Fact learning in complex arithmetic and figural-spatial tasks: the role of the angular gyrus and its relation to mathematical competence

Add, subtract and multiply: Meta-analyses of brain correlates of arithmetic operations in children and adults

Mathematical operations are cognitive actions we take to calculate relations among numbers. Arithmetic operations, addition, subtraction, multiplication, and division are elemental in education. Addition is the first one taught in school and is most popular in functional magnetic resonance imaging (fMRI) studies. Division, typically taught last is least studied with fMRI. fMRI meta-analyses show that arithmetic operations activate brain areas in parietal, cingulate and insular cortices for children and adults. Critically, no meta-analysis examines concordance across brain correlates of separate arithmetic operations in children and adults. We review and examine using quantitative meta-analyses data from fMRI articles that report brain coordinates separately for addition, subtraction, multiplication, and division in children and adults. Results show that arithmetic operations elicit common areas of concordance in fronto-parietal and cingulo-opercular networks in adults and children. Between operations differences are observed primarily for adults. Interestingly, higher within-group concordance, expressed in activation likelihood estimates, is found in brain areas associated with the cingulo-opercular network rather than the fronto-parietal network in children, areas also common between adults and children. Findings are discussed in relation to constructivist cognitive theory and practical directions for future research.

Spatiotemporal Dynamics of Successive Activations across the Human Brain during Simple Arithmetic Processing

Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain; however, these were not powered to explore the exact timing of events at the subsecond scale combined with a precise anatomical source of information at the level of individual brains. As a result, we know little about the order of engagement across different brain regions during a given cognitive task. Using experimental arithmetic tasks as a prototype for human-unique symbolic processing, we recorded directly across 10,076 brain sites in 85 human subjects (52% female) using the intracranial electroencephalography. Our data revealed a remarkably distributed change of activity in almost half of the sampled sites. In each activated brain region, we found juxtaposed neuronal populations preferentially responsive to either the target or control conditions, arranged in an anatomically orderly manner. Notably, an orderly successive activation of a set of brain regions-anatomically consistent across subjects-was observed in individual brains. The temporal order of activations across these sites was replicable across subjects and trials. Moreover, the degree of functional connectivity between the sites decreased as a function of temporal distance between regions, suggesting that the information is partially leaked or transformed along the processing chain. Our study complements prior imaging studies by providing hitherto unknown information about the timing of events in the brain during arithmetic processing. Such findings can be a basis for developing mechanistic computational models of human-specific cognitive symbolic systems.

Neural evidence for procedural automatization during cognitive development: Intraparietal response to changes in very-small addition problem-size increases with age

Cognitive development is often thought to depend on qualitative changes in problem-solving strategies, with early developing algorithmic procedures (e.g., counting when adding numbers) considered being replaced by retrieval of associations (e.g., between operands and answers of addition problems) in adults. However, algorithmic procedures might also become automatized with practice. In a large cross-sectional fMRI study from age 8 to adulthood (n = 128), we evaluate this hypothesis by measuring neural changes associated with age-related reductions in a behavioral hallmark of mental addition, the problem-size effect (an increase in solving time as problem sum increases). We found that age-related decreases in problem-size effect were paralleled by age-related increases of activity in a region of the intraparietal sulcus that already supported the problem-size effect in 8- to 9-year-olds, at an age the effect is at least partly due to explicit counting. This developmental effect, which was also observed in the basal ganglia and prefrontal cortex, was restricted to problems with operands ≤ 4. These findings are consistent with a model positing that very-small arithmetic problems-and not larger problems-might rely on an automatization of counting procedures rather than a shift towards retrieval, and suggest a neural automatization of procedural knowledge during cognitive development.

Identifying the Neural Bases of Math Competence Based on Structural and Functional Properties of the Human Brain

Human populations show large individual differences in math performance and math learning abilities. Early math skill acquisition is critical for providing the foundation for higher quantitative skill acquisition and succeeding in modern society. However, the neural bases underlying individual differences in math competence remain unclear. Modern neuroimaging techniques allow us to not only identify distinct local cortical regions but also investigate large-scale neural networks underlying math competence both structurally and functionally. To gain insights into the neural bases of math competence, this review provides an overview of the structural and functional neural markers for math competence in both typical and atypical populations of children and adults. Although including discussion of arithmetic skills in children, this review primarily focuses on the neural markers associated with complex math skills. Basic number comprehension and number comparison skills are outside the scope of this review. By synthesizing current research findings, we conclude that neural markers related to math competence are not confined to one particular region; rather, they are characterized by a distributed and interconnected network of regions across the brain, primarily focused on frontal and parietal cortices. Given that human brain is a complex network organized to minimize the cost of information processing, an efficient brain is capable of integrating information from different regions and coordinating the activity of various brain regions in a manner that maximizes the overall efficiency of the network to achieve the goal. We end by proposing that frontoparietal network efficiency is critical for math competence, which enables the recruitment of task-relevant neural resources and the engagement of distributed neural circuits in a goal-oriented manner. Thus, it will be important for future studies to not only examine brain activation patterns of discrete regions but also examine distributed network patterns across the brain, both structurally and functionally.

Disconnection in a left-hemispheric temporo-parietal network impairs multiplication fact retrieval

Arithmetic fact retrieval has been suggested to recruit a left-lateralized network comprising perisylvian language areas, parietal areas such as the angular gyrus (AG), and non-neocortical structures such as the hippocampus. However, the underlying white matter connectivity of these areas has not been evaluated systematically so far. Using simple multiplication problems, we evaluated how disconnections in parietal brain areas affected arithmetic fact retrieval following stroke. We derived disconnectivity measures by jointly considering data from n = 73 patients with acute unilateral lesions in either hemisphere and a white-matter tractography atlas (HCP-842) using the Lesion Quantification Toolbox (LQT). Whole-brain voxel-based analysis indicated a left-hemispheric cluster of white matter fibers connecting the AG and superior temporal areas to be associated with a fact retrieval deficit. Subsequent analyses of direct gray-to-gray matter disconnections revealed that disconnections of additional left-hemispheric areas (e.g., between the superior temporal gyrus and parietal areas) were significantly associated with the observed fact retrieval deficit. Results imply that disconnections of parietal areas (i.e., the AG) with language-related areas (i.e., superior and middle temporal gyri) seem specifically detrimental to arithmetic fact retrieval. This suggests that arithmetic fact retrieval recruits a widespread left-hemispheric network and emphasizes the relevance of white matter connectivity for number processing.

