The functional anatomy of single-digit arithmetic in children with developmental dyslexia

Neuroanatomical, transcriptomic, and molecular correlates of math ability and their prognostic value for predicting learning outcomes

Foundational mathematical abilities, acquired in early childhood, are essential for success in our technology-driven society. Yet, the neurobiological mechanisms underlying individual differences in children's mathematical abilities and learning outcomes remain largely unexplored. Leveraging one of the largest multicohort datasets from children at a pivotal stage of knowledge acquisition, we first establish a replicable mathematical ability-related imaging phenotype (MAIP). We then show that brain gene expression profiles enriched for candidate math ability-related genes, neuronal signaling, synaptic transmission, and voltage-gated potassium channel activity contributed to the MAIP. Furthermore, the similarity between MAIP gene expression signatures and brain structure, acquired before intervention, predicted learning outcomes in two independent math tutoring cohorts. These findings advance our knowledge of the interplay between neuroanatomical, transcriptomic, and molecular mechanisms underlying mathematical ability and reveal predictive biomarkers of learning. Our findings have implications for the development of personalized education and interventions.

Activation and functional connectivity of cerebellum during reading and during arithmetic in children with combined reading and math disabilities

Background

Reading and math constitute important academic skills, and as such, reading disability (RD or developmental dyslexia) and math disability (MD or developmental dyscalculia) can have negative consequences for children's educational progress. Although RD and MD are different learning disabilities, they frequently co-occur. Separate theories have implicated the cerebellum and its cortical connections in RD and in MD, suggesting that children with combined reading and math disability (RD + MD) may have altered cerebellar function and disrupted functional connectivity between the cerebellum and cortex during reading and during arithmetic processing.

Methods

Here we compared Control and RD + MD groups during a reading task as well as during an arithmetic task on (i) activation of the cerebellum, (ii) background functional connectivity, and (iii) task-dependent functional connectivity between the cerebellum and the cortex.

Results

The two groups (Control, RD + MD) did not differ for either task (reading, arithmetic) on any of the three measures (activation, background functional connectivity, task-dependent functional connectivity).

Conclusion

These results do not support theories that children's deficits in reading and math originate in the cerebellum.

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.

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.

Examination of common and unique brain regions for atypical reading and math: a meta-analysis

The purpose of this study is to identify consistencies across functional neuroimaging studies regarding common and unique brain regions/networks for individuals with reading difficulties (RD) and math difficulties (MD) compared to typically developing (TD) individuals. A systematic search of the literature, utilizing multiple databases, yielded 116 functional magnetic resonance imaging and positron emission tomography studies that met the criteria. Coordinates that directly compared TD with either RD or MD were entered into GingerALE (Brainmap.org). An activation likelihood estimate (ALE) meta-analysis was conducted to examine common and unique brain regions for RD and MD. Overall, more studies examined RD (n = 96) than MD (n = 20). Across studies, overactivation for reading and math occurred in the right insula and inferior frontal gyrus for atypically developing (AD) > TD comparisons, albeit in slightly different areas of these regions; however, inherent threshold variability across imaging studies could diminish overlying regions. For TD > AD comparisons, there were no similar or overlapping brain regions. Results indicate there were domain-specific differences for RD and MD; however, there were some similarities in the ancillary recruitment of executive functioning skills. Theoretical and practical implications for researchers and educators are discussed.

An fMRI study of finger movements in children with and without dyslexia

Introduction

Developmental dyslexia is a language-based reading disability, yet some have reported motor impairments, usually attributed to cerebellar dysfunction.

Methods

Using fMRI, we compared children with and without dyslexia during irregularly paced, left or right-hand finger tapping. Next, we examined seed-to-voxel intrinsic functional connectivity (iFC) using six seed regions of the motor system (left and right anterior lobe of the cerebellum, SM1 and SMA).

