Meta-analyses of developmental fMRI studies investigating typical and atypical trajectories of number processing and calculation

Plasticity of left perisylvian white-matter tracts is associated with individual differences in math learning

Plasticity of white matter tracts is thought to be essential for cognitive development and academic skill acquisition in children. However, a dearth of high-quality diffusion tensor imaging (DTI) data measuring longitudinal changes with learning, as well as methodological difficulties in multi-time point tract identification have limited our ability to investigate plasticity of specific white matter tracts. Here, we examine learning-related changes of white matter tracts innervating inferior parietal, prefrontal and temporal regions following an intense 2-month math tutoring program. DTI data were acquired from 18 third grade children, both before and after tutoring. A novel fiber tracking algorithm based on a White Matter Query Language (WMQL) was used to identify three sections of the superior longitudinal fasciculus (SLF) linking frontal and parietal (SLF-FP), parietal and temporal (SLF-PT) and frontal and temporal (SLF-FT) cortices, from which we created child-specific probabilistic maps. The SLF-FP, SLF-FT, and SLF-PT tracts identified with the WMQL method were highly reliable across the two time points and showed close correspondence to tracts previously described in adults. Notably, individual differences in behavioral gains after 2 months of tutoring were specifically correlated with plasticity in the left SLF-FT tract. Our results extend previous findings of individual differences in white matter integrity, and provide important new insights into white matter plasticity related to math learning in childhood. More generally, our quantitative approach will be useful for future studies examining longitudinal changes in white matter integrity associated with cognitive skill development.

Developmental dyscalculia

Numerical skills are essential in our everyday life, and impairments in the development of number processing and calculation have a negative impact on schooling and professional careers. Approximately 3 to 6 % of children are affected from specific disorders of numerical understanding (developmental dyscalculia (DD)). Impaired development of number processing skills in these children is characterized by problems in various aspects of numeracy as well as alterations of brain activation and brain structure. Moreover, DD is assumed to be a very heterogeneous disorder putting special challenges to define homogeneous diagnostic criteria. Finally, interdisciplinary perspectives from psychology, neuroscience and education can contribute to the design for interventions, and although results are still sparse, they are promising and have shown positive effects on behaviour as well as brain function.

CONCLUSION

In the current review, we are going to give an overview about typical and atypical development of numerical abilities at the behavioural and neuronal level. Furthermore, current status and obstacles in the definition and diagnostics of DD are discussed, and finally, relevant points that should be considered to make an intervention as successful as possible are summarized.

How number line estimation skills relate to neural activations in single digit subtraction problems

The Number Line (NL) task requires judging the relative numerical magnitude of a number and estimating its value spatially on a continuous line. Children's skill on this task has been shown to correlate with and predict future mathematical competence. Neurofunctionally, this task has been shown to rely on brain regions involved in numerical processing. However, there is no direct evidence that performance on the NL task is related to brain areas recruited during arithmetical processing and that these areas are domain-specific to numerical processing. In this study, we test whether 8- to 14-year-old's behavioral performance on the NL task is related to fMRI activation during small and large single-digit subtraction problems. Domain-specific areas for numerical processing were independently localized through a numerosity judgment task. Results show a direct relation between NL estimation performance and the amount of the activation in key areas for arithmetical processing. Better NL estimators showed a larger problem size effect than poorer NL estimators in numerical magnitude (i.e., intraparietal sulcus) and visuospatial areas (i.e., posterior superior parietal lobules), marked by less activation for small problems. In addition, the direction of the activation with problem size within the IPS was associated with differences in accuracies for small subtraction problems. This study is the first to show that performance in the NL task, i.e. estimating the spatial position of a number on an interval, correlates with brain activity observed during single-digit subtraction problem in regions thought to be involved in numerical magnitude and spatial processes.

Processing of intentional and automatic number magnitudes in children born prematurely: evidence from fMRI

This study examined the neural correlates of intentional and automatic number processing (indexed by number comparison and physical Stroop task, respectively) in 6- and 7-year-old children born prematurely. Behavioral results revealed significant numerical distance and size congruity effects. Imaging results disclosed (1) largely overlapping fronto-parietal activation for intentional and automatic number processing, (2) a frontal to parietal shift of activation upon considering the risk factors gestational age and birth weight, and (3) a task-specific link between math proficiency and functional magnetic resonance imaging (fMRI) signal within distinct regions of the parietal lobes—indicating commonalities but also specificities of intentional and automatic number processing.

The differential role of verbal and spatial working memory in the neural basis of arithmetic

We examine the relations of verbal and spatial working memory (WM) ability to the neural bases of arithmetic in school-age children. We independently localize brain regions subserving verbal versus spatial representations. For multiplication, higher verbal WM ability is associated with greater recruitment of the left temporal cortex, identified by the verbal localizer. For multiplication and subtraction, higher spatial WM ability is associated with greater recruitment of right parietal cortex, identified by the spatial localizer. Depending on their WM ability, children engage different neural systems that manipulate different representations to solve arithmetic problems.