The two-network framework of number processing: a step towards a better understanding of the neural origins of developmental dyscalculia

Developmental dyscalculia is a specific learning disorder that persists over lifetime and can have an enormous impact on personal, health-related, and professional aspects of life. Despite its central importance, the origin both at the cognitive and neural level is not yet well understood. Several classification schemas of dyscalculia have been proposed, sometimes together with an associated deficit at the neural level. However, these explanations are (a) not providing an exhaustive framework that is at levels with the observed complexity of developmental dyscalculia at the behavioral level and (b) are largely mono-causal approaches focusing on gray matter deficits. We suggest that number processing is instead the result of context-dependent interaction of two anatomically largely separate, distributed but overlapping networks that function/cooperate in a closely integrated fashion. The proposed two-network framework (TNF) is the result of a series of studies in adults on the neural correlates underlying magnitude processing and arithmetic fact retrieval, which comprised neurofunctional imaging of various numerical tasks, the application of probabilistic fiber tracking to obtain well-defined connections, and the validation and modification of these results using disconnectome mapping in acute stroke patients. Emerged from data in adults, it represents the endpoint of the acquisition and use of mathematical competencies in adults. Yet, we argue that its main characteristics should already emerge earlier during development. Based on this TNF, we develop a classification schema of phenomenological subtypes and their underlying neural origin that we evaluate against existing propositions and the available empirical data.

Structural and metabolic brain correlates of arithmetic word-problem solving in Huntington's disease

Individuals with pre-manifest and early symptomatic Huntington's disease (HD) have shown deficits in solving arithmetic word-problems. However, the neural correlates of these deficits in HD are poorly understood. We explored the structural (gray-matter volume; GMV) and metabolic (18F-FDG PET; SUVr) brain correlates of arithmetic performance using the recently developed HD-word problem arithmetic task (HD-WPA) in seventeen preHD and sixteen HD individuals. Symptomatic participants showed significantly lower scores in the HD-WPA than preHD participants. Lower performance in the HD-WPA was associated with reduced GMV in subcortical, medial frontal, and several posterior-cortical clusters in HD participants. No significant GMV loss was found in preHD participants. 18F-FDG data revealed a widespread pattern of hypometabolism in association with lower arithmetic performance in all participants. In preHD participants, this pattern was restricted to the ventrolateral and orbital prefrontal cortex, the insula, and the precentral gyrus. In HD participants, the pattern extended to several parietal-temporal regions. Word-problem solving arithmetic deficits in HD is subserved by a pattern of asynchronous metabolic and structural compromise across the cerebral cortex as a function of disease stage. In preHD individuals, arithmetic deficits were associated with prefrontal alterations, whereas in symptomatic HD patients, more severe arithmetic deficits are associated with the compromise of several frontal-subcortical and temporo-parietal regions. Our results support the hypothesis that cognitive deficits in HD are not exclusively dominated by frontal-striatal dysfunctions but also involve fronto-temporal and parieto-occipital damage.

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.

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.

Impaired Arithmetic Fact Retrieval in an Adult with Developmental Dyscalculia: Evidence from Behavioral and Functional Brain Imaging Data

Developmental dyscalculia (DD) is a developmental disorder characterized by arithmetic difficulties. Recently, it has been suggested that the neural networks supporting procedure-based calculation (e.g., in subtraction) and left-hemispheric verbal arithmetic fact retrieval (e.g., in multiplication) are partially distinct. Here we compared the neurofunctional correlates of subtraction and multiplication in a 19-year-old student (RM) with DD to 18 age-matched controls. Behaviorally, RM performed significantly worse than controls in multiplication, while subtraction was unaffected. Neurofunctional differences were most pronounced regarding multiplication: RM showed significantly stronger activation than controls not only in left angular gyrus but also in a fronto-parietal network (including left intraparietal sulcus and inferior frontal gyrus) typically activated during procedure-based calculation. Region-of-interest analyses indicated group differences in multiplication only, which, however, did not survive correction for multiple comparisons. Our results are consistent with dissociable and processing-specific, but not operation-specific neurofunctional networks. Procedure-based calculation is not only associated with subtraction but also with (untrained) multiplication facts. Only after rote learning, facts can be retrieved quasi automatically from memory. We suggest that this learning process and the associated shift in activation patterns has not fully occurred in RM, as reflected in her need to resort to procedure-based strategies to solve multiplication facts.

A connectivity model of the anatomic substrates underlying Gerstmann syndrome

The Gerstmann syndrome is a constellation of neurological deficits that include agraphia, acalculia, left-right discrimination and finger agnosia. Despite a growing interest in this clinical phenomenon, there remains controversy regarding the specific neuroanatomic substrates involved. Advancements in data-driven, computational modelling provides an opportunity to create a unified cortical model with greater anatomic precision based on underlying structural and functional connectivity across complex cognitive domains. A literature search was conducted for healthy task-based functional MRI and PET studies for the four cognitive domains underlying Gerstmann's tetrad using the electronic databases PubMed, Medline, and BrainMap Sleuth (2.4). Coordinate-based, meta-analytic software was utilized to gather relevant regions of interest from included studies to create an activation likelihood estimation (ALE) map for each cognitive domain. Machine-learning was used to match activated regions of the ALE to the corresponding parcel from the cortical parcellation scheme previously published under the Human Connectome Project (HCP). Diffusion spectrum imaging-based tractography was performed to determine the structural connectivity between relevant parcels in each domain on 51 healthy subjects from the HCP database. Ultimately 102 functional MRI studies met our inclusion criteria. A frontoparietal network was found to be involved in the four cognitive domains: calculation, writing, finger gnosis, and left-right orientation. There were three parcels in the left hemisphere, where the ALE of at least three cognitive domains were found to be overlapping, specifically the anterior intraparietal area, area 7 postcentral (7PC) and the medial intraparietal sulcus. These parcels surround the anteromedial portion of the intraparietal sulcus. Area 7PC was found to be involved in all four domains. These regions were extensively connected in the intraparietal sulcus, as well as with a number of surrounding large-scale brain networks involved in higher-order functions. We present a tractographic model of the four neural networks involved in the functions which are impaired in Gerstmann syndrome. We identified a 'Gerstmann Core' of extensively connected functional regions where at least three of the four networks overlap. These results provide clinically actionable and precise anatomic information which may help guide clinical translation in this region, such as during resective brain surgery in or near the intraparietal sulcus, and provides an empiric basis for future study.

Training causes activation increase in temporo-parietal and parietal regions in children with mathematical disabilities

While arithmetic training reduces fronto-temporo-parietal activation related to domain-general processes in typically developing (TD) children, we know very little about the training-related neurocognitive changes in children with mathematical disabilities (MD), who seek evidenced-based educational interventions. In a within-participant design, a group of 20 children (age range = 10-15 years old) with MD underwent 2 weeks of arithmetic training. Brain activation was measured using functional near-infrared spectroscopy (fNIRS) before and after training to assess training-related changes. Two weeks of training led to both behavioral and brain changes. Training-specific change for trained versus untrained (control) simple multiplication solving was observed as activation increase in the bilateral temporo-parietal region including angular gyrus and middle temporal gyrus. Training-specific change for trained versus untrained (control) complex multiplication solving was observed as activation increase in the bilateral parietal region including intraparietal sulcus, superior parietal lobule, and supramarginal gyrus. Unlike the findings of a similar study in TD children, 2 weeks of multiplication training led to brain activation increase in the fronto-parietal network in children with MD. Interestingly, these brain activation differences between the current findings and a recent similar study in TD children underlie a rather similar behavioral improvement as regards response time and accuracy after 2 weeks of training. This finding provides valuable insights into underlying mechanisms of mathematics learning in special samples and suggests that the findings in TD children may not be readily generalized to children with MD.

