were required to complete learning and transfer behavioural tests. Results of single-trial interindividual brain-behaviour correlation analysis found that brain activity in the semantic and visuospatial networks, and the functional connectivity within the semantic network during advanced mathematical learning were positively correlated with learning and transfer effects. Additionally, the functional connectivity between the semantic and visuospatial networks was negatively correlated with the learning and transfer effects. These findings suggest that advanced mathematical learning relies on both semantic and visuospatial networks.

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.

Long-term abacus training gains in children are predicted by medial temporal lobe anatomy and circuitry

Abacus-based mental calculation (AMC) is a widely used educational tool for enhancing math learning, offering an accessible and cost-effective method for classroom implementation. Despite its universal appeal, the neurocognitive mechanisms that drive the efficacy of AMC training remain poorly understood. Notably, although abacus training relies heavily on the rapid recall of number positions and sequences, the role of memory systems in driving long-term AMC learning remains unknown. Here, we sought to address this gap by investigating the role of the medial temporal lobe (MTL) memory system in predicting long-term AMC training gains in second-grade children, who were longitudinally assessed up to fifth grade. Leveraging multimodal neuroimaging data, we tested the hypothesis that MTL systems, known for their involvement in associative memory, are instrumental in facilitating AMC-induced improvements in math skills. We found that gray matter volume in bilateral MTL, along with functional connectivity between the MTL and frontal and ventral temporal-occipital cortices, significantly predicted learning gains. Intriguingly, greater gray matter volume but weaker connectivity of the posterior parietal cortex predicted better learning outcomes, offering a more nuanced view of brain systems at play in AMC training. Our findings not only underscore the critical role of the MTL memory system in AMC training but also illuminate the neurobiological factors contributing to individual differences in cognitive skill acquisition. A video abstract of this article can be viewed at https://youtu.be/StVooNRc7T8. RESEARCH HIGHLIGHTS: We investigated the role of medial temporal lobe (MTL) memory system in driving children's math learning following abacus-based mental calculation (AMC) training. AMC training improved math skills in elementary school children across their second and fifth grade. MTL structural integrity and functional connectivity with prefrontal and ventral temporal-occipital cortices predicted long-term AMC training-related gains.

Neurocognitive mechanisms of co-occurring math difficulties in dyslexia: Differences in executive function and visuospatial processing

Children with dyslexia frequently also struggle with math. However, studies of reading disability (RD) rarely assess math skill, and the neurocognitive mechanisms underlying co-occurring reading and math disability (RD+MD) are not clear. The current study aimed to identify behavioral and neurocognitive factors associated with co-occurring MD among 86 children with RD. Within this sample, 43% had co-occurring RD+MD and 22% demonstrated a possible vulnerability in math, while 35% had no math difficulties (RD-Only). We investigated whether RD-Only and RD+MD students differed behaviorally in their phonological awareness, reading skills, or executive functions, as well as in the brain mechanisms underlying word reading and visuospatial working memory using functional magnetic resonance imaging (fMRI). The RD+MD group did not differ from RD-Only on behavioral or brain measures of phonological awareness related to speech or print. However, the RD+MD group demonstrated significantly worse working memory and processing speed performance than the RD-Only group. The RD+MD group also exhibited reduced brain activations for visuospatial working memory relative to RD-Only. Exploratory brain-behavior correlations along a broad spectrum of math ability revealed that stronger math skills were associated with greater activation in bilateral visual cortex. These converging neuro-behavioral findings suggest that poor executive functions in general, including differences in visuospatial working memory, are specifically associated with co-occurring MD in the context of RD. RESEARCH HIGHLIGHTS: Children with reading disabilities (RD) frequently have a co-occurring math disability (MD), but the mechanisms behind this high comorbidity are not well understood. We examined differences in phonological awareness, reading skills, and executive function between children with RD only versus co-occurring RD+MD using behavioral and fMRI measures. Children with RD only versus RD+MD did not differ in their phonological processing, either behaviorally or in the brain. RD+MD was associated with additional behavioral difficulties in working memory, and reduced visual cortex activation during a visuospatial working memory task.

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.