Results

A whole-brain task-evoked analysis revealed relatively less activation in the group with dyslexia in right anterior cerebellum during right hand tapping. For iFC, we found the group with dyslexia to have greater iFC between the right SM1 seed and a medial aspect of right postcentral gyrus for left hand tapping; and greater iFC between the left SM1 seed and left thalamus, as well as weaker local iFC around the left SM1 seed region for right hand tapping. Lastly, extracted activity and connectivity values that had been identified in these between-group comparisons were not correlated with measures of reading.

Discussion

We conclude that there are some aberrations in motor system function in children with dyslexia, but these are not tied to reading ability.

EEG based functional brain networks analysis in dyslexic children during arithmetic task

Developmental Dyslexia is a neuro-developmental disorder that often refers to a phonological processing deficit regardless of average IQ. The present study investigated the distinct functional changes in brain networks of dyslexic children during arithmetic task performance using an electroencephalogram. Fifteen dyslexic children and fifteen normally developing children (NDC) were recruited and performed an arithmetic task. Brain functional network measures such as node strength, clustering coefficient, characteristic pathlength and small-world were calculated using graph theory methods for both groups. Task performance showed significantly less performance accuracy in dyslexics against NDC. The neural findings showed increased connectivity in the delta band and reduced connectivity in theta, alpha, and beta band at temporoparietal, and prefrontal regions in dyslexic group while performing the task. The node strengths were found to be significantly high in delta band (T3, O1, F8 regions) and low in theta (T5, P3, Pz regions), beta (Pz) and gamma band (T4 and prefrontal regions) during the task in dyslexics compared to the NDC. The clustering coefficient was found to be significantly low in the dyslexic group (theta and alpha band) and characteristic pathlength was found to be significantly high in the dyslexic group (theta and alpha band) compared to the NDC group while performing task. In conclusion, the present study shows evidence for poor fact-retrieval mechanism and altered network topology in dyslexic brain networks during arithmetic task performance.

Anxiety, Motivation, and Competence in Mathematics and Reading for Children With and Without Learning Difficulties

Knowledge of the relations among learners' socio-emotional characteristics and competencies as they engage in mathematics and reading is limited, especially for children with academic difficulties. This study examined the relations between anxiety, motivation, and competence in mathematics and reading, within and across domains, in an academically-diverse set of 8-13-year-old learners (n = 146). To measure anxiety and motivation across domains, we paired existing measures of math anxiety and reading motivation with researcher-developed analogs for reading anxiety and math motivation. Participants completed standardized assessments of mathematics and reading, anxiety and motivation surveys for math and reading, and a measure of nonverbal cognitive ability. Results showed high internal consistency for all anxiety and motivation scales (Cronbach's alpha = 0.76-0.91). Pearson correlations showed that within and across domains, participants with higher competence had lower anxiety and higher motivation. Higher anxiety was also associated with lower motivation. Regression analyses showed that for both math and reading, within-domain motivation was a stronger predictor of competence than anxiety. There was a unidirectional across-domain relation: socio-emotional characteristics for reading predicted math competence, after accounting for nonverbal cognitive ability, age, gender, and within-domain anxiety and motivation. Results contribute to knowledge of the socio-emotional characteristics of children with and without learning difficulties in association with reading and math activities. Implications of a unidirectional socio-emotional link between the two domains can advance research and theory of the relations among socio-emotional characteristics and competence for academically-diverse learners.

Functional neuroanatomy of arithmetic in monolingual and bilingual adults and children

Prior studies on the brain bases of arithmetic have not focused on (or even described) their participants' language backgrounds. Yet, unlike monolinguals, early bilinguals have the capacity to solve arithmetic problems in both of their two languages. This raises the question whether this ability, or any other experience that comes with being bilingual, affects brain activity for arithmetic in bilinguals relative to monolinguals. Here, we used functional magnetic resonance imaging to compare brain activity in 44 English monolinguals and 44 Spanish-English early bilinguals, during the solving of arithmetic problems in English. We used a factorial design to test for a main effect of bilingual Language Experience. Based on the known modulating roles of arithmetic operation and age, we used two arithmetic tasks (addition and subtraction) and studied two age groups (adults and children). When collapsing across operations and age, we found broad bilateral activation for arithmetic in both the monolingual group and the bilingual group. However, an analysis of variance revealed that there was no effect of Language Experience, nor an interaction of Language Experience with Operation or Age Group. Bayesian analyses within regions of interest chosen for their role in arithmetic further supported the finding of no effect of Language Experience on brain activity underlying arithmetic. We conclude that early bilingualism does not influence the functional neuroanatomy of simple arithmetic.