Analysis of fMRI Signals from Working Memory Tasks and Resting-State of Brain: Neutrosophic-Entropy-Based Clustering Algorithm

This study applies a neutrosophic-entropy-based clustering algorithm (NEBCA) to analyze the fMRI signals. We consider the data obtained from four different working memory tasks and the brain's resting state for the experimental purpose. Three non-overlapping clusters of data related to temporal brain activity are determined and statistically analyzed. Moreover, we used the Uniform Manifold Approximation and Projection (UMAP) method to reduce system dimensionality and present the effectiveness of NEBCA. The results show that using NEBCA, we are able to distinguish between different working memory tasks and resting-state and identify subtle differences in the related activity of brain regions. By analyzing the statistical properties of the entropy inside the clusters, the various regions of interest (ROIs), according to Automated Anatomical Labeling (AAL) atlas crucial for clustering procedure, are determined. The inferior occipital gyrus is established as an important brain region in distinguishing the resting state from the tasks. Moreover, the inferior occipital gyrus and superior parietal lobule are identified as necessary to correct the data discrimination related to the different memory tasks. We verified the statistical significance of the results through the two-sample t-test and analysis of surrogates performed by randomization of the cluster elements. The presented methodology is also appropriate to determine the influence of time of day on brain activity patterns. The differences between working memory tasks and resting-state in the morning are related to a lower index of small-worldness and sleep inertia in the first hours after waking. We also compared the performance of NEBCA to two existing algorithms, KMCA and FKMCA. We showed the advantage of the NEBCA over these algorithms that could not effectively accumulate fMRI signals with higher variability.

Arithmetic learning in children: An fMRI training study

Arithmetic learning is characterized by a change from procedural strategies to fact retrieval. fMRI training studies in adults have revealed that this change coincides with decreased activation in the prefrontal cortex (PFC) and that within the parietal lobe, a shift occurs from the intraparietal sulcus (IPS) to the angular gyrus (AG) during this change. It remains to be determined whether similar changes can be observed in children, particularly because children often recruit the hippocampus (HC) during fact retrieval, an observation that has not consistently been found in adults. In order to experimentally manipulate arithmetic strategy change, 26 typically developing 9- to-10-year-olds completed a six day at-home training of complex multiplication items (e.g. 16 × 4). Before and after training, children were presented with three multiplication conditions during fMRI: (1) complex to-be-trained/trained items, (2) complex untrained items and (3) single-digit items. Behavioral data indicated that training was successful. Similar to adults, children showed greater activity in the IPS and PFC for the untrained condition post-training, indicating that the fronto-parietal network during procedural arithmetic problem solving is already in place in children of this age. We did not observe the expected training-related changes in the HC. In contrast to what has been observed in adults, greater activity in the AG was not observed for the trained items. These results show that the brain processes that accompany the learning of arithmetic facts are different in children as compared to adults.

Groupitizing modifies neural coding of numerosity

Numerical estimation of arrays of objects is faster and more accurate when items can be clustered into groups, a phenomenon termed “groupitizing.” Grouping can facilitate segregation into subitizable “chunks,” each easily estimated, then summed. The current study investigates whether spatial grouping of arrays drives specific neural responses during numerical estimation, reflecting strategies such as exact calculation and fact retrieval. Fourteen adults were scanned with fMRI while estimating either the numerosity or shape of arrays of items, either randomly distributed or spatially grouped. Numerosity estimation of both classes of stimuli elicited common activation of a right lateralized frontoparietal network. Grouped stimuli additionally recruited regions in the left hemisphere and bilaterally in the angular gyrus. Multivariate pattern analysis showed that classifiers trained with the pattern of neural activations read out from parietal regions, but not from the primary visual areas, can decode different numerosities both within and across spatial arrangements. The behavioral numerical acuity correlated with the decoding performance of the parietal but not with occipital regions. Overall, this experiment suggests that the estimation of grouped stimuli relies on the approximate number system for numerosity estimation, but additionally recruits regions involved in calculation.

The neuroscience of advanced scientific concepts

Cognitive neuroscience methods can identify the fMRI-measured neural representation of familiar individual concepts, such as apple, and decompose them into meaningful neural and semantic components. This approach was applied here to determine the neural representations and underlying dimensions of representation of far more abstract physics concepts related to matter and energy, such as fermion and dark matter, in the brains of 10 Carnegie Mellon physics faculty members who thought about the main properties of each of the concepts. One novel dimension coded the measurability vs. immeasurability of a concept. Another novel dimension of representation evoked particularly by post-classical concepts was associated with four types of cognitive processes, each linked to particular brain regions: (1) Reasoning about intangibles, taking into account their separation from direct experience and observability; (2) Assessing consilience with other, firmer knowledge; (3) Causal reasoning about relations that are not apparent or observable; and (4) Knowledge management of a large knowledge organization consisting of a multi-level structure of other concepts. Two other underlying dimensions, previously found in physics students, periodicity, and mathematical formulation, were also present in this faculty sample. The data were analyzed using factor analysis of stably responding voxels, a Gaussian-naïve Bayes machine-learning classification of the activation patterns associated with each concept, and a regression model that predicted activation patterns associated with each concept based on independent ratings of the dimensions of the concepts. The findings indicate that the human brain systematically organizes novel scientific concepts in terms of new dimensions of neural representation.

Neural evidence for cognitive reappraisal as a strategy to alleviate the effects of math anxiety

Math anxiety (MA) describes feelings of tension, apprehension and fear that interfere with math performance. High MA (HMA) is correlated with negative consequences, including lower math grades, and ultimately an avoidance of quantitative careers. Given these adverse consequences, it is essential to explore effective intervention strategies to reduce MA. In the present functional magnetic resonance imaging (fMRI) study, we investigated the efficacy of cognitive reappraisal as a strategy to alleviate the effects of MA. Cognitive reappraisal, an emotion regulation strategy, has been shown to decrease negative affect and amygdala responsivity to stimuli that elicit negative emotion. We compared a reappraisal strategy to participants’ natural strategy for solving math problems and analogies. We found that HMA individuals showed an increase in accuracy and a decrease in negative affect during the reappraisal condition as compared to the control condition. During math reappraise trials, increased activity in a network of regions associated with arithmetic correlated with improved performance for HMA individuals. These results suggest that increased engagement of arithmetic regions underlies the performance increases we identify in HMA students when they use reappraisal to augment their math performance. Overall, cognitive reappraisal is a promising strategy for enhancing math performance and reducing anxiety in math anxious individuals.