Early Gray Matter Structural Covariance Predicts Longitudinal Gain in Arithmetic Ability in Children

Previous neuroimaging studies on arithmetic development have mainly focused on functional activation or functional connectivity between brain regions. It remains largely unknown how brain structures support arithmetic development. The present study investigated whether early gray matter structural covariance contributes to later gain in arithmetic ability in children. We used a public longitudinal sample comprising 63 typically developing children. The participants received structural magnetic resonance imaging scanning when they were 11 years old and were tested with a multiplication task at 11 years old (time 1) and 13 years old (time 2), respectively. Mean gray matter volumes were extracted from eight brain regions of interest to anchor salience network (SN), frontal-parietal network (FPN), motor network (MN), and default mode network (DMN) at time 1. We found that longitudinal gain in arithmetic ability was associated with stronger structural covariance of the SN seed with frontal and parietal regions and stronger structural covariance of the FPN seed with insula, but weaker structural covariance of the FPN seed with motor and temporal regions, weaker structural covariance of the MN seed with frontal and motor regions, and weaker structural covariance of the DMN seed with temporal region. However, we did not detect correlation between longitudinal gain in arithmetic ability and behavioral measure or regional gray matter volume at time 1. Our study provides novel evidence for a specific contribution of gray matter structural covariance to longitudinal gain in arithmetic ability in childhood.

Systems-level decoding reveals the cognitive and behavioral profile of the human intraparietal sulcus

INTRODUCTION

The human intraparietal sulcus (IPS) covers large portions of the posterior cortical surface and has been implicated in a variety of cognitive functions. It is, however, unclear how cognitive functions dissociate between the IPS's heterogeneous subdivisions, particularly in perspective to their connectivity profile.

METHODS

We applied a neuroinformatics driven system-level decoding on three cytoarchitectural distinct subdivisions (hIP1, hIP2, hIP3) per hemisphere, with the aim to disentangle the cognitive profile of the IPS in conjunction with functionally connected cortical regions.

RESULTS

The system-level decoding revealed nine functional systems based on meta-analytical associations of IPS subdivisions and their cortical coactivations: Two systems-working memory and numeric cognition-which are centered on all IPS subdivisions, and seven systems-attention, language, grasping, recognition memory, rotation, detection of motions/shapes and navigation-with varying degrees of dissociation across subdivisions and hemispheres. By probing the spatial overlap between systems-level co-activations of the IPS and seven canonical intrinsic resting state networks, we observed a trend toward more co-activation between hIP1 and the front parietal network, between hIP2 and hIP3 and the dorsal attention network, and between hIP3 and the visual and somatomotor network.

DISCUSSION

Our results confirm previous findings on the IPS's role in cognition but also point to previously unknown differentiation along the IPS, which present viable starting points for future work. We also present the systems-level decoding as promising approach toward functional decoding of the human connectome.

The role of the angular gyrus in arithmetic processing: a literature review

Since the pioneering work of the early 20th century neuropsychologists, the angular gyrus (AG), particularly in the left hemisphere, has been associated with numerical and mathematical processing. The association between the AG and numerical and mathematical processing has been substantiated by neuroimaging research. In the present review article, we will examine what is currently known about the role of the AG in numerical and mathematical processing with a particular focus on arithmetic. Specifically, we will examine the role of the AG in the retrieval of arithmetic facts in both typically developing children and adults. The review article will consider alternative accounts that posit that the involvement of the AG is not specific to arithmetic processing and will consider how numerical and mathematical processing and their association with the AG overlap with other neurocognitive processes. The review closes with a discussion of future directions to further characterize the relationship between the angular gyrus and arithmetic processing.

Diffusion kurtosis imaging and diffusion tensor imaging parameters applied to white matter and gray matter of patients with anti-N-methyl-D-aspartate receptor encephalitis

Objectives

To compare parameters of diffusion tensor imaging (DTI) and diffusion kurtosis imaging (DKI) to evaluate which can better describe the microstructural changes of anti-N-methyl-D-aspartate receptor (NMDAR) encephalitis patients and to characterize the non-Gaussian diffusion patterns of the whole brain and their correlation with neuropsychological impairments in these patients.

Materials and methods

DTI and DKI parameters were measured in 57 patients with anti-NMDAR encephalitis and 42 healthy controls. Voxel-based analysis was used to evaluate group differences between white matter and gray matter separately. The modified Rankin Scale (mRS) was used to evaluate the severity of the neurofunctional recovery of patients, the Montreal Cognitive Assessment (MoCA) was used to assess global cognitive performance, and the Hamilton Depression Scale (HAMD) and fatigue severity scale (FSS) were used to evaluate depressive and fatigue states.

