Why mental arithmetic counts: brain activation during single digit arithmetic predicts high school math scores

Concurrent and predictive associations between executive function and numerical skills in early childhood

The importance of early numerical and executive function (EF) skills is well-established, with each skill set positively and specifically predicting later mathematics achievement, income, postsecondary education, and more. Less is known, however, about the relations between EF and numerical skills. Therefore, we examined the concurrent and predictive relations between EF and numerical skills in preschoolers to third graders (N = 205; 4.67-8.75 years of age; 43.9% female; 51.2% White non-Hispanic, 18% multiracial, 6.3% Hispanic, 12.2% Black, 2% American Indian/Alaska Native, 4.9% Asian, 1% not otherwise listed). We found positive concurrent relations between EF and all six numerical skills examined: nonsymbolic magnitude comparison, verbal counting, numerical literacy, count on, non-rote counting, and numerical problem solving. There were unidirectional predictive relations between EF and four of the six numerical skills after controlling for covariates and prior performance on the skill of interest. Bidirectional relations were found only for EF and nonsymbolic magnitude comparison. We also found that the concurrent relation between EF and count on was higher for children with typical versus persistently low mathematics achievement. All other concurrent and predictive relations were similar for children with typical and persistently low mathematics achievement. Overall, these findings show that the relations between EF and numerical skills are both pervasive and nuanced, such that they vary by timing of assessments (i.e., concurrent or predictive) and numerical skill. These results can inform future theoretical models on the role of EF in numerical development and have practical implications for designing interventions targeting these skill sets in early childhood.

Bridging the Connection between Fluency in Reading and Arithmetic

This study examines the contribution of early executive functions (EFs) in the association between fluency in reading and arithmetic. Kindergarten children (N = 1185) were assessed on executive functions skills and on reading and arithmetic fluency in Grade 1 and Grade 3. The analysis revealed that beyond the connection within each domain there is a unidirectional effect between fluency measures, with Grade 1 reading fluency significantly influencing the development of arithmetic fluency in Grade 3. Furthermore, the findings indicate that kindergarten EFs significantly contribute to arithmetic fluency at both time points and to reading fluency in the first grade. Early EF skills also emerged as significant contributors to the associations between fluency performance in reading and arithmetic, suggesting that the influence of EFs extends beyond individual academic domains. These findings have implications for understanding the cognitive mechanisms that underlie the relations between these academic skills.

Polygenic Risk of Mental Disorders and Subject-Specific School Grades

BACKGROUND

Education is essential for socioeconomic security and long-term mental health; however, mental disorders are often detrimental to the educational trajectory. Genetic correlations between mental disorders and educational attainment do not always align with corresponding phenotypic associations, implying heterogeneity in the genetic overlap.

METHODS

We unraveled this heterogeneity by investigating associations between polygenic risk scores for 6 mental disorders and fine-grained school outcomes: school grades in language and mathematics in ninth grade and high school, as well as educational attainment by age 25, using nationwide-representative data from established cohorts (N = 79,489).

RESULTS

High polygenic liability of attention-deficit/hyperactivity disorder was associated with lower grades in language and mathematics, whereas high polygenic risk of anorexia nervosa or bipolar disorder was associated with higher grades in language and mathematics. Associations between polygenic risk and school grades were mixed for schizophrenia and major depressive disorder and neutral for autism spectrum disorder.

CONCLUSIONS

Polygenic risk scores for mental disorders are differentially associated with language and mathematics school grades.

Are numerical abilities determined at early age? A brain morphology study in children and adolescents with and without developmental dyscalculia

The intraparietal sulcus (IPS) has been associated with numerical processing. A recent study reported that the IPS sulcal pattern was associated with arithmetic and symbolic number abilities in children and adults. In the present study, we evaluated the link between numerical abilities and the IPS sulcal pattern in children with Developmental Dyscalculia (DD) and typically developing children (TD), extending previous analyses considering other sulcal features and the postcentral sulcus (PoCS). First, we confirm the longitudinal sulcal pattern stability of the IPS and the PoCS. Second, we found a lower proportion of left sectioned IPS and a higher proportion of a double-horizontal IPS shape bilaterally in DD compared to TD. Third, our analyses revealed that arithmetic is the only aspect of numerical processing that is significantly related to the IPS sulcal pattern (sectioned vs not sectioned), and that this relationship is specific to the left hemisphere. And last, correlation analyses of age and arithmetic in children without a sectioned left IPS indicate that although they may have an inherent disadvantage in numerical abilities, these may improve with age. Thus, our results indicate that only the left IPS sulcal pattern is related to numerical abilities and that other factors co-determine numerical abilities.