Emerging neurodevelopmental perspectives on mathematical learning

Strong foundational skills in mathematical problem solving, acquired in early childhood, are critical not only for success in the science, technology, engineering, and mathematical (STEM) fields but also for quantitative reasoning in everyday life. The acquisition of mathematical skills relies on protracted interactive specialization of functional brain networks across development. Using a systems neuroscience approach, this review synthesizes emerging perspectives on neurodevelopmental pathways of mathematical learning, highlighting the functional brain architecture that supports these processes and sources of heterogeneity in mathematical skill acquisition. We identify the core neural building blocks of numerical cognition, anchored in the posterior parietal and ventral temporal-occipital cortices, and describe how memory and cognitive control systems, anchored in the medial temporal lobe and prefrontal cortex, help scaffold mathematical skill development. We highlight how interactive specialization of functional circuits influences mathematical learning across different stages of development. Functional and structural brain integrity and plasticity associated with math learning can be examined using an individual differences approach to better understand sources of heterogeneity in learning, including cognitive, affective, motivational, and sociocultural factors. Our review emphasizes the dynamic role of neurodevelopmental processes in mathematical learning and cognitive development more generally.

Primitive visual channels have a causal role in cognitive transfer

Scientific investigations have long emphasized the cortex's role in cognitive transfer and arithmetic abilities. To date, however, this assumption has not been thoroughly empirically investigated. Here we demonstrated that primitive mechanisms-lower visual channels-have a causal role in cognitive transfer of complex skills such as symbolic arithmetic. We found that exposing only one monocular channel to a visuospatial training resulted in a larger transfer effect in the trained monocular channel compared to the untrained monocular channel. Such cognitive transfer was found for both novel figural-spatial problems (near transfer) and novel subtraction problems (far transfer). Importantly, the benefits of the trained eye were not observed in old problems and in other tasks that did not involve visuospatial abilities (the Stroop task, a multiplication task). These results challenge the exclusive role of the cortex in cognitive transfer and complex arithmetic. In addition, the results suggest a new mechanism for the emergence of cognitive skills, that could be shared across different species.

Can the interference effect in multiplication fact retrieval be modulated by an arithmetic training? An fMRI study

Single-digit multiplications are thought to be associated with different levels of interference because they show different degrees of feature overlap (i.e., digits) with previously learnt problems. Recent behavioral and neuroimaging studies provided evidence for this interference effect and showed that individual differences in arithmetic fact retrieval are related to differences in sensitivity to interference (STI). The present study investigated whether and to what extent competence-related differences in STI and its neurophysiological correlates can be modulated by a multiplication facts training. Participants were 23 adults with high and 23 adults with low arithmetic competencies who underwent a five-day multiplication facts training in which they intensively practiced sets of low- and high-interfering multiplication problems. In a functional magnetic resonance imaging (fMRI) test session after the training, participants worked on a multiplication verification task that comprised trained and untrained problems. Analyses of the behavioral data revealed an interference effect only in the low competence group, which could be reduced but not resolved by training. On the neural level, competence-related differences in the interference effect were observed in the left supramarginal gyrus (SMG), showing activation differences between low- and high-interfering problems only in the low competent group. These findings support the idea that individuals' low arithmetic skills are related to the development of insufficient memory representations because of STI. Further, our results indicate that a short training by drill (i.e., learning associations between operands and solutions) was not fully effective to resolve existing interference effects in arithmetic fact knowledge.

Hand preference and Mathematical Learning Difficulties: New data from Greece, the United Kingdom, and Germany and two meta-analyses of the literature

Increased rates of atypical handedness are observed in neurotypical individuals who are low-performing in mathematical tasks as well as in individuals with special educational needs, such as dyslexia. This is the first investigation of handedness in individuals with Mathematical Learning Difficulties (MLD). We report three new studies (N = 134; N = 1,893; N = 153) and two sets of meta-analyses (22 studies; N = 3,667). No difference in atypical hand preference between MLD and Typically Achieving (TA) individuals was found when handedness was assessed with self-report questionnaires, but weak evidence of a difference was found when writing hand was the handedness criterion in Study 1 (p = .049). Similarly, when combining data meta-analytically, no hand preference differences were detected. We suggest that: (i) potential handedness effects require larger samples, (ii) direction of hand preference is not a sensitive enough measure of handedness in this context, or that (iii) increased rates of atypical hand preference are not associated with MLD. The latter scenario would suggest that handedness is specifically linked to language-related conditions rather than conditions related to cognitive abilities at large. Future studies need to consider hand skill and degree of hand preference in MLD.

Children's neural responses to a novel mathematics concept

BACKGROUND

Functional MRI studies have suggested a 'frontoparietal shift' over the course of development, whereby children tend to engage prefrontal neural regions to a greater extent than adults when completing mathematics tasks. Although this literature hints that lateral prefrontal regions may be involved in acquiring mathematics knowledge, a key limitation of existing studies is that they have included mathematics content that children already are familiar with as opposed to examining the dynamic learning process. We aimed to address this gap by examining children's neural responses when exposed to a new, unfamiliar mathematics concept.

METHOD

Eighteen 8-11 year old children viewed blocked demonstrations of base-2/binary (unfamiliar) and base-10/decimal (familiar) number systems while undergoing functional MRI (fMRI). Children's behavioral understanding of binary numbers was measured between fMRI runs.

RESULTS

Counter to hypotheses, there were no overall differences in prefrontal activity for binary relative to decimal blocks. However, children with higher levels of behavioral understanding of the novel, binary concept showed enhanced neural activity in the left rostral middle frontal gyrus specifically during binary concept exposure. They also showed enhanced connectivity between this region and pre-and post-central gyri and left parahippocampal regions.

CONCLUSIONS

Individual differences in children's behavioral grasp of a new mathematics concept correlate with prefrontal activity and functional connectivity during exposure to the concept, suggesting that rostral prefrontal cortex may play a role in mathematics learning.

Hemispheric Lateralization of Arithmetic Facts and Magnitude Processing for Two-Digit Numbers

In the human brain, a (relative) functional asymmetry (i.e., laterality; functional and performance differences between the two cerebral hemispheres) exists for a variety of cognitive domains (e.g., language, visual-spatial processing, etc.). For numerical cognition, both bi-lateral and unilateral processing has been proposed with the retrieval of arithmetic facts postulated as being lateralized to the left hemisphere. In this study, we aimed at evaluating this claim by investigating whether processing of multiplicatively related triplets in a number bisection task (e.g., 12_16_20) in healthy participants (n = 23) shows a significant advantage when transmitted to the right hemisphere only as compared to transmission to the left hemisphere. As expected, a control task revealed that stimulus presentation to the left or both visual hemifields did not increase processing disadvantages of unit-decade incompatible number pairs in magnitude comparison. For the number bisection task, we replicated the multiplicativity effect. However, in contrast to the hypothesis deriving from the triple code model, we did not observe significant hemispheric processing asymmetries for multiplicative items. We suggest that participants resorted to keep number triplets in verbal working memory after perceiving them only very briefly for 150 ms. Rehearsal of the three numbers was probably slow and time-consuming so allowing for interhemispheric communication in the meantime. We suggest that an effect of lateralized presentation may only be expected for early effects when the task is sufficiently easy.