Results

Patients with anti-NMDAR encephalitis showed significantly decreased radial kurtosis (RK) in the right extranucleus in white matter (P < 0.001) and notably decreased kurtosis fractional anisotropy (KFA) in the right precuneus, the right superior parietal gyrus (SPG), the left precuneus, left middle occipital gyrus, and left superior occipital gyrus in gray matter (P < 0.001). Gray matter regions with decreased KFA overlapped with those with decreased RK in the left middle temporal gyrus, superior temporal gyrus (STG), supramarginal gyrus (SMG), postcentral gyrus (POCG), inferior parietal but supramarginal gyrus, angular gyrus (IPL) and angular gyrus (ANG) (P < 0.001). The KFA and RK in the left ANG, IPL and POCG correlated positively with MoCA scores. KFA and RK in the left ANG, IPL, POCG and SMG correlated negatively with mRS scores. KFA in the left precuneus and right SPG as well as RK in the left STG correlated negatively with mRS scores. No significant correlation between KFA and RK in the abnormal brain regions and HAMD and FSS scores was found.

Conclusion

The microstructural changes in gray matter were much more extensive than those in white matter in patients with anti-NMDAR encephalitis. The brain damage reflected by DKI parameters, which have higher sensitivity than parameters of DTI, correlated with cognitive impairment and the severity of the neurofunctional recovery.

Predicting children's math skills from task-based and resting-state functional brain connectivity

A critical goal of cognitive neuroscience is to predict behavior from neural structure and function, thereby providing crucial insights into who might benefit from clinical and/or educational interventions. Across development, the strength of functional connectivity among a distributed set of brain regions is associated with children's math skills. Therefore, in the present study we use connectome-based predictive modeling to investigate whether functional connectivity during numerical processing and at rest "predicts" children's math skills (N = 31, Mage = 9.21 years, 14 Female). Overall, we found that functional connectivity during symbolic number comparison and rest, but not during nonsymbolic number comparison, predicts children's math skills. Each task revealed a largely distinct set of predictive connections distributed across canonical brain networks and major brain lobes. Most of these predictive connections were negatively correlated with children's math skills so that weaker connectivity predicted better math skills. Notably, these predictive connections were largely nonoverlapping across task states, suggesting children's math abilities may depend on state-dependent patterns of network segregation and/or regional specialization. Furthermore, the current predictive modeling approach moves beyond brain-behavior correlations and toward building models of brain connectivity that may eventually aid in predicting future math skills.

Is the Discount Really Favorable? The Effect of Numeracy on Price Magnitude Judgment: Evidence From Electroencephalography

Attractive price promotion will induce an unreasonable willingness to purchase, especially through shopping. However, it is not clear how numeracy, one of the essential abilities for understanding and applying numbers, influences the process of purchase judgment. In total, 61 participants were recruited to perform a price promotion task using electroencephalography. The results showed that consumers with low numeracy performed worse than their peers with high numeracy at the behavioral level, and they also had lower P3b amplitude and less alpha desynchronization, regardless of price promotion frameworks. These findings provided evidence on the processing of price information and provided further insights into how numeracy impacts price magnitude judgment.

Parietal and hippocampal hyper-connectivity is associated with low math achievement in adolescence - A preliminary study

Mathematical cognition requires coordinated activity across multiple brain regions, leading to the emergence of resting-state functional connectivity as a method for studying the neural basis of differences in mathematical achievement. Hyper-connectivity of the intraparietal sulcus (IPS), a key locus of mathematical and numerical processing, has been associated with poor mathematical skills in childhood, whereas greater connectivity has been related to better performance in adulthood. No studies to date have considered its role in adolescence. Further, hippocampal connectivity can predict mathematical learning, yet no studies have considered its contributions to contemporaneous measures of math achievement. Here, we used seed-based resting-state fMRI analyses to examine IPS and hippocampal intrinsic functional connectivity relations to math achievement in a group of 31 adolescents (mean age = 16.42 years, range 15-17), whose math performance spanned the 1% to 99% percentile. After controlling for IQ, IPS connectivity was negatively related to math achievement, akin to findings in children. However, the specific temporo-occipital regions were more akin to the posterior loci implicated in adults. Hippocampal connectivity with frontal regions was also negatively correlated with concurrent math measures, which contrasts with results from learning studies. Finally, hyper-connectivity was not a global feature of low math performance, as math performance did not modulate connectivity of Heschl's gyrus, a control seed not involved in math cognition. Our results provide preliminary evidence that adolescence is a transitional stage in which patterns found in childhood and adulthood can be observed; most notably, hyper-connectivity continues to be related to low math ability into this period.