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.

Digital twins for understanding mechanisms of learning disabilities: Personalized deep neural networks reveal impact of neuronal hyperexcitability

Learning disabilities affect a significant proportion of children worldwide, with far-reaching consequences for their academic, professional, and personal lives. Here we develop digital twins - biologically plausible personalized Deep Neural Networks (pDNNs) - to investigate the neurophysiological mechanisms underlying learning disabilities in children. Our pDNN reproduces behavioral and neural activity patterns observed in affected children, including lower performance accuracy, slower learning rates, neural hyper-excitability, and reduced neural differentiation of numerical problems. Crucially, pDNN models reveal aberrancies in the geometry of manifold structure, providing a comprehensive view of how neural excitability influences both learning performance and the internal structure of neural representations. Our findings not only advance knowledge of the neurophysiological underpinnings of learning differences but also open avenues for targeted, personalized strategies designed to bridge cognitive gaps in affected children. This work reveals the power of digital twins integrating AI and neuroscience to uncover mechanisms underlying neurodevelopmental disorders.

Stand up to better pay attention, sit down to better subtract: a new perspective on the advantage of cognitive-motor interactions

The Stroop task and subtraction rely on the different cognitive processes and cerebral regions, but both these cognitive functions interact with posture. The study of cognitive-motor interactions falls under the concept of sharing resources, implying that resources for processing are limited. Researchers try to understand this interaction by constructing dual task (DT) paradigms. None have investigated the Stroop and subtraction tasks in three inherently simple postures in two groups of young adults. This study aimed to test whether a given posture benefits a given cognitive function when cognitive and postural tasks are not overly demanding and are underpinned by common cerebral structures. This study presents the results of 60 healthy young adults performing a subtraction task in three postures (sitting, standing, and walking) and 57 healthy young adults performing the Stroop task in the same three postures. Our results showed that performance at the Stroop task, in terms of number of correct answers and interference, are better while standing or even walking compared to sitting while subtraction is better sitting compared to standing and walking. Moreover, static postural parameters did not vary when in DT compared to single task. This means that there was no additional cost on posture when achieving the cognitive activity simultaneously. The absence of impact of the DT on postural parameters in static postures and the changes in the gait pace when walking suggest that cognitive tasks can be achieved in various postures, without being too costly on posture.

Arithmetic skills are associated with left fronto-temporal gray matter volume in 536 children and adolescents

There are large individual differences in arithmetic skills. Although a number of brain-wide association studies have attempted to identify the neural correlates of these individual differences, studies have focused on relatively small sample sizes and have yielded inconsistent results. In the current voxel-based morphometry study, we merged six structural imaging datasets of children and adolescents (from 7.5 to 15 years) whose levels of arithmetic skills were assessed, leading to a combined sample of n = 536. Controlling for individual differences in age, gender, as well as language, and intelligence, we found a unique positive relation between arithmetic skill and gray matter volume in the left inferior frontal gyrus (IFG) and middle temporal gyrus (MTG). Our results suggest that individual differences in arithmetic skills are associated with structural differences in left fronto-temporal areas, rather than in regions of the parietal cortex and hippocampus that are often associated with arithmetic processing.

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.

