Residual number processing in dyscalculia

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.

The structure correspondence hypothesis predicts how word and sentence in language correlate with term and principle in mathematics

The association between language and mathematics is an important debated topic. Here, we proposed a structure correspondence hypothesis to explain under what conditions language and mathematics are closely related. According to the hypothesis, there would be an association when they have equivalent structure. One hundred and fifty high school students were recruited to finish mathematical and language tests at the element level (i.e., geometric term processing and word analogy) and at the low-dimensional combination level (i.e., geometric principle processing and sentence completion) as well as the tests to measure cognitive covariates (general intelligence and spatial processing). After controlling for age, gender and cognitive covariates, geometric term processing and word analogy were closely correlated, and geometric principle processing and sentence completion were significantly correlated. No other correlations were found. The results support the structure correspondence hypothesis and provide a new perspective of structure of language and verbalized mathematics for the relation between language and mathematics.

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.

Dyscalculia in Early Adulthood: Implications for Numerical Activities of Daily Living

Numerical abilities are fundamental in our society. As a consequence, poor numerical skills might have a great impact on daily living. This study analyzes the extent to which the numerical deficit observed in young adults with Developmental Dyscalculia (DD) impacts their activities of everyday life. For this purpose, 26 adults with DD and 26 healthy controls completed the NADL, a standardized battery that assesses numerical skills in both formal and informal contexts. The results showed that adults with DD had poorer arithmetical skills in both formal and informal settings. In particular, adults with DD presented difficulties in time and measure estimation as well as money usage in real-world numerical tasks. In contrast, everyday tasks regarding distance estimation were preserved. In addition, the assessment revealed that adults with DD were aware of their numerical difficulties, which were often related to emotional problems and negatively impacted their academic and occupational decisions. Our study highlights the need to design innovative interventions and age-appropriate training for adults with DD to support their numerical skills as well as their social and emotional well-being.

Bilateral intraparietal activation for number tasks in studies using an adaptation paradigm: A meta-analysis

Mathematical processing is important for professional successes. The Adaptation Paradigm has been widely used to study the brain underpinnings of mathematical processing. In this study, we aim at shedding light on an important component of mathematical processing, namely numerical cognition. To do so, we performed a meta-analysis using the Activation Likelihood Estimation method on studies that have employed the Adaptation Paradigm for examining numerical cognition. We found a bilateral Intraparietal Sulcus (IPS) activation in studies using both symbolic and non-symbolic stimuli formats. We also found a right lateralized brain activation for the non-symbolic condition and a left lateralized brain activation for the symbolic condition. These results imply that the Adaptation Paradigm likely targets numeric magnitude processing and confirms the potency of this paradigm to activate the Intraparietal Sulcus.

A connectome-based neuromarker of nonverbal number acuity and arithmetic skills

The approximate number system (ANS) is vital for survival and reproduction in animals and is crucial for constructing abstract mathematical abilities in humans. Most previous neuroimaging studies focused on identifying discrete brain regions responsible for the ANS and characterizing their functions in numerosity perception. However, a neuromarker to characterize an individual's ANS acuity is lacking, especially one based on whole-brain functional connectivity (FC). Here, based on the resting-state functional magnetic resonance imaging (rs-fMRI) data obtained from a large sample, we identified a distributed brain network (i.e. a numerosity network) using a connectome-based predictive modeling (CPM) analysis. The summed FC strength within the numerosity network reliably predicted individual differences in ANS acuity regarding behavior, as measured using a nonsymbolic number-comparison task. Furthermore, in an independent dataset of the Human Connectome Project (HCP), we found that the summed FC strength within the numerosity network also specifically predicted individual differences in arithmetic skills, but not domain-general cognitive abilities. Therefore, our findings revealed that the identified numerosity network could serve as an applicable neuroimaging-based biomarker of nonverbal number acuity and arithmetic skills.