Associations Between Individual Differences in Mathematical Competencies and Surface Anatomy of the Adult Brain

Previously conducted structural magnetic resonance imaging (MRI) studies on the neuroanatomical correlates of mathematical abilities and competencies have several methodological limitations. Besides small sample sizes, the majority of these studies have employed voxel-based morphometry (VBM)-a method that, although it is easy to implement, has some major drawbacks. Taking this into account, the current study is the first to investigate in a large sample of typically developed adults the associations between mathematical abilities and variations in brain surface structure by using surface-based morphometry (SBM). SBM is a method that also allows the investigation of brain morphometry by avoiding the pitfalls of VBM. Eighty-nine young adults were tested with a large battery of psychometric tests to measure mathematical competencies in four different areas: (1) simple arithmetic; (2) complex arithmetic; (3) higher-order mathematics; and (4) numerical intelligence. Also, we asked participants for their mathematics grades for their final school exams. Inside the MRI scanner, we collected high-resolution T1-weighted anatomical images from each subject. SBM analyses were performed with the computational anatomy toolbox (CAT12) and indices for cortical thickness, for cortical surface complexity, for gyrification, and sulcal depth were calculated. Further analyses revealed associations between: (1) the cortical surface complexity of the right superior temporal gyrus and numerical intelligence; (2) the depth of the right central sulcus and adults' ability to solve complex arithmetic problems; and (3) the depth of the left parieto-occipital sulcus and adults' higher-order mathematics competence. Interestingly, no relationships with previously reported brain regions were observed, thus, suggesting the importance of similar research to confirm the role of the brain regions found in this study.

Faster learners transfer their knowledge better: Behavioral, mnemonic, and neural mechanisms of individual differences in children's learning

Why some children learn, and transfer their knowledge to novel problems, better than others remains an important unresolved question in the science of learning. Here we developed an innovative tutoring program and data analysis approach to investigate individual differences in neurocognitive mechanisms that support math learning and "near" transfer to novel, but structurally related, problems in elementary school children. Following just five days of training, children performed recently trained math problems more efficiently, with greater use of memory-retrieval-based strategies. Crucially, children who learned faster during training performed better not only on trained problems but also on novel problems, and better discriminated trained and novel problems in a subsequent recognition memory task. Faster learners exhibited increased similarity of neural representations between trained and novel problems, and greater differentiation of functional brain circuits engaged by trained and novel problems. These results suggest that learning and near transfer are characterized by parallel learning-rate dependent local integration and large-scale segregation of functional brain circuits. Our findings demonstrate that speed of learning and near transfer are interrelated and identify the neural mechanisms by which faster learners transfer their knowledge better. Our study provides new insights into the behavioral, mnemonic, and neural mechanisms underlying children's learning.

Individual Differences in Math Ability Determine Neurocognitive Processing of Arithmetic Complexity: A Combined fNIRS-EEG Study

Some individuals experience more difficulties with math than others, in particular when arithmetic problems get more complex. Math ability, on one hand, and arithmetic complexity, on the other hand, seem to partly share neural underpinnings. This study addresses the question of whether this leads to an interaction of math ability and arithmetic complexity for multiplication and division on behavioral and neural levels. Previously screened individuals with high and low math ability solved multiplication and division problems in a written production paradigm while brain activation was assessed by combined functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). Arithmetic complexity was manipulated by using single-digit operands for simple multiplication problems and operands between 2 and 19 for complex multiplication problems and the corresponding division problems. On the behavioral level, individuals with low math ability needed more time for calculation, especially for complex arithmetic. On the neural level, fNIRS results revealed that these individuals showed less activation in the left supramarginal gyrus (SMG), superior temporal gyrus (STG) and inferior frontal gyrus (IFG) than individuals with high math ability when solving complex compared to simple arithmetic. This reflects the greater use of arithmetic fact retrieval and also the more efficient processing of arithmetic complexity by individuals with high math ability. Oscillatory EEG analysis generally revealed theta and alpha desynchronization with increasing arithmetic complexity but showed no interaction with math ability. Because of the discovered interaction for behavior and brain activation, we conclude that the consideration of individual differences is essential when investigating the neurocognitive processing of arithmetic.

Unbalanced Occlusion Modifies the Pattern of Brain Activity During Execution of a Finger to Thumb Motor Task

In order to assess possible influences of occlusion on motor performance, we studied by functional magnetic resonance imaging (fMRI) the changes in the blood oxygenation level dependent (BOLD) signal induced at brain level by a finger to thumb motor task in a population of subjects characterized by an asymmetric activation of jaw muscles during clenching (malocclusion). In these subjects, appropriate occlusal correction by an oral orthotic (bite) reduced the masticatory asymmetry. The finger to thumb task was performed while the subject's dental arches were touching, in two conditions: (a) with the teeth in direct contact (Bite OFF) and (b) with the bite interposed between the arches (Bite ON). Both conditions required only a very slight activation of masticatory muscles. Maps of the BOLD signal recorded during the movement were contrasted with the resting condition (activation maps). Between conditions comparison of the activation maps (Bite OFF/Bite ON) showed that, in Bite OFF, the BOLD signal was significantly higher in the trigeminal sensorimotor region, the premotor cortex, the cerebellum, the inferior temporal and occipital cortex, the calcarine cortex, the precuneus on both sides, as well as in the right posterior cingulate cortex. These data are consistent with the hypothesis that malocclusion makes movement performance more difficult, leading to a stronger activation of (a) sensorimotor areas not dealing with the control of the involved body part, (b) regions planning the motor sequence, and (c) the cerebellum, which is essential in motor coordination. Moreover, the findings of a higher activation of temporo-occipital cortex and precuneus/cingulus, respectively, suggest that, during malocclusion, the movement occurs with an increased visual imagery activity, and requires a stronger attentive effort.

Is an intact hippocampus necessary for answering 3 × 3? - Evidence from Alzheimer's disease

Recent evidence has suggested that the hippocampus supports learning and retrieval of arithmetic facts during childhood and adolescence. Whether the hippocampus is also involved in retrieving overlearned arithmetic facts (such as 3 × 5 = 15) during adult age is open for investigation. In this study, we assessed whether patients with hippocampal atrophy due to Alzheimer's disease (AD) are still able to retrieve overlearned arithmetic facts from memory. Sixteen patients (n = 13 with AD, n = 3 with Mild Cognitive Impairment - MCI) were evaluated using standard radiological, neurological, and neuropsychological test procedures. We adopted a multiple single-case analysis in order to acknowledge possible dissociations between hippocampal degeneration and intact arithmetic fact retrieval. All patients performed a neuropsychological screening battery assessing episodic memory as well as arithmetic processing, and underwent a 3-Tesla MRI procedure. A morphometric analysis comprising estimation of both cortical thickness and hippocampal volume, which also included a subfield analysis, was conducted. All patients had marked hippocampal atrophy (bilateral n = 15, unilateral n = 1) in comparison to healthy matched controls and showed deficits in episodic memory (delayed recall). However, 13 out of 16 patients performed in the average range of standardised norms during retrieval of overlearned arithmetic facts (i.e. multiplication tables). Our results suggest that intact retrieval of consolidated arithmetic facts from memory does not depend on the integrity of the hippocampus. This is in line with the view that the hippocampus plays a dynamic and time-limited role in arithmetic processing. While the hippocampus seems to be necessary for learning and consolidating new arithmetic facts in memory, it might not be critically involved in retrieving arithmetic facts when these are well consolidated in memory.