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

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

Entropy, complexity, and maturity in children’s neural responses to naturalistic video lessons

Temporal characteristics of neural signals are often overlooked in traditional fMRI developmental studies but are critical to studying brain functions in ecologically valid settings. In the present study, we explore the temporal properties of children's neural responses during naturalistic mathematics and grammar tasks. To do so, we introduce a novel measure in developmental fMRI: neural entropy, which indicates temporal complexity of BOLD signals. We show that temporal patterns of neural activity have lower complexity and greater variability in children than in adults in the association cortex but not in the sensory-motor cortex. We also show that neural entropy is associated with both child-adult similarity in functional connectivity and neural synchrony, and that neural entropy increases with the size of functionally connected networks in the association cortex. In addition, neural entropy increases with functional maturity (i.e., child-adult neural synchrony) in content-specific regions. These exploratory findings suggest the hypothesis that neural entropy indexes the increasing breadth and diversity of neural processes available to children for analyzing mathematical information over development.

An fMRI intervention study of creative mathematical reasoning: behavioral and brain effects across different levels of cognitive ability

BACKGROUND

Many learning methods of mathematical reasoning encourage imitative procedures (algorithmic reasoning, AR) instead of more constructive reasoning processes (creative mathematical reasoning, CMR). Recent research suggest that learning with CMR compared to AR leads to better performance and differential brain activity during a subsequent test. Here, we considered the role of individual differences in cognitive ability in relation to effects of CMR.

METHODS

We employed a within-subject intervention (N=72, M_Age=18.0) followed by a brain-imaging session (fMRI) one week later. A battery of cognitive tests preceded the intervention. Participants were divided into three cognitive ability groups based on their cognitive score (low, intermediate and high).

RESULTS

On mathematical tasks previously practiced with CMR compared to AR we observed better performance, and higher brain activity in key regions for mathematical cognition such as left angular gyrus and left inferior/middle frontal gyrus. The CMR-effects did not interact with cognitive ability, albeit the effects on performance were driven by the intermediate and high cognitive ability groups.

CONCLUSIONS

Encouraging pupils to engage in constructive processes when learning mathematical reasoning confers lasting learning effects on brain activation, independent of cognitive ability. However, the lack of a CMR-effect on performance for the low cognitive ability group suggest future studies should focus on individualized learning interventions, allowing more opportunities for effortful struggle with CMR.

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.

Investigating the association between variability in sulcal pattern and academic achievement

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

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

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

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

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

Nurturing the Mathematical Brain: Home Numeracy Practices Are Associated With Children's Neural Responses to Arabic Numerals

Disparities in home numeracy environments contribute to variations in children's mathematical skills. However, the neural mechanisms underlying the relation between home numeracy experiences and mathematical learning are unknown. Here, parents of 66 eight-year-olds completed a questionnaire assessing the frequency of home numeracy practices. Neural adaptation to the repetition of Arabic numerals and words was measured in children using functional MRI (n = 50) to assess how sensitive the brain is to the presentation of numerical and nonnumerical information. Disparities in home numeracy practices were related to differences in digit (but not word) processing in a region of the left intraparietal sulcus (IPS) that was also related to children's arithmetic fluency. Furthermore, digit-related processing in the IPS influenced the relation between home numeracy practices and arithmetic fluency. Results were consistent with a model hypothesizing that home numeracy practices may affect children's mathematical skills by modulating the IPS response to symbolic numerical information.

Developmental dyscalculia: the progress of cognitive modeling in the field of numerical cognition deficits for children

The study of dyscalculia requires an analysis of the current developed hypotheses which describe the cognitive mechanisms involved in this neurodevelopmental disorder. The objective of our review is to determine any progress in modeling developmental dyscalculia. The first hypothesis suggests that dyscalculia is the consequence of a specific deficit level number on the precise number system and the approximate system. Then, the second hypothesis states that developmental dyscalculia is linked to a failure to process non-symbolic representations of numbers. On the other hand, the third suggests that dyscalculia is caused by a lack of access to numerical quantities from symbols. However, the last hypothesis asserts that developmental dyscalculia is linked to general deficits. All these hypotheses are compatible with recent neuroimaging results and raise new horizons for experimentation, which will allow the development of precise diagnostic tools and the improvement of intervention strategies and the remediation of developmental dyscalculia.

Developmental brain dynamics of numerical and arithmetic abilities

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

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.