Convergent and divergent brain structural and functional abnormalities associated with developmental dyslexia

Brain abnormalities in the reading network have been repeatedly reported in individuals with developmental dyslexia (DD); however, it is still not totally understood where the structural and functional abnormalities are consistent/inconsistent across languages. In the current multimodal meta-analysis, we found convergent structural and functional alterations in the left superior temporal gyrus across languages, suggesting a neural signature of DD. We found greater reduction in grey matter volume and brain activation in the left inferior frontal gyrus in morpho-syllabic languages (e.g. Chinese) than in alphabetic languages, and greater reduction in brain activation in the left middle temporal gyrus and fusiform gyrus in alphabetic languages than in morpho-syllabic languages. These language differences are explained as consequences of being DD while learning a specific language. In addition, we also found brain regions that showed increased grey matter volume and brain activation, presumably suggesting compensations and brain regions that showed inconsistent alterations in brain structure and function. Our study provides important insights about the etiology of DD from a cross-linguistic perspective with considerations of consistency/inconsistency between structural and functional alterations.

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.

Cerebellar function in children with and without dyslexia during single word processing

The cerebellar deficit hypothesis of dyslexia posits that dysfunction of the cerebellum is the underlying cause for reading difficulties observed in this common learning disability. The present study used functional magnetic resonance imaging (fMRI) and a single word processing task to test for differences in activity and connectivity in children with (n = 23) and without (n = 23) dyslexia. We found cerebellar activity in the control group when word processing was compared to fixation, but not when it was compared to the active baseline task designed to reveal activity specific to reading. In the group with dyslexia there was no cerebellar activity for either contrasts and there were no differences when they were compared to children without dyslexia. Turning to functional connectivity (FC) in the controls, background FC (i.e., not specific to reading) was predominately found between the cerebellum and the occipitaltemporal cortex. In the group with dyslexia, there was background FC between the cerebellum and several cortical regions. When comparing the two groups, they differed in background FC in connections between the seed region right crus I and three left‐hemisphere perisylvian target regions. However, there was no task‐specific FC for word processing in either group and no between‐group differences. Together the results do not support the theory that the cerebellum is affected functionally during reading in children with dyslexia.

Are specific learning disorders truly specific, and are they disorders?

Specific learning disorders, such as dyslexia and dyscalculia, are frequently studied to inform our understanding of cognitive development, genetic mechanisms and brain function. In this Opinion Paper, we discuss limitations of this research approach, including the use of arbitrary criteria to select groups of children, heterogeneity within groups and overlap between domains of learning. By drawing on evidence from cognitive science, neuroscience and genetics, we propose an alternative, dimensional framework. We argue that we need to overcome the problems associated with a categorical approach by taking into account interacting factors at multiple levels of analysis that are associated with overlapping rather than entirely distinct domains of learning. We conclude that this research strategy will allow for a richer understanding of learning and development.

Visual form perception is fundamental for both reading comprehension and arithmetic computation

Visual perception has been found to be a critical factor for reading comprehension and arithmetic computation in separate lines of research with different measures of visual form perception. The current study of 1099 Chinese elementary school students investigated whether the same visual form perception (assessed by a geometric figure matching task) underlies both reading comprehension and arithmetic computation. The results showed that visual form perception had close relations with both reading comprehension and arithmetic computation, even after controlling for age, gender, and cognitive factors such as processing speed, attention, working memory, visuo-spatial processing, and general intelligence. Results also showed that numerosity comparison's relations with reading comprehension and arithmetic computation were fully accounted for by visual form perception. These results suggest that reading comprehension and arithmetic computation might share a similar visual form processing mechanism.