Increased structural covariance in brain regions for number processing and memory in children with developmental dyscalculia

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Several studies demonstrated functional network alterations in DD. Yet, there are no studies, which examined the structural network integrity in DD. We compared whole‐brain maps of volume based structural covariance between 19 (4 males) children with DD and 18 (4 males) typically developing children. We found elevated structural covariance in the DD group between the anterior intraparietal sulcus to the middle temporal and frontal gyrus (p < 0.05, corrected). A hippocampus subfield analysis showed higher structural covariance in the DD group for area CA3 to the parahippocampal and calcarine sulcus, angular gyrus and anterior part of the intraparietal sulcus as well as to the lingual gyrus. Lower structural covariance in this group was seen for the subiculum to orbitofrontal gyrus, anterior insula and middle frontal gyrus. In contrast, the primary motor cortex (control region) revealed no difference in structural covariance between groups. Our results extend functional magnetic resonance studies by revealing abnormal gray matter integrity in children with DD. These findings thus indicate that the pathophysiology of DD is mediated by both structural and functional abnormalities in a network involved in number processing and memory function.

Gray matter volume in left intraparietal sulcus predicts longitudinal gains in subtraction skill in elementary school

Although behavioral studies show large improvements in arithmetic skills in elementary school, we do not know how brain structure supports math gains in typically developing children. While some correlational studies have investigated the concurrent association between math performance and brain structure, such as gray matter volume (GMV), longitudinal studies are needed to infer if there is a causal relation. Although discrepancies in the literature on the relation between GMV and math performance have been attributed to the different demands on quantity vs. retrieval mechanisms, no study has experimentally tested this assumption. We defined regions of interests (ROIs) associated with quantity representations in the bilateral intraparietal sulcus (IPS) and associated with the storage of arithmetic facts in long-term memory in the left middle and superior temporal gyri (MTG/STG), and studied associations between GMV in these ROIs and children's performance on operations having greater demands on quantity vs. retrieval mechanisms, namely subtraction vs. multiplication. The aims of this study were threefold: First, to study concurrent associations between GMV and math performance, second, to investigate the role of GMV at the first time-point (T1) in predicting longitudinal gains in math skill to the second time-point (T2), and third, to study whether changes in GMV over time were associated with gains in math skill. Results showed no concurrent association between GMV in IPS and math performance, but a concurrent association between GMV in left MTG/STG and multiplication skill at T1. This association showed that the higher the GMV in this ROI, the higher the children's multiplication skill. Results also revealed that GMV in left IPS and left MTG/STG predicted longitudinal gains in subtraction skill only for younger children (approximately 10 years old). Whereas higher levels of GMV in left IPS at T1 predicted larger subtraction gains, higher levels of GMV in left MTG/STG predicted smaller gains. GMV in left MTG/STG did not predict longitudinal gains in multiplication skill. No significant association was found between changes in GMV over time and longitudinal gains in math. Our findings support the early importance of brain structure in the IPS for mathematical skills that rely on quantity mechanisms.

Emerging neurodevelopmental perspectives on mathematical learning

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

Persistent Differences in Brain Structure in Developmental Dyscalculia: A Longitudinal Morphometry Study

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2-10.4 years) and 10 typically developing (TD) children (8.0-10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas.

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

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

The interplay between non-symbolic number and its continuous visual properties revisited: Effects of mixing trials of different types

In the last few years, the existence of a pure number sense has been challenged. Recent studies suggest that numerosity processing is influenced not only by the number of elements in a display but also by continuous magnitudes, such as the size of the elements. The aim of our study was to replicate and extend the findings by Gebuis and Reynvoet, who systematically manipulated different continuous magnitudes either congruently or incongruently with discrete numerosity. We were particularly interested in finding the same pattern of congruency effects and assess its stability and robustness as this pattern indicates a complex influence of continuous magnitudes on numerosity judgements. We did so by showing stimuli of different conditions either in separate blocks or mixed together while participants solved a dot comparison task. Our results are in line with the notion that discrete number and continuous magnitudes are integrated in numerosity judgements by means of a weighing process. Moreover, our findings suggest that this integration is modified by the mode of presentation (blocked vs. mixed).