Functional Connectivity Fingerprints at Rest Are Similar across Youths and Adults and Vary with Genetic Similarity

Distinguishing individuals from brain connectivity, and studying the genetic influences on that identification across different ages, improves our basic understanding of functional brain network organization. We applied support vector machine classifiers to two datasets of twins (adult, pediatric) and two datasets of repeat-scan individuals (adult, pediatric). Classifiers were trained on resting state functional connectivity magnetic resonance imaging (rs-fcMRI) data and used to predict individuals and co-twin pairs from independent data. The classifiers successfully identified individuals from a previous scan with 100% accuracy, even when scans were separated by months. In twin samples, classifier accuracy decreased as genetic similarity decreased. Our results demonstrate that classification is stable within individuals, similar within families, and contains similar representations of functional connections over a few decades of life. Moreover, the degree to which these patterns of connections predict siblings' data varied by genetic relatedness, suggesting that genetic influences on rs-fcMRI connectivity are established early in life.

A brain connectivity characterization of children with different levels of mathematical achievement based on graph metrics

Recent studies aiming to facilitate mathematical skill development in primary school children have explored the electrophysiological characteristics associated with different levels of arithmetic achievement. The present work introduces an alternative EEG signal characterization using graph metrics and, based on such features, a classification analysis using a decision tree model. This proposal aims to identify group differences in brain connectivity networks with respect to mathematical skills in elementary school children. The methods of analysis utilized were signal-processing (EEG artifact removal, Laplacian filtering, and magnitude square coherence measurement) and the characterization (Graph metrics) and classification (Decision Tree) of EEG signals recorded during performance of a numerical comparison task. Our results suggest that the analysis of quantitative EEG frequency-band parameters can be used successfully to discriminate several levels of arithmetic achievement. Specifically, the most significant results showed an accuracy of 80.00% (α band), 78.33% (δ band), and 76.67% (θ band) in differentiating high-skilled participants from low-skilled ones, averaged-skilled subjects from all others, and averaged-skilled participants from low-skilled ones, respectively. The use of a decision tree tool during the classification stage allows the identification of several brain areas that seem to be more specialized in numerical processing.

Disentangling Mathematics from Executive Functions by Investigating Unique Functional Connectivity Patterns Predictive of Mathematics Ability

What are the underlying neurocognitive mechanisms that give rise to mathematical competence? This study investigated the relationship between tests of mathematical ability completed outside the scanner and resting-state functional connectivity (FC) of cytoarchitectonically defined subdivisions of the parietal cortex in adults. These parietal areas are also involved in executive functions (EFs). Therefore, it remains unclear whether there are unique networks for mathematical processing. We investigate the neural networks for mathematical cognition and three measures of EF using resting-state fMRI data collected from 51 healthy adults. Using 10 ROIs in seed to whole-brain voxel-wise analyses, the results showed that arithmetical ability was correlated with FC between the right anterior intraparietal sulcus (hIP1) and the left supramarginal gyrus and between the right posterior intraparietal sulcus (hIP3) and the left middle frontal gyrus and the right premotor cortex. The connection between the posterior portion of the left angular gyrus and the left inferior frontal gyrus was also correlated with mathematical ability. Covariates of EF eliminated connectivity patterns with nodes in inferior frontal gyrus, angular gyrus, and middle frontal gyrus, suggesting neural overlap. Controlling for EF, we found unique connections correlated with mathematical ability between the right hIP1 and the left supramarginal gyrus and between hIP3 bilaterally to premotor cortex bilaterally. This is partly in line with the “mapping hypothesis” of numerical cognition in which the right intraparietal sulcus subserves nonsymbolic number processing and connects to the left parietal cortex, responsible for calculation procedures. We show that FC within this circuitry is a significant predictor of math ability in adulthood.