Understanding comorbidity of learning disorders: task-dependent estimates of prevalence

BACKGROUND

Reading disorder (RD) and mathematics disorder (MD) frequently co-occur. However, the exact comorbidity rates differ largely between studies. Given that MD is characterised by high heterogeneity on the symptom level, differences in comorbidity rates may result from different mathematical subskills used to define MD. Comorbidity rates with RD are likely to be higher when MD is measured by mathematical subskills that do not only build on number processing, but also require language (i.e. arithmetic fluency), than when measured by magnitude processing skills.

METHODS

The association between literacy, arithmetic fluency and magnitude processing as well as the overlap between deficits in these domains were assessed in a representative sample of 1,454 third Graders.

RESULTS

Associations were significantly higher between literacy and arithmetic, than between literacy and magnitude processing. This was also reflected in comorbidity rates: comorbidity rates between literacy and arithmetic deficits were four times higher than expected by chance, whereas comorbidity rates between literacy and magnitude processing deficits did not exceed chance rate. Deficits in the two mathematical subskills showed some overlap, but also revealed dissociations, corroborating the high heterogeneity of MD. Results are interpreted within a multiple-deficit framework and implications for diagnosis and intervention are discussed.

CONCLUSIONS

The overlap between RD and MD depends on the subskills used to define MD. Due to shared domain-general factors mathematical subskills that draw on language skills are more strongly associated with literacy than those that do not require language. The findings further indicate that the same symptom, such as deficits in arithmetic, can be associated with different cognitive deficits, a deficit in language skills or a deficit in number processing.

Electrophysiological markers of poor versus superior math abilities in healthy individuals

Interindividual differences in the numerical ability of healthy adults have been previously demonstrated, mainly with tasks involving mental number line or size representation. However, electrophysiological correlates of superior versus poor arithmetic ability (in the healthy population) have been scarcely investigated. We correlated electric potentials with math performance in 13 skilled and 13 poor calculators selected from a sample of 41 graduate students on the basis of their poor or superior math abilities assessed through a timed test. EEG was recorded from 128 channels while participants solved 352 arithmetical operations (additions, subtractions, multiplications, divisions) and decided whether the provided solution was correct or incorrect. Overall skilled individuals correctly solved a higher number of operations than poor calculators and had faster response times. Consistently, the latency of fronto-central P300 component of event-related potentials (ERPs) peaked earlier in the skilled than poor group. The P300 was larger in amplitude to correct than incorrect solutions, but just in the skilled group, with a tendency found in poor calculators. Spearman's ρ correlation coefficient analyses showed that the larger P300 response was to correct arithmetic solutions, the better the performance; conversely, the larger the P300 amplitude was to incorrect solutions, the worse the performance. The results suggest that poor calculators had a less clear representation of arithmetic solutions and difficulty in quickly accessing it. This study provides a standard method for directly investigating math abilities throughout ERP recordings that could be useful for assessing acalculia/dyscalculia in the clinical population (children, elderly, brain-damaged patients).

Neural signatures of co-occurring reading and mathematical difficulties

Impaired abilities in multiple domains is common in children with learning difficulties. Co-occurrence of low reading and mathematical abilities (LRLM) appears in almost every second child with learning difficulties. However, little is known regarding the neural bases of this combination. Leveraging a unique and tightly controlled sample including children with LRLM, isolated low reading ability (LR), and isolated low mathematical ability (LM), we uncover a distinct neural signature in children with co-occurring low reading and mathematical abilities differentiable from LR and LM. Specifically, we show that LRLM is neuroanatomically distinct from both LR and LM based on reduced cortical folding of the right parahippocampal gyrus, a medial temporal lobe region implicated in visual associative learning. LRLM children were further distinguished from LR and LM by patterns of intrinsic functional connectivity between parahippocampal gyrus and brain circuitry underlying reading and numerical quantity processing. Our results critically inform cognitive and neural models of LRLM by implicating aberrations in both domain-specific and domain-general brain regions involved in reading and mathematics. More generally, our results provide the first evidence for distinct multimodal neural signatures associated with LRLM, and suggest that this population displays an independent phenotype of learning difficulty that cannot be explained simply as a combination of isolated low reading and mathematical abilities.