Challenging the neurobiological link between number sense and symbolic numerical abilities

A significant body of research links individual differences in symbolic numerical abilities, such as arithmetic, to number sense, the neurobiological system used to approximate and manipulate quantities without language or symbols. However, recent findings from cognitive neuroscience challenge this influential theory. Our current review presents an overview of evidence for the number sense account of symbolic numerical abilities and then reviews recent studies that challenge this account, organized around the following four assertions. (1) There is no number sense as traditionally conceived. (2) Neural substrates of number sense are more widely distributed than common consensus asserts, complicating the neurobiological evidence linking number sense to numerical abilities. (3) The most common measures of number sense are confounded by other cognitive demands, which drive key correlations. (4) Number sense and symbolic number systems (Arabic digits, number words, and so on) rely on distinct neural mechanisms and follow independent developmental trajectories. The review follows each assertion with comments on future directions that may bring resolution to these issues.

Asymmetrical interference between number and item size perception provides evidence for a domain specific impairment in dyscalculia

Dyscalculia, a specific learning disability that impacts arithmetical skills, has previously been associated to a deficit in the precision of the system that estimates the approximate number of objects in visual scenes (the so called 'number sense' system). However, because in tasks involving numerosity comparisons dyscalculics' judgements appears disproportionally affected by continuous quantitative dimensions (such as the size of the items), an alternative view linked dyscalculia to a domain-general difficulty in inhibiting task-irrelevant responses. To arbitrate between these views, we evaluated the degree of reciprocal interference between numerical and non-numerical quantitative dimensions in adult dyscalculics and matched controls. We used a novel stimulus set orthogonally varying in mean item size and numerosity, putting particular attention into matching both features' perceptual discriminability. Participants compared those stimuli based on each of the two dimensions. While control subjects showed no significant size interference when judging numerosity, dyscalculics' numerosity judgments were strongly biased by the unattended size dimension. Importantly however, both groups showed the same degree of interference from the unattended dimension when judging mean size. Moreover, only the ability to discard the irrelevant size information when comparing numerosity (but not the reverse) significantly predicted calculation ability across subjects. Overall, our results show that numerosity discrimination is less prone to interference than discrimination of another quantitative feature (mean item size) when the perceptual discriminability of these features is matched, as here in control subjects. By quantifying, for the first time, dyscalculic subjects' degree of interference on another orthogonal dimension of the same stimuli, we are able to exclude a domain-general inhibition deficit as explanation for their poor / biased numerical judgement. We suggest that enhanced reliance on non-numerical cues during numerosity discrimination can represent a strategy to cope with a less precise number sense.

The brain-structural correlates of mathematical expertise

Studies in several domains of expertise have established that experience-dependent plasticity brings about both functional and anatomical changes. However, little is known about how such changes come to shape the brain in the case of expertise acquired by professional mathematicians. Here, we aimed to identify cognitive and brain-structural (grey and white matter) characteristics of mathematicians as compared to non-mathematicians. Mathematicians and non-mathematician academics from the University of Oxford underwent structural and diffusion MRI scans, and were tested on a cognitive battery assessing working memory, attention, IQ, numerical and social skills. At the behavioural level, mathematical expertise was associated with better performance in domain-general and domain-specific dimensions. At the grey matter level, in a whole-brain analysis, behavioural performance correlated with grey matter density in left superior frontal gyrus – positively for mathematicians but negatively for non-mathematicians; in a region of interest analysis, we found in mathematicians higher grey matter density in the right superior parietal lobule, but lower grey matter density in the right intraparietal sulcus and in the left inferior frontal gyrus. In terms of white matter, there were no significant group differences in fractional anisotropy or mean diffusivity. These results reveal new insights into the relationship between mathematical expertise and grey matter metrics in brain regions previously implicated in numerical cognition, as well as in regions that have so far received less attention in this field. Further studies, based on longitudinal designs and cognitive training, could examine the conjecture that such cross-sectional findings arise from a bidirectional link between experience and structural brain changes that is itself subject to change across the lifespan.