Neuroplasticity, bilingualism, and mental mathematics: A behavior-MEG study

Bilingual experience alters brain structure and enhances certain cognitive functions. Bilingualism can also affect mathematical processing. Reduced accuracy is commonly reported when arithmetic problems are presented in bilinguals' second (L2) vs. first (L1) language. We used MEG brain imaging during mental addition to characterize spatiotemporal dynamics during mental addition in bilingual adults. Numbers were presented auditorally and sequentially in bilinguals' L1 and L2, and brain and behavioral data were collected simultaneously. Behaviorally, bilinguals showed lower accuracy for two-digit addition in L2 compared to L1. Brain data showed stronger response magnitude in L2 versus L1 prior to calculation, especially when two-digit numbers were involved. Brain and behavioral data were significantly correlated. Taken together, our results suggest that differences between languages emerge prior to mathematical calculation, with implications for the role of language in mathematics.

Shared and distinct neural circuitry for nonsymbolic and symbolic double-digit addition

Symbolic arithmetic is a complex, uniquely human ability that is acquired through direct instruction. In contrast, the capacity to mentally add and subtract nonsymbolic quantities such as dot arrays emerges without instruction and can be seen in human infants and nonhuman animals. One possibility is that the mental manipulation of nonsymbolic arrays provides a critical scaffold for developing symbolic arithmetic abilities. To explore this hypothesis, we examined whether there is a shared neural basis for nonsymbolic and symbolic double-digit addition. In parallel, we asked whether there are brain regions that are associated with nonsymbolic and symbolic addition independently. First, relative to visually matched control tasks, we found that both nonsymbolic and symbolic addition elicited greater neural signal in the bilateral intraparietal sulcus (IPS), bilateral inferior temporal gyrus, and the right superior parietal lobule. Subsequent representational similarity analyses revealed that the neural similarity between nonsymbolic and symbolic addition was stronger relative to the similarity between each addition condition and its visually matched control task, but only in the bilateral IPS. These findings suggest that the IPS is involved in arithmetic calculation independent of stimulus format.

White matter neuro-plasticity in mental arithmetic: Changes in hippocampal connectivity following arithmetic drill training

Verbally-mediated arithmetic fact retrieval has been suggested to be subserved by a left-lateralized network including angular gyrus and hippocampus. However, the contribution of these areas to retrieval of arithmetic facts has been under debate lately, challenging the prominent role of the angular gyrus in arithmetic fact retrieval. In the present study, we evaluated changes in structural connectivity of left hippocampus and left angular gyrus in 32 participants following a short extensive drill training of complex multiplication. We observed a significant increase of structural connectivity in fibers encompassing the left hippocampus but not the left angular gyrus. As such, our findings substantiate that the left hippocampus plays a central role in arithmetic fact retrieval. While both structures, left angular gyrus and left hippocampus seem to be parts of the network processing arithmetic facts, hippocampus actually seems to subserve encoding and retrieval of arithmetic facts. In turn, the role of the left angular gyrus might rather be to mediate the fact retrieval network as to whether or not processes of fact retrieval are referred to.

What Does "Being an Expert" Mean to the Brain? Functional Specificity and Connectivity in Expertise

To what extent is varying cognitive expertise reflected in the brain's functional specificity and connectivity? We addressed this question by examining expertise in mathematics based on the fact that mathematical skills are one of the most critical cognitive abilities known to be a good predictor of academic achievement. We investigated processing of hierarchical structures, which is a fundamental process for building complex cognitive architecture. Experts and nonexperts in mathematics participated in processing hierarchical structures using algebraic expressions. Results showed that a modulating effect depending on expertise was observed specifically in nonexperts in the left inferior frontal gyrus around pars triangularis and frontal sulcus, the left intraparietal sulcus, and the right inferior parietal lobule. This expertise-dependent pattern of activation led to a crucial dissociation within the left prefrontal cortex. More interestingly, task-related functional networks were also modulated differently in the frontoparietal network for relatively good performance and in the frontostriatal network for poor performance. The present study indicates that a high level of expertise is evident in a small number of specific brain regions, whereas a low level of expertise is reflected by broadly distributed brain areas, along with divergent functional connectivity between experts and nonexperts.

Balancing the 2 Hemispheres in Simple Calculation: Evidence From Direct Cortical Electrostimulation

How do the parietal lobes contribute to simple calculation? Clinical and neuroimaging methods, which are based mainly on correlational evidence, have provided contrasting results so far. Here we used direct cortical electrostimulation during brain surgery to causally infer the role of the left and right parietal lobes in simple calculation. Stimulation provoked errors for addition and multiplication in different parietal areas on both hemispheres. Crucially, an innovative qualitative error analysis unveiled the functional contrast of the 2 parietal lobes. Right or left stimulation led to different types of substitution errors in multiplication, unveiling the function of the more active hemisphere. While inhibition of the left hemisphere led mainly to approximation errors, right hemisphere inhibition enhanced retrieval within a stored repertory. These results highlight the respective roles of each hemisphere in the network: rote retrieval of possible solutions by the left parietal areas and approximation to the correct solution by the right hemisphere. The bilateral orchestration between these functions guarantees precise calculation.

Where arithmetic and phonology meet: The meta-analytic convergence of arithmetic and phonological processing in the brain

Arithmetic facts can be solved using different strategies. Research suggests that some arithmetic problems, particularly those solved by fact retrieval, are related to phonological processing ability and elicit activity in left-lateralized brain regions that support phonological processing. However, it is unclear whether common brain regions support both retrieval-based arithmetic and phonological processing, and if these regions differ across children and adults. This study used activation likelihood estimation to investigate functional neural overlap between arithmetic and phonological processing, separately for children and adults. The meta-analyses in children showed six clusters of overlapping activation concentrated in bilateral frontal regions and in the left fusiform gyrus. The meta-analyses in adults yielded two clusters of concordant activity, one in the left inferior frontal gyrus and one in the left inferior parietal lobule. A qualitative comparison across the two age groups suggests that children show more bilateral and diffuse activation than adults, which may reflect attentional processes that support more effortful processing in children. The present meta-analyses contribute novel insights into the relationship between retrieval-based arithmetic and phonological processing in the brain across children and adults, and brain regions that may support processing of more complex symbolic representations, such as arithmetic facts and words.