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.

Arithmetic in the developing brain: A review of brain imaging studies

Brain imaging studies on academic achievement offer an exciting window on experience-dependent cortical plasticity, as they allow us to understand how developing brains change when children acquire culturally transmitted skills. This contribution focuses on the learning of arithmetic, which is quintessential to mathematical development. The nascent body of brain imaging studies reveals that arithmetic recruits a large set of interconnected areas, including prefrontal, posterior parietal, occipito-temporal and hippocampal areas. This network undergoes developmental changes in its function, connectivity and structure, which are not yet fully understood. This network only partially overlaps with what has been found in adults, and clear differences are observed in the recruitment of the hippocampus, which are related to the development of arithmetic fact retrieval. Despite these emerging trends, the literature remains scattered, particularly in the context of atypical development. Acknowledging the distributed nature of the arithmetic network, future studies should focus on connectivity and analytic approaches that investigate patterns of brain activity, coupled with a careful design of the arithmetic tasks and assessments of arithmetic strategies. Such studies will produce a more comprehensive understanding of how the arithmetical brain unfolds, how it changes over time, and how it is impaired in atypical development.

Dyscalculia and dyslexia: Different behavioral, yet similar brain activity profiles during arithmetic

Brain disorders are often investigated in isolation, but very different conclusions might be reached when studies directly contrast multiple disorders. Here, we illustrate this in the context of specific learning disorders, such as dyscalculia and dyslexia. While children with dyscalculia show deficits in arithmetic, children with dyslexia present with reading difficulties. Furthermore, the comorbidity between dyslexia and dyscalculia is surprisingly high. Different hypotheses have been proposed on the origin of these disorders (number processing deficits in dyscalculia, phonological deficits in dyslexia) but these have never been directly contrasted in one brain imaging study. Therefore, we compared the brain activity of children with dyslexia, children with dyscalculia, children with comorbid dyslexia/dyscalculia and healthy controls during arithmetic in a design that allowed us to disentangle various processes that might be associated with the specific or common neural origins of these learning disorders. Participants were 62 children aged 9 to 12, 39 of whom had been clinically diagnosed with a specific learning disorder (dyscalculia and/or dyslexia). All children underwent fMRI scanning while performing an arithmetic task in different formats (dot arrays, digits and number words). At the behavioral level, children with dyscalculia showed lower accuracy when subtracting dot arrays, and all children with learning disorders were slower in responding compared to typically developing children (especially in symbolic formats). However, at the neural level, analyses pointed towards substantial neural similarity between children with learning disorders: Control children demonstrated higher activation levels in frontal and parietal areas than the three groups of children with learning disorders, regardless of the disorder. A direct comparison between the groups of children with learning disorders revealed similar levels of neural activation throughout the brain across these groups. Multivariate subject generalization analyses were used to statistically test the degree of similarity, and confirmed that the neural activation patterns of children with dyslexia, dyscalculia and dyslexia/dyscalculia were highly similar in how they deviated from neural activation patterns in control children. Collectively, these results suggest that, despite differences at the behavioral level, the brain activity profiles of children with different learning disorders during arithmetic may be more similar than initially thought.

Strategy over operation: neural activation in subtraction and multiplication during fact retrieval and procedural strategy use in children

Arithmetic development is characterized by strategy shifts between procedural strategy use and fact retrieval. This study is the first to explicitly investigate children's neural activation associated with the use of these different strategies. Participants were 26 typically developing 4th graders (9- to 10-year-olds), who, in a behavioral session, were asked to verbally report on a trial-by-trial basis how they had solved 100 subtraction and multiplication items. These items were subsequently presented during functional magnetic resonance imaging. An event-related design allowed us to analyze the brain responses during retrieval and procedural trials, based on the children's verbal reports. During procedural strategy use, and more specifically for the decomposition of operands strategy, activation increases were observed in the inferior and superior parietal lobes (intraparietal sulci), inferior to superior frontal gyri, bilateral areas in the occipital lobe, and insular cortex. For retrieval, in comparison to procedural strategy use, we observed increased activity in the bilateral angular and supramarginal gyri, left middle to inferior temporal gyrus, right superior temporal gyrus, and superior medial frontal gyrus. No neural differences were found between the two operations under study. These results are the first in children to provide direct evidence for alternate neural activation when different arithmetic strategies are used and further unravel that previously found effects of operation on brain activity reflect differences in arithmetic strategy use. Hum Brain Mapp 38:4657-4670, 2017. © 2017 Wiley Periodicals, Inc.