A Translational Framework of Educational Neuroscience in Learning Disorders

Neuroimaging has undergone enormous progress during the last two and a half decades. The combination of neuroscientific methods and educational practice has become a focus of interdisciplinary research in order to answer more applied questions. In this realm, conditions that hamper learning success and have deleterious effects in the population - such as learning disorders (LD) - could especially profit from neuroimaging findings. At the moment, however, there is an ongoing debate about how far neuroscientific research can go to inform the practical work in educational settings. Here, we put forward a theoretical translational framework as a method of conducting neuroimaging and bridging it to education, with a main focus on dyscalculia and dyslexia. Our work seeks to represent a theoretical but mainly empirical guide on the benefits of neuroimaging, which can help people working with different aspects of LD, who need to act collaboratively to reach the full potential of neuroimaging. We provide possible ideas regarding how neuroimaging can inform LD at different levels within our multidirectional framework, i.e., mechanisms, diagnosis/prognosis, training/intervention, and community/education. In addition, we discuss methodological, conceptual, and structural limitations that need to be addressed by future research.

The relation between 1st grade grey matter volume and 2nd grade math competence

Mathematical and numerical competence is a critical foundation for individual success in modern society yet the neurobiological sources of individual differences in math competence are poorly understood. Neuroimaging research over the last decade suggests that neural mechanisms in the parietal lobe, particularly the intraparietal sulcus (IPS) are structurally aberrant in individuals with mathematical learning disabilities. However, whether those same brain regions underlie individual differences in math performance across the full range of math abilities is unknown. Furthermore, previous studies have been exclusively cross-sectional, making it unclear whether variations in the structure of the IPS are caused by or consequences of the development of math skills. The present study investigates the relation between grey matter volume across the whole brain and math competence longitudinally in a representative sample of 50 elementary school children. Results show that grey matter volume in the left IPS at the end of 1st grade relates to math competence a year later at the end of 2nd grade. Grey matter volume in this region did not change over that year, and was still correlated with math competence at the end of 2nd grade. These findings support the hypothesis that the IPS and its associated functions represent a critical foundation for the acquisition of mathematical competence.

Cognitive tutoring induces widespread neuroplasticity and remediates brain function in children with mathematical learning disabilities

Competency with numbers is essential in today's society; yet, up to 20% of children exhibit moderate to severe mathematical learning disabilities (MLD). Behavioural intervention can be effective, but the neurobiological mechanisms underlying successful intervention are unknown. Here we demonstrate that eight weeks of 1:1 cognitive tutoring not only remediates poor performance in children with MLD, but also induces widespread changes in brain activity. Neuroplasticity manifests as normalization of aberrant functional responses in a distributed network of parietal, prefrontal and ventral temporal-occipital areas that support successful numerical problem solving, and is correlated with performance gains. Remarkably, machine learning algorithms show that brain activity patterns in children with MLD are significantly discriminable from neurotypical peers before, but not after, tutoring, suggesting that behavioural gains are not due to compensatory mechanisms. Our study identifies functional brain mechanisms underlying effective intervention in children with MLD and provides novel metrics for assessing response to intervention.

Commonalities for Numerical and Continuous Quantity Skills at Temporo-parietal Junction

How do our abilities to process number and other continuous quantities such as time and space relate to each other? Recent evidence suggests that these abilities share common magnitude processing and neural resources, although other findings also highlight the role of dimension-specific processes. To further characterize the relation between number, time, and space, we first examined them in a population with a developmental numerical dysfunction (developmental dyscalculia) and then assessed the extent to which these abilities correlated both behaviorally and anatomically in numerically normal participants. We found that (1) participants with dyscalculia showed preserved continuous quantity processing and (2) in numerically normal adults, numerical and continuous quantity abilities were at least partially dissociated both behaviorally and anatomically. Specifically, gray matter volume correlated with both measures of numerical and continuous quantity processing in the right TPJ; in contrast, individual differences in number proficiency were associated with gray matter volume in number-specific cortical regions in the right parietal lobe. Together, our new converging evidence of selective numerical impairment and of number-specific brain areas at least partially distinct from common magnitude areas suggests that the human brain is equipped with different ways of quantifying the outside world.