Numerical Magnitude Processing in Deaf Adolescents and Its Contribution to Arithmetical Ability

Although most deaf individuals could use sign language or sign/spoken language mix, hearing loss would still affect their language acquisition. Compensatory plasticity holds that the lack of auditory stimulation experienced by deaf individuals, such as congenital deafness, can be met by enhancements in visual cognition. And the studies of hearing individuals have showed that visual form perception is the cognitive mechanism that could explain the association between numerical magnitude processing and arithmetic computation. Therefore, we examined numerical magnitude processing and its contribution to arithmetical ability in deaf adolescents, and explored the differences between the congenital and acquired deafness. 112 deaf adolescents (58 congenital deafness) and 58 hearing adolescents performed a series of cognitive and mathematical tests, and it was found there was no significant differences between the congenital group and the hearing group, but congenital group outperformed acquired group in numerical magnitude processing (reaction time) and arithmetic computation. It was also found there was a close association between numerical magnitude processing and arithmetic computation in all deaf adolescents, and after controlling for the demographic variables (age, gender, onset of hearing loss) and general cognitive abilities (non-verbal IQ, processing speed, reading comprehension), numerical magnitude processing could predict arithmetic computation in all deaf adolescents but not in congenital group. The role of numerical magnitude processing (symbolic and non-symbolic) in deaf adolescents' mathematical performance should be paid attention in the training of arithmetical ability.

Shared Neural Circuits for Visuospatial Working Memory and Arithmetic in Children and Adults

Visuospatial working memory (VSWM) plays an important role in arithmetic problem solving, and the relationship between these two skills is thought to change over development. Even though neuroimaging studies have demonstrated that VSWM and arithmetic both recruit frontoparietal networks, inferences about common neural substrates have largely been made by comparisons across studies. Little work has examined how brain activation for VSWM and arithmetic converge within the same participants and whether there are age-related changes in the overlap of these neural networks. In this study, we examined how brain activity for VSWM and arithmetic overlap in 38 children and 26 adults. Although both children and adults recruited the intraparietal sulcus (IPS) for VSWM and arithmetic, children showed more focal activation within the right IPS, whereas adults recruited the bilateral IPS, superior frontal sulcus/middle frontal gyrus, and right insula. A comparison of the two groups revealed that adults recruited a more left-lateralized network of frontoparietal regions for VSWM and arithmetic compared with children. Together, these findings suggest possible neurocognitive mechanisms underlying the strong relationship between VSWM and arithmetic and provide evidence that the association between VSWM and arithmetic networks changes with age.

Meaning to multiply: Electrophysiological evidence that children and adults treat multiplication facts differently

Multiplication tables are typically memorized verbally, with fluent retrieval leading to better performance in advanced math. Arithmetic development is characterized by strategy shifts from procedural operations to direct fact retrieval, which would not necessitate access to the facts' conceptual meaning. This study tested this hypothesis using a combination of event related brain potentials (ERP) and behavioral measures with 3rd-5th grade children and young adults. Participants verified the solutions to simple multiplication problems (2 × 3 = 6 or = 7) and the semantic fit of word-picture pairs, separately. Children showed an N400 effect to multiplication solutions with larger (more negative) amplitude for incorrect than correct solutions, reflecting meaning-level processing. A similar ERP response was observed in the word-picture verification task, with larger negative amplitude for word-picture pairs that were semantically mismatched compared to matched. In contrast, adults showed a P300 response for correct solutions, suggesting that they treated these solutions as potential targets in over-rehearsed mathematical expressions. This P300 response was specific to math fact processing, as the word-picture verification task elicited a classic N400 in adults. These ERP findings reveal an overlooked developmental transition that occurs after fifth grade, and speak to theories of arithmetic that have been based primarily on adult data.