Distinct influences of affective and cognitive factors on children's non-verbal and verbal mathematical abilities

Individual differences in children's math performance have been associated with math anxiety, attention problems, working memory (WM), and reading skills, but the mechanisms by which these factors jointly contribute to children's math achievement are unknown. Here, we use structural equation modeling to characterize the relation between these factors and their influence on non-verbal Numerical Operations (NO) and verbal Math Reasoning (MR) in 330 children (M=8.34years). Our findings indicate that WM plays a central role in both non-verbal NO and verbal MR, whereas math anxiety and reading comprehension have unique and more pronounced influences on MR, compared to NO. Our study elucidates how affective and cognitive factors distinctly influence non-verbal and verbal mathematical problem solving.

The functional architectures of addition and subtraction: Network discovery using fMRI and DCM

The neuronal mechanisms underlying arithmetic calculations are not well understood but the differences between mental addition and subtraction could be particularly revealing. Using fMRI and dynamic causal modeling (DCM), this study aimed to identify the distinct neuronal architectures engaged by the cognitive processes of simple addition and subtraction. Our results revealed significantly greater activation during subtraction in regions along the dorsal pathway, including the left inferior frontal gyrus (IFG), middle portion of dorsolateral prefrontal cortex (mDLPFC), and supplementary motor area (SMA), compared with addition. Subsequent analysis of the underlying changes in connectivity - with DCM - revealed a common circuit processing basic (numeric) attributes and the retrieval of arithmetic facts. However, DCM showed that addition was more likely to engage (numeric) retrieval-based circuits in the left hemisphere, while subtraction tended to draw on (magnitude) processing in bilateral parietal cortex, especially the right intraparietal sulcus (IPS). Our findings endorse previous hypotheses about the differences in strategic implementation, dominant hemisphere, and the neuronal circuits underlying addition and subtraction. Moreover, for simple arithmetic, our connectivity results suggest that subtraction calls on more complex processing than addition: auxiliary phonological, visual, and motor processes, for representing numbers, were engaged by subtraction, relative to addition. Hum Brain Mapp 38:3210-3225, 2017. © 2017 Wiley Periodicals, Inc.

An Extension of the Procedural Deficit Hypothesis from Developmental Language Disorders to Mathematical Disability

Mathematical disability (MD) is a neurodevelopmental disorder affecting math abilities. Here, we propose a new explanatory account of MD, the procedural deficit hypothesis (PDH), which may further our understanding of the disorder. According to the PDH of MD, abnormalities of brain structures subserving the procedural memory system can lead to difficulties with math skills learned in this system, as well as problems with other functions that depend on these brain structures. This brain-based account is motivated in part by the high comorbidity between MD and language disorders such as dyslexia that may be explained by the PDH, and in part by the likelihood that learning automatized math skills should depend on procedural memory. Here, we first lay out the PDH of MD, and present specific predictions. We then examine the existing literature for each prediction, while pointing out weaknesses and gaps to be addressed by future research. Although we do not claim that the PDH is likely to fully explain MD, we do suggest that the hypothesis could have substantial explanatory power, and that it provides a useful theoretical framework that may advance our understanding of the disorder.