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

The present study investigates the relation between resting-state functional connectivity (rsFC) of cytoarchitectonically defined subdivisions of the parietal cortex at the end of 1st grade and arithmetic performance at the end of 2nd grade. Results revealed a dissociable pattern of relations between rsFC and arithmetic competence among subdivisions of intraparietal sulcus (IPS) and angular gyrus (AG). rsFC between right hemisphere IPS subdivisions and contralateral IPS subdivisions positively correlated with arithmetic competence. In contrast, rsFC between the left hIP1 and the right medial temporal lobe, and rsFC between the left AG and left superior frontal gyrus, were negatively correlated with arithmetic competence. These results suggest that strong inter-hemispheric IPS connectivity is important for math development, reflecting either neurocognitive mechanisms specific to arithmetic processing, domain-general mechanisms that are particularly relevant to arithmetic competence, or structural 'cortical maturity'. Stronger connectivity between IPS, and AG, subdivisions and frontal and temporal cortices, however, appears to be negatively associated with math development, possibly reflecting the ability to disengage suboptimal problem-solving strategies during mathematical processing, or to flexibly reorient task-based networks. Importantly, the reported results pertain even when controlling for reading, spatial attention, and working memory, suggesting that the observed rsFC-behavior relations are specific to arithmetic competence.

Arithmetic learning in advanced age

Acquisition of numerical knowledge and understanding of numerical information are crucial for coping with the changing demands of our digital society. In this study, we assessed arithmetic learning in older and younger individuals in a training experiment including brain imaging. In particular, we assessed age-related effects of training intensity, prior arithmetic competence, and neuropsychological variables on the acquisition of new arithmetic knowledge and on the transfer to new, unknown problems. Effects were assessed immediately after training and after 3 months. Behavioural results showed higher training effects for younger individuals than for older individuals and significantly better performance after 90 problem repetitions than after 30 repetitions in both age groups. A correlation analysis indicated that older adults with lower memory and executive functions at baseline could profit more from intensive training. Similarly, training effects in the younger group were higher for those individuals who had lower arithmetic competence and executive functions prior to intervention. In younger adults, successful transfer was associated with higher executive functions. Memory and set-shifting emerged as significant predictors of training effects in the older group. For the younger group, prior arithmetic competence was a significant predictor of training effects, while cognitive flexibility was a predictor of transfer effects. After training, a subgroup of participants underwent an MRI assessment. A voxel-based morphometry analysis showed a significant interaction between training effects and grey matter volume of the right middle temporal gyrus extending to the angular gyrus for the younger group relative to the older group. The reverse contrast (older group vs. younger group) did not yield any significant results. These results suggest that improvements in arithmetic competence are supported by temporo-parietal areas in the right hemisphere in younger participants, while learning in older people might be more widespread. Overall, our study indicates that arithmetic learning depends on the training intensity as well as on person-related factors including individual age, arithmetic competence before training, memory, and executive functions. In conclusion, we suggest that major progress can be also achieved by older participants, but that interventions have to take into account individual variables in order to provide maximal benefit.

Reduction but no shift in brain activation after arithmetic learning in children: A simultaneous fNIRS-EEG study

Neurocognitive studies of arithmetic learning in adults have revealed decreasing brain activation in the fronto-parietal network, along with increasing activation of specific cortical and subcortical areas during learning. Both changes are associated with a shift from procedural to retrieval strategies for problem-solving. Here we address the critical, open question of whether similar neurocognitive changes are also evident in children. In this study, 20 typically developing children were trained to solve simple and complex multiplication problems. The one-session and two-week training effects were monitored using simultaneous functional near-infrared spectroscopy (fNIRS) and electroencephalography (EEG). FNIRS measurement after one session of training on complex multiplication problems revealed decreased activation at the left angular gyrus (AG), right superior parietal lobule, and right intraparietal sulcus. Two weeks of training led to decreased activation at the left AG and right middle frontal gyrus. For both simple and complex problems, we observed increased alpha power in EEG measurements as children worked on trained versus untrained problems. In line with previous multiplication training studies in adults, reduced activation within the fronto-parietal network was observed after training. Contrary to adults, we found that strategy shifts via arithmetic learning were not contingent on the activation of the left AG in children.

Mental arithmetic in the bilingual brain: Language matters

How do bilinguals solve arithmetic problems in each of their languages? We investigated this question by exploring the neural substrates of mental arithmetic in bilinguals. Critically, our population was composed of a homogeneous group of adults who were fluent in both of their instruction languages (i.e., German as first instruction language and French as second instruction language). Twenty bilinguals were scanned with fMRI (3T) while performing mental arithmetic. Both simple and complex problems were presented to disentangle memory retrieval occuring in very simple problems from arithmetic computation occuring in more complex problems. In simple additions, the left temporal regions were more activated in German than in French, whereas no brain regions showed additional activity in the reverse constrast. Complex additions revealed the reverse pattern, since the activations of regions for French surpassed the same computations in German and the extra regions were located predominantly in occipital regions. Our results thus highlight that highly proficient bilinguals rely on differential activation patterns to solve simple and complex additions in each of their languages, suggesting different solving procedures. The present study confirms the critical role of language in arithmetic problem solving and provides novel insights into how highly proficient bilinguals solve arithmetic problems.

15q11.2 CNV affects cognitive, structural and functional correlates of dyslexia and dyscalculia

Several copy number variants have been associated with neuropsychiatric disorders and these variants have been shown to also influence cognitive abilities in carriers unaffected by psychiatric disorders. Previously, we associated the 15q11.2(BP1-BP2) deletion with specific learning disabilities and a larger corpus callosum. Here we investigate, in a much larger sample, the effect of the 15q11.2(BP1-BP2) deletion on cognitive, structural and functional correlates of dyslexia and dyscalculia. We report that the deletion confers greatest risk of the combined phenotype of dyslexia and dyscalculia. We also show that the deletion associates with a smaller left fusiform gyrus. Moreover, tailored functional magnetic resonance imaging experiments using phonological lexical decision and multiplication verification tasks demonstrate altered activation in the left fusiform and the left angular gyri in carriers. Thus, by using convergent evidence from neuropsychological testing, and structural and functional neuroimaging, we show that the 15q11.2(BP1-BP2) deletion affects cognitive, structural and functional correlates of both dyslexia and dyscalculia.