Early Engagement of Parietal Cortex for Subtraction Solving Predicts Longitudinal Gains in Behavioral Fluency in Children

There is debate in the literature regarding how single-digit arithmetic fluency is achieved over development. While the Fact-retrieval hypothesis suggests that with practice, children shift from quantity-based procedures to verbally retrieving arithmetic problems from long-term memory, the Schema-based hypothesis claims that problems are solved through quantity-based procedures and that practice leads to these procedures becoming more automatic. To test these hypotheses, a sample of 46 typically developing children underwent functional magnetic resonance imaging (fMRI) when they were 11 years old (time 1), and 2 years later (time 2). We independently defined regions of interest (ROIs) involved in verbal and quantity processing using rhyming and numerosity judgment localizer tasks, respectively. The verbal ROIs consisted of left middle/superior temporal gyri (MTG/STG) and left inferior frontal gyrus (IFG), whereas the quantity ROIs consisted of bilateral inferior/superior parietal lobules (IPL/SPL) and bilateral middle frontal gyri (MFG)/right IFG. Participants also solved a single-digit subtraction task in the scanner. We defined the extent to which children relied on verbal vs. quantity mechanisms by selecting the 100 voxels showing maximal activation at time 1 from each ROI, separately for small and large subtractions. We studied the brain mechanisms at time 1 that predicted gains in subtraction fluency and how these mechanisms changed over time with improvement. When looking at brain activation at time 1, we found that improvers showed a larger neural problem size effect in bilateral parietal cortex, whereas no effects were found in verbal regions. Results also revealed that children who showed improvement in behavioral fluency for large subtraction problems showed decreased activation over time for large subtractions in both parietal and frontal regions implicated in quantity, whereas non-improvers maintained similar levels of activation. All children, regardless of improvement, showed decreased activation over time for large subtraction problems in verbal regions. The greater parietal problem size effect at time 1 and the reduction in activation over time for the improvers in parietal and frontal regions implicated in quantity processing is consistent with the Schema-based hypothesis arguing for more automatic procedures with increasing skill. The lack of a problem size effect at time 1 and the overall decrease in verbal regions, regardless of improvement, is inconsistent with the Fact-retrieval hypothesis.

Effects of Anodal tDCS on Arithmetic Performance and Electrophysiological Activity

Arithmetic abilities are among the most important school-taught skills and form the basis for higher mathematical competencies. At the same time, their acquisition and application can be challenging. Hence, there is broad interest in methods to improve arithmetic abilities. One promising method is transcranial direct current stimulation (tDCS). In the present study, we compared two anodal tDCS protocols in their efficacy to improve arithmetic performance and working memory. In addition, we investigated stimulation-related electrophysiological changes. Three groups of participants solved arithmetic problems (additions and subtractions) and an n-back task before, during, and after receiving either frontal or parietal anodal tDCS (25 min; 1 mA) or sham stimulation. EEG was simultaneously recorded to assess stimulation effects on event-related (de-) synchronisation (ERS/ERD) in theta and alpha bands. Persons receiving frontal stimulation showed an acceleration of calculation speed in large subtractions from before to during and after stimulation. However, a comparable, but delayed (apparent only after stimulation) increase was also found in the sham stimulation group, while it was absent in the group receiving parietal stimulation. In additions and small subtractions as well as the working memory task, analyses showed no effects of stimulation. Results of ERS/ERD during large subtractions indicate changes in ERS/ERD patterns over time. In the left hemisphere there was a change from theta band ERD to ERS in all three groups, whereas a similar change in the right hemisphere was restricted to the sham group. Taken together, tDCS did not lead to a general improvement of arithmetic performance. However, results indicate that frontal stimulation accelerated training gains, while parietal stimulation halted them. The absence of general performance improvements, but acceleration of training effects might be a further indicator of the advantages of using tDCS as training or learning support over tDCS as a sole performance enhancer.

Temporo-frontal activation during phonological processing predicts gains in arithmetic facts in young children

Behavioral studies have shown discrepant results regarding the role of phonology in predicting math gains. The objective of this study was to use fMRI to study the role of activation during a rhyming judgment task in predicting behavioral gains on math fluency, multiplication, and subtraction skill. We focused within the left middle/superior temporal gyrus and left inferior frontal gyrus, brain areas associated with the storage of phonological representations and with their access, respectively. We ran multiple regression analyses to determine whether activation predicted gains in the three math measures, separately for younger (i.e. 10 years old) and older (i.e 12 years old) children. Results showed that activation in both temporal and frontal cortex only predicted gains in fluency and multiplication skill, and only for younger children. This study suggests that both temporal and frontal cortex activation during phonological processing are important in predicting gains in math tasks that involve the retrieval of facts that are stored as phonological codes in memory. Moreover, these results were specific to younger children, suggesting that phonology is most important in the early stages of math development. When the math task involved subtractions, which relies on quantity representations, phonological processes were not important in driving gains.