Functional neuroanatomy of arithmetic and word reading and its relationship to age

Arithmetic and written language are uniquely human skills acquired during early schooling and used daily. While prior studies have independently characterized the neural bases for arithmetic and reading, here we examine both skills in a single study to capture their shared and unique cognitive mechanisms, as well as the role of age/experience in modulating their neural representations. We used functional MRI in 7- to 29-year-olds who performed single-digit subtraction, single-digit addition, and single-word reading. Using a factorial design, we examined the main effects of Task (subtraction, addition, reading) and Age (as a continuous variable), and their interactions. A main effect of Task revealed preferential activation for subtraction in bilateral intraparietal sulci and supramarginal gyri, right insula, inferior frontal gyrus, and cingulate. The right middle temporal gyrus and left superior temporal gyrus were preferentially active for both addition and reading, and left fusiform gyrus was preferentially active for reading. A main effect of Age revealed increased activity in older participants in right angular gyrus, superior temporal sulcus, and putamen, and less activity in left supplementary motor area, suggesting a left frontal to right temporo-parietal shift of activity with increasing age/experience across all tasks. Interactions for Task by Age were found in right hippocampus and left middle frontal gyrus, with older age invoking greater activity for addition and at the same time less activity for subtraction and reading. Together, in a study conducted in the same participants using similar task and acquisition parameters, the results reveal the neural substrates of these educationally relevant cognitive skills in typical participants in the context of age/experience.

Individual differences in children's mathematics achievement: The roles of symbolic numerical magnitude processing and domain-general cognitive functions

This contribution reviewed the available evidence on the domain-specific and domain-general neurocognitive determinants of children's arithmetic development, other than nonsymbolic numerical magnitude processing, which might have been overemphasized as a core factor of individual differences in mathematics and dyscalculia. We focused on symbolic numerical magnitude processing, working memory, and phonological processing, as these determinants have been most researched and their roles in arithmetic can be predicted against the background of brain imaging data. Our review indicates that symbolic numerical magnitude processing is a major determinant of individual differences in arithmetic. Working memory, particularly the central executive, also plays a role in learning arithmetic, but its influence appears to be dependent on the learning stage and experience of children. The available evidence on phonological processing suggests that it plays a more subtle role in children's acquisition of arithmetic facts. Future longitudinal studies should investigate these factors in concert to understand their relative contribution as well as their mediating and moderating roles in children's arithmetic development.

Dyslexic children lack word selectivity gradients in occipito-temporal and inferior frontal cortex

fMRI studies using a region-of-interest approach have revealed that the ventral portion of the left occipito-temporal cortex, which is specialized for orthographic processing of visually presented words (and includes the so-called "visual word form area", VWFA), is characterized by a posterior-to-anterior gradient of increasing selectivity for words in typically reading adults, adolescents, and children (e.g. Brem et al., 2006, 2009). Similarly, the left inferior frontal cortex (IFC) has been shown to exhibit a medial-to-lateral gradient of print selectivity in typically reading adults (Vinckier et al., 2007). Functional brain imaging studies of dyslexia have reported relative underactivity in left hemisphere occipito-temporal and inferior frontal regions using whole-brain analyses during word processing tasks. Hence, the question arises whether gradient sensitivities in these regions are altered in dyslexia. Indeed, a region-of-interest analysis revealed the gradient-specific functional specialization in the occipito-temporal cortex to be disrupted in dyslexic children (van der Mark et al., 2009). Building on these studies, we here (1) investigate if a word-selective gradient exists in the inferior frontal cortex in addition to the occipito-temporal cortex in normally reading children, (2) compare typically reading with dyslexic children, and (3) examine functional connections between these regions in both groups. We replicated the previously reported anterior-to-posterior gradient of increasing selectivity for words in the left occipito-temporal cortex in typically reading children, and its absence in the dyslexic children. Our novel finding is the detection of a pattern of increasing selectivity for words along the medial-to-lateral axis of the left inferior frontal cortex in typically reading children and evidence of functional connectivity between the most lateral aspect of this area and the anterior aspects of the occipito-temporal cortex. We report absence of an IFC gradient and connectivity between the lateral aspect of the IFC and the anterior occipito-temporal cortex in the dyslexic children. Together, our results provide insights into the source of the anomalies reported in previous studies of dyslexia and add to the growing evidence of an orthographic role of IFC in reading.