Re-assessing acalculia: Distinguishing spatial and purely arithmetical deficits in right-hemisphere damaged patients

Arithmetical deficits in right-hemisphere damaged patients have been traditionally considered secondary to visuo-spatial impairments, although the exact relationship between the two deficits has rarely been assessed. The present study implemented a voxelwise lesion analysis among 30 right-hemisphere damaged patients and a controlled, matched-sample, cross-sectional analysis with 35 cognitively normal controls regressing three composite cognitive measures on standardized numerical measures. The results showed that patients and controls significantly differ in Number comprehension, Transcoding, and Written operations, particularly subtractions and multiplications. The percentage of patients performing below the cutoffs ranged between 27% and 47% across these tasks. Spatial errors were associated with extensive lesions in fronto-temporo-parietal regions -which frequently lead to neglect- whereas pure arithmetical errors appeared related to more confined lesions in the right angular gyrus and its proximity. Stepwise regression models consistently revealed that spatial errors were primarily predicted by composite measures of visuo-spatial attention/neglect and representational abilities. Conversely, specific errors of arithmetic nature linked to representational abilities only. Crucially, the proportion of arithmetical errors (ranging from 65% to 100% across tasks) was higher than that of spatial ones. These findings thus suggest that unilateral right hemisphere lesions can directly affect core numerical/arithmetical processes, and that right-hemisphere acalculia is not only ascribable to visuo-spatial deficits as traditionally thought.

Fact learning in complex arithmetic-the role of the angular gyrus revisited

In recent theoretical considerations as well as in neuroimaging findings the left angular gyrus (AG) has been associated with the retrieval of arithmetic facts. This interpretation was corroborated by higher AG activity when processing trained as compared with untrained multiplication problems. However, so far neural correlates of processing trained versus untrained problems were only compared after training. We employed an established learning paradigm (i.e., extensive training of multiplication problems) but measured brain activation before and afte training to evaluate neural correlates of arithmetic fact acquisition more specifically. When comparing activation patterns for trained and untrained problems of the post-training session, higher AG activation for trained problems was replicated. However, when activation for trained problems was compared to activation for the same problems in the pre-training session, no signal change in the AG was observed. Instead, our results point toward a central role of hippocampal, para-hippocampal, and retrosplenial structures in arithmetic fact retrieval. We suggest that the AG might not be associated with the actual retrieval of arithmetic facts, and outline an attentional account of the role of the AG in arithmetic fact retrieval that is compatible with recent attention to memory hypotheses. Hum Brain Mapp 37:3061-3079, 2016. © 2016 Wiley Periodicals, Inc.

Dyscalculia and the Calculating Brain

Dyscalculia, like dyslexia, affects some 5% of school-age children but has received much less investigative attention. In two thirds of affected children, dyscalculia is associated with another developmental disorder like dyslexia, attention-deficit disorder, anxiety disorder, visual and spatial disorder, or cultural deprivation. Infants, primates, some birds, and other animals are born with the innate ability, called subitizing, to tell at a glance whether small sets of scattered dots or other items differ by one or more item. This nonverbal approximate number system extends mostly to single digit sets as visual discrimination drops logarithmically to "many" with increasing numerosity (size effect) and crowding (distance effect). Preschoolers need several years and specific teaching to learn verbal names and visual symbols for numbers and school agers to understand their cardinality and ordinality and the invariance of their sequence (arithmetic number line) that enables calculation. This arithmetic linear line differs drastically from the nonlinear approximate number system mental number line that parallels the individual number-tuned neurons in the intraparietal sulcus in monkeys and overlying scalp distribution of discrete functional magnetic resonance imaging activations by number tasks in man. Calculation is a complex skill that activates both visual and spatial and visual and verbal networks. It is less strongly left lateralized than language, with approximate number system activation somewhat more right sided and exact number and arithmetic activation more left sided. Maturation and increasing number skill decrease associated widespread non-numerical brain activations that persist in some individuals with dyscalculia, which has no single, universal neurological cause or underlying mechanism in all affected individuals.

Neurocognitive Effects of Transcranial Direct Current Stimulation in Arithmetic Learning and Performance: A Simultaneous tDCS-fMRI Study

BACKGROUND

A small but increasing number of studies suggest that non-invasive brain stimulation by means of transcranial direct current stimulation (tDCS) can modulate arithmetic processes that are essential for higher-order mathematical skills and that are impaired in dyscalculic individuals. However, little is known about the neural mechanisms underlying such stimulation effects, and whether they are specific to cognitive processes involved in different arithmetic tasks.

METHODS

We addressed these questions by applying tDCS during simultaneous functional magnetic resonance imaging (fMRI) while participants were solving two types of complex subtraction problems: repeated problems, relying on arithmetic fact learning and problem-solving by fact retrieval, and novel problems, requiring calculation procedures. Twenty participants receiving left parietal anodal plus right frontal cathodal stimulation were compared with 20 participants in a sham condition.

RESULTS

We found a strong cognitive and neural dissociation between repeated and novel problems. Repeated problems were solved more accurately and elicited increased activity in the bilateral angular gyri and medial plus lateral prefrontal cortices. Solving novel problems, in contrast, was accompanied by stronger activation in the bilateral intraparietal sulci and the dorsomedial prefrontal cortex. Most importantly, tDCS decreased the activation of the right inferior frontal cortex while solving novel (compared to repeated) problems, suggesting that the cathodal stimulation rendered this region unable to respond to the task-specific cognitive demand.

CONCLUSIONS

The present study revealed that tDCS during arithmetic problem-solving can modulate the neural activity in proximity to the electrodes specifically when the current demands lead to an engagement of this area.

What letters can "learn" from Arabic digits--fMRI-controlled single case therapy study of peripheral agraphia

Research on (hand-)writing has revealed that Exner's area subserves transferring linguistic impulses into writing programmes. We report on a patient with a lesion affecting Broca's and Exner's area suffering from severe peripheral agraphia for letters but not for Arabic digits. Analogous to semantic (magnitude) information in numbers, we developed a specifically tailored writing training: additional mental imagery based semantic information was attached to letters. The training resulted in significant improvements. Imaging data revealed stronger fronto-parietal network activity including perilesional activation around Exner's area and precuneus for writing letters to dictation than for writing letters corresponding to their mental image expressions. Follow-up testing showed not only stable training effects but also an activation shift into the left angular gyrus. Results document neuronal correlates of a successful intervention by attaching additional meanings to letters in order to retrieve their grapho-motor patterns. These findings contribute to understanding the impact of Exner's area.

Left inferior-parietal lobe activity in perspective tasks: identity statements

We investigate the theory that the left inferior parietal lobe (IPL) is closely associated with tracking potential differences of perspective. Developmental studies find that perspective tasks are mastered at around 4 years of age. Our first study, meta-analyses of brain imaging studies shows that perspective tasks specifically activate a region in the left IPL and precuneus. These tasks include processing of false belief, visual perspective, and episodic memory. We test the location specificity theory in our second study with an unusual and novel kind of perspective task: identity statements. According to Frege's classical logical analysis, identity statements require appreciation of modes of presentation (perspectives). We show that identity statements, e.g., "the tour guide is also the driver" activate the left IPL in contrast to a control statements, "the tour guide has an apprentice." This activation overlaps with the activations found in the meta-analysis. This finding is confirmed in a third study with different types of statements and different comparisons. All studies support the theory that the left IPL has as one of its overarching functions the tracking of perspective differences. We discuss how this function relates to the bottom-up attention function proposed for the bilateral IPL.