Bilingual children access multiplication facts from semantic memory equivalently across languages: Evidence from the N400

Typically, bilinguals learn multiplication facts in only one instruction language. Consequently, these facts may be represented and/or accessed as language-specific memories, requiring a qualitatively different retrieval process in their other language. Indeed, behavioral studies reveal that bilinguals verify arithmetic facts faster and better in the language of learning. Here, event-related potentials (ERPs) were used as a window into the neurocognitive processes underlying this language bias in children. ERPs were recorded while bilingual children verified the correctness of multiplication solutions. Operands were presented as spoken number words in Spanish and English, separately. Although a language bias was revealed in behavior, both languages elicited the same ERP correctness effect, an N400, reflecting similar cognitive processes in both languages. This suggests that the source of the behavioral difference is not at the level of semantic access. Our findings highlight the flexibility of the bilingual brain, especially when both languages are learned early.

A cluster-randomized controlled trial of the effectiveness of the JUMP Math program of math instruction for improving elementary math achievement

Students in many western countries struggle to achieve acceptable standards in numeracy despite its recognition as an important 21^st century skill. As commercial math programs remain a staple of classroom instruction, investigations of their effectiveness are essential to inform decision-making regarding how to invest limited resources while maximizing student gains. We conducted a cluster randomized-controlled trial of the effectiveness of JUMP Math, a distinctive math program whose central tenets are empirically supported, for improving elementary math achievement (clinical trial.gov no. NCT02456181). The study involved 554 grade 2 (primary) and 592 grade 5 (junior) students and 193 teachers in 41 schools, in an urban-rural Canadian school board. Schools were randomly assigned to use either JUMP Math or their business-as-usual, problem-based approach to math instruction. We tracked student progress in math achievement on standardized and curriculum-based measures of computation and problem solving, for 2 consecutive school years. Junior students taught with JUMP Math made significantly greater progress in computation than their non-JUMP peers but the groups did not differ significantly in problem solving. Effects took hold relatively quickly, replicating the results from an earlier pilot study. Primary students in the non-JUMP group made significantly greater gains in problem solving and computation in year 1. But those taught with JUMP Math made significantly greater gains in problem solving and the groups did not differ in computation, in year 2. The positive effects of JUMP Math are noteworthy given that the JUMP Math teachers were likely still adjusting to the new program. That these positive findings were obtained in an effectiveness study (i.e. in real-world conditions), suggests that JUMP Math may be a valuable evidence-based addition to the teacher’s toolbox. Given the importance of numeracy for 21^st century functioning, identifying and implementing effective math instruction programs could have far-reaching, positive implications.

Developing, mature, and unique functions of the child's brain in reading and mathematics

Cognitive development research shows that children use basic "child-unique" strategies for reading and mathematics. This suggests that children's neural processes will differ qualitatively from those of adults during this developmental period. The goals of the current study were to 1) establish whether a within-subjects neural dissociation between reading and mathematics exists in early childhood as it does in adulthood, and 2) use a novel, developmental intersubject correlation method to test for "child-unique", developing, and adult-like patterns of neural activation within those networks. Across multiple tasks, children's reading and mathematics activity converged in prefrontal cortex, but dissociated in temporal and parietal cortices, showing similarities to the adult pattern of dissociation. "Child-unique" patterns of neural activity were observed in multiple regions, including the anterior temporal lobe and inferior frontal gyri, and showed "child-unique" profiles of functional connectivity to prefrontal cortex. This provides a new demonstration that "children are not just little adults" - the developing brain is not only quantitatively different from adults, it is also qualitatively different.