Impaired neural processing of transitive relations in children with math learning difficulty

Math learning difficulty (i.e., MLD) is common in children and can have far-reaching consequences in personal and professional life. Converging evidence suggests that MLD is associated with impairments in the intraparietal sulcus (IPS). However, the role that these impairments play in MLD remains unclear. Although it is often assumed that IPS deficits affect core numerical abilities, the IPS is also involved in several non-numerical processes that may contribute to math skills. For instance, the IPS supports transitive reasoning (i.e., the ability to integrate relations such as A > B and B > C to infer that A > C), a skill that is central to many aspects of math learning in children. Here we measured fMRI activity of 8- to 12-year-olds with MLD and typically developing (TD) peers while they listened to stories that included transitive relations. Children also answered questions evaluating whether transitive inferences were made during story comprehension. Compared to non-transitive relations (e.g., A > B and C > D), listening to transitive relations (e.g., A > B and B > C) was associated with enhanced activity in the IPS in TD children. In children with MLD, the difference in activity between transitive and non-transitive relations in the IPS was (i) non-reliable and (ii) smaller than in TD children. Finally, children with MLD were less accurate than TD peers when making transitive inferences based on transitive relations. Thus, a deficit in the online processing of transitive relations in the IPS might contribute to math difficulties in children with MLD.

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Transitive reasoning is central to mathematical thinking.

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Transitive reasoning relies on the intra-parietal sulcus (IPS) in healthy children.

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Math learning difficulty (MLD) is associated with IPS impairments.

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Transitive reasoning is impaired in children with MLD.

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Transitive reasoning does not engage the IPS in children with MLD.

Decoding the processing stages of mental arithmetic with magnetoencephalography

Elementary arithmetic is highly prevalent in our daily lives. However, despite decades of research, we are only beginning to understand how the brain solves simple calculations. Here, we applied machine learning techniques to magnetoencephalography (MEG) signals in an effort to decompose the successive processing stages and mental transformations underlying elementary arithmetic. Adults subjects verified single-digit addition and subtraction problems such as 3 + 2 = 9 in which each successive symbol was presented sequentially. MEG signals revealed a cascade of partially overlapping brain states. While the first operand could be transiently decoded above chance level, primarily based on its visual properties, the decoding of the second operand was more accurate and lasted longer. Representational similarity analyses suggested that this decoding rested on both visual and magnitude codes. We were also able to decode the operation type (additions vs. subtraction) during practically the entire trial after the presentation of the operation sign. At the decision stage, MEG indicated a fast and highly overlapping temporal dynamics for (1) identifying the proposed result, (2) judging whether it was correct or incorrect, and (3) pressing the response button. Surprisingly, however, the internally computed result could not be decoded. Our results provide a first comprehensive picture of the unfolding processing stages underlying arithmetic calculations at a single-trial level, and suggest that externally and internally generated neural codes may have different neural substrates.

Examining the Triple Code Model in numerical cognition: An fMRI study

The Triple Code Model (TCM) of numerical cognition argues for the existence of three representational codes for number: Arabic digits, verbal number words, and analog nonsymbolic magnitude representations, each subserved by functionally dissociated neural substrates. Despite the popularity of the TCM, no study to date has explored all three numerical codes within one fMRI paradigm. We administered three tasks, associated with each of the aforementioned numerical codes, in order to explore the neural correlates of numerosity processing in a sample of adults (N = 46). Independent task-control contrast analyses revealed task-dependent activity in partial support of the model, but also highlight the inherent complexity of a distributed and overlapping fronto-parietal network involved in all numerical codes. The results indicate that the TCM correctly predicts the existence of some functionally dissociated neural substrates, but requires an update that accounts for interactions with attentional processes. Parametric contrasts corresponding to differences in task difficulty revealed specific neural correlates of the distance effect, where closely spaced numbers become more difficult to discriminate than numbers spaced further apart. A conjunction analysis illustrated overlapping neural correlates across all tasks, in line with recent proposals for a fronto-parietal network of number processing. We additionally provide tentative results suggesting the involvement of format-independent numerosity-sensitive retinotopic maps in the early visual stream, extending previous findings of nonsymbolic stimulus selectivity. We discuss the functional roles of the components associated with the model, as well as the purported fronto-parietal network, and offer arguments in favor of revising the TCM.