P300 amplitude and latency reflect arithmetic skill: An ERP study of the problem size effect

The effect of arithmetic problem size is widespread in behavior (e.g., slower responses to 8 × 7 than 2 × 2). Here, we measure event related potentials (ERPs) to determine how the problem size effect unfolds under different conditions. Adults judged the correctness of simple multiplication problems (2 × 4 = 8 versus 9) that varied in size and operand number format (written digits versus spoken number words). The P300, an ERP component associated with stimulus categorization, was measured from solution onset. P300 amplitude was greatest for small and correct solutions, as expected for easily categorized stimuli. Large incorrect solutions elicited a disproportionately reduced P300, an interaction not measurable in verification behavior. Additionally, ERP measures revealed effects of operand format preceding, but not following, solution onset. The significance of these findings for theories of mathematical cognition are addressed.

Assessment of Mathematics Difficulties for Second and Third Graders: Cognitive and Psychological Parameters

Mathematical achievement during the first years of primary school seems to be a reliable predictor of students’ later performance. In addition, cognitive, metacognitive, and psychological parameters are considered to be factors related to mathematical achievement. However, in the Greek educational system, there is a shortage of valid and reliable tools for the assessment of mathematics difficulties and as a consequence, identification of children with these difficulties does not take place before the last years of primary school. This study aims to investigate the relationship between working memory, sustained attention, executive functions, and math anxiety with mathematical achievement in 2nd and 3rd graders. The design of the study was based on the parameters of mathematics difficulties, as they arise from the literature review. Ninety-one Year 2 and Year 3 primary school students (mean age 8.06 years) from three public schools situated in Attica, Greece participated in the study. The students completed three different scales including educational, cognitive, and psychological tasks. Results showed that mathematical skills were significantly correlated with sustained attention, inductive reasoning, math anxiety, and working memory. Moreover, mental arithmetic ability, sustained attention, and working memory predicted mathematical achievement of second and third graders. The study’s outcomes verify that sustained attention, inductive reasoning, working memory, and math anxiety are correlated with young students’ mathematical performance. The implications of the results for the development of an assessment tool for early detection of mathematics difficulties will be discussed.

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.

The neural association between arithmetic and basic numerical processing depends on arithmetic problem size and not chronological age

The intraparietal sulcus (IPS) is thought to be an important region for basic number processing (e.g. symbol-quantity associations) and arithmetic (e.g. addition). Evidence for shared circuitry within the IPS is largely based on comparisons across studies, and little research has investigated number processing and arithmetic in the same individuals. It is also unclear how the neural overlap between number processing and arithmetic is influenced by age and arithmetic problem difficulty. This study investigated these unresolved questions by examining basic number processing (symbol-quantity matching) and arithmetic (addition) networks in 26 adults and 42 children. Number processing and arithmetic elicited overlapping activity in the IPS in children and adults, however, the overlap was influenced by arithmetic problem size (i.e. which modulated the need to use procedural strategies). The IPS was recruited for number processing, and for arithmetic problems more likely to be solved using procedural strategies. We also found that the overlap between number processing and small-problem addition in children was comparable to the overlap between number processing and large-problem addition in adults. This finding suggests that the association between number processing and arithmetic in the IPS is related to the cognitive operation being performed rather than age.

The effect of pain on balancing behavior: Complexity analysis of mediolateral force trajectories

BACKGROUND

Postural instability is a prevalent and deleterious consequence of aging. It is unclear how the occurrence of chronic pain augments balance issues as age progresses.

RESEARCH QUESTION

We investigated how postural stability is influenced by aging and chronic pain.

METHODS

Fifty-five participants with and without recent chronic pain balanced on one foot while performing three tasks, a standard balancing task with no challenge, a mental task in which participants answered arithmetic questions while balancing on one foot, and a knot-tying task in which participants tied knots in a ribbon while balancing on one foot. General linear models were used to assess the relationship between age, sex, BMI, and pain category for the three different balancing tasks. In addition, a multivariate analysis of variance was used to test the effect of age and pain category on Hurst exponents from all of three different balancing tasks.

RESULTS

Our results show that aging changes the control strategy of balancing from less persistent to more repetitive. The strong feedback elements intrinsic to healthy stability ensure quick reactions and strong capacity to compensate for balance checks; this reactive state changes into a less reactive and more predictable balance strategy with age while balancing on one foot. Mental tasks during balancing also decreased the feedback in balancing strategy. Balance strategy during the knot-tying task was correlated with age, but unaffected by chronic pain. Overall, the chronic pain group had a worse balance strategy while performing the mental task in comparison with healthy people, but were not differentiable from controls in the standard or knot-tying tasks.

SIGNIFICANCE

Scores from balancing while engaging in cognitive tasks may provide evidence of health decline, and contribute to our knowledge about how pain affects feedback mechanisms.

The Relationship Between Reading Fluency and Arithmetic Fact Fluency and Their Shared Cognitive Skills: A Developmental Perspective

This study investigated the underlying cognitive abilities which are related to both fluency in reading and arithmetic across different developmental phases of their acquisition. An unselected sample of children in first (N = 83), second (N = 66), and third (N = 67) grades completed several reading and arithmetic fluency tasks, as well as rapid automatized naming (RAN), working memory (WM), and inhibition measures. The results of a stepwise regression analysis revealed differences in the predictive models of fluency in both academic domains in first grade. However, similar patterns were found in the second and third grades. Specifically, in first grade reading fluency was predicted by inhibition and WM, while arithmetic fact fluency was predicted by RAN and WM. In contrast, in second grade both types of fluency were predicted by RAN and WM, and in third grade only RAN was found to be a predictor. Alongside the gradual reduction in the cognitive components participating in reading and arithmetic fluency, the results of the present study suggest that both fluencies share the same underlying cognitive mechanisms. Practical implications of the current results are discussed.

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.

Fronto-insular-parietal network engagement underlying arithmetic word problem solving

Mathematical word problems are ubiquitous and standard for teaching and evaluating generalization of mathematical knowledge for real-world contexts. It is therefore concerning that the neural mechanisms of word problem solving are not well understood, as these insights represent strong potential for improving education and remediating deficits in this domain. Here, we investigate neural response to word problems via functional magnetic resonance imaging (fMRI). Healthy adults performed sentence judgment tasks on word problems that either contained one-step mathematical operations, or nonarithmetic judgments on parallel narratives without any numerical information. Behavioral results suggested that the composite efficiency measurement of combining accuracy and RT did not differ between the two problem types. Arithmetic sentence judgments elicited greater activation in the fronto-insular-parietal network including intraparietal sulcus (IPS), dorsolateral prefrontal cortex (PFC), and anterior insula (AI) than narrative sentence judgment. Narrative sentence judgments, conversely, resulted in greater activation predominantly in the left ventral PFC, angular gyrus and perisylvian cortex compared with reading arithmetic sentences. Moreover, task-dependent functional connectivity analyses showed the AI circuits were more strongly coupled with IPS during arithmetic sentence judgments than nonarithmetic sentences. Finally, activations in the IPS during arithmetic were highly correlated with out-of-scanner performance on a distinct set of problems with the same characteristics. These results show arithmetic word problem performance differences may rely more heavily on fronto-insular-parietal circuits for mathematical model building than narrative text comprehension of similar difficulty. More broadly, our study suggests that quantitative measurements of brain mechanisms can provide pivotal role for uncovering crucial arithmetic skills.

Shared genetic aetiology between cognitive performance and brain activations in language and math tasks

Cognitive performance is highly heritable. However, little is known about common genetic influences on cognitive ability and brain activation when engaged in a cognitive task. The Human Connectome Project (HCP) offers a unique opportunity to study this shared genetic etiology with an extended pedigree of 785 individuals. To investigate this common genetic origin, we took advantage of the HCP dataset, which includes both language and mathematics activation tasks. Using the HCP multimodal parcellation, we identified areals in which inter-individual functional MRI (fMRI) activation variance was significantly explained by genetics. Then, we performed bivariate genetic analyses between the neural activations and behavioral scores, corresponding to the fMRI task accuracies, fluid intelligence, working memory and language performance. We observed that several parts of the language network along the superior temporal sulcus, as well as the angular gyrus belonging to the math processing network, are significantly genetically correlated with these indicators of cognitive performance. This shared genetic etiology provides insights into the brain areas where the human-specific genetic repertoire is expressed. Studying the association of polygenic risk scores, using variants associated with human cognitive ability and brain activation, would provide an opportunity to better understand where these variants are influential.

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.

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.

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.