Development of brain systems for nonsymbolic numerosity and the relationship to formal math academic achievement

A central question in cognitive and educational neuroscience is whether brain operations supporting nonlinguistic intuitive number sense (numerosity) predict individual acquisition and academic achievement for symbolic or "formal" math knowledge. Here, we conducted a developmental functional magnetic resonance imaging (MRI) study of nonsymbolic numerosity task performance in 44 participants including 14 school age children (6-12 years old), 14 adolescents (13-17 years old), and 16 adults and compared a brain activity measure of numerosity precision to scores from the Woodcock-Johnson III Broad Math index of math academic achievement. Accuracy and reaction time from the numerosity task did not reliably predict formal math achievement. We found a significant positive developmental trend for improved numerosity precision in the parietal cortex and intraparietal sulcus specifically. Controlling for age and overall cognitive ability, we found a reliable positive relationship between individual math achievement scores and parietal lobe activity only in children. In addition, children showed robust positive relationships between math achievement and numerosity precision within ventral stream processing areas bilaterally. The pattern of results suggests a dynamic developmental trajectory for visual discrimination strategies that predict the acquisition of formal math knowledge. In adults, the efficiency of visual discrimination marked by numerosity acuity in ventral occipital-temporal cortex and hippocampus differentiated individuals with better or worse formal math achievement, respectively. Overall, these results suggest that two different brain systems for nonsymbolic numerosity acuity may contribute to individual differences in math achievement and that the contribution of these systems differs across development.

The arithmetic problem size effect in children: an event-related potential study

This study used for the first time event-related potentials (ERPs) to examine the well-known arithmetic problem size effect in children. The electrophysiological correlates of this problem size effect have been well documented in adults, but such information in children is lacking. In the present study, 22 typically developing 12-year-olds were asked to solve single-digit addition problems of small (sum ≤ 10) and large problem size (sum > 10) and to speak the solution into a voice key while ERPs were recorded. Children displayed similar early and late components compared to previous adult studies on the problem size effect. There was no effect of problem size on the early components P1, N1, and P2. The peak amplitude of the N2 component showed more negative potentials on left and right anterior electrodes for large additions compared to small additions, which might reflect differences in attentional and working memory resources between large and small problems. The mean amplitude of the late positivity component which follows the N2, was significantly larger for large than for small additions at right parieto-occipital electrodes, in line with previous adult data. The ERPs of the problem size effect during arithmetic might be a useful neural marker for future studies on fact retrieval impairments in children with mathematical difficulties.

Brain hyper-connectivity and operation-specific deficits during arithmetic problem solving in children with developmental dyscalculia

Developmental dyscalculia (DD) is marked by specific deficits in processing numerical and mathematical information despite normal intelligence (IQ) and reading ability. We examined how brain circuits used by young children with DD to solve simple addition and subtraction problems differ from those used by typically developing (TD) children who were matched on age, IQ, reading ability, and working memory. Children with DD were slower and less accurate during problem solving than TD children, and were especially impaired on their ability to solve subtraction problems. Children with DD showed significantly greater activity in multiple parietal, occipito-temporal and prefrontal cortex regions while solving addition and subtraction problems. Despite poorer performance during subtraction, children with DD showed greater activity in multiple intra-parietal sulcus (IPS) and superior parietal lobule subdivisions in the dorsal posterior parietal cortex as well as fusiform gyrus in the ventral occipito-temporal cortex. Critically, effective connectivity analyses revealed hyper-connectivity, rather than reduced connectivity, between the IPS and multiple brain systems including the lateral fronto-parietal and default mode networks in children with DD during both addition and subtraction. These findings suggest the IPS and its functional circuits are a major locus of dysfunction during both addition and subtraction problem solving in DD, and that inappropriate task modulation and hyper-connectivity, rather than under-engagement and under-connectivity, are the neural mechanisms underlying problem solving difficulties in children with DD. We discuss our findings in the broader context of multiple levels of analysis and performance issues inherent in neuroimaging studies of typical and atypical development.

[From brain imaging to good teaching? implicating from neuroscience for research on learning and instruction]

Psychiatric disorders in childhood and adolescence, in particular attention deficit disorder or specific learning disorders like developmental dyslexia and developmental dyscalculia, affect academic performance and learning at school. Recent advances in neuroscientific research have incited an intensive debate both in the general public and in the field of educational and instructional science as well as to whether and to what extent these new findings in the field of neuroscience might be of importance for school-related learning and instruction. In this review, we first summarize neuroscientific findings related to the development of attention, working memory and executive functions in typically developing children and then evaluate their relevance for school-related learning. We present an overview of neuroimaging studies of specific learning disabilities such as developmental dyslexia and developmental dyscalculia, and critically discuss their practical implications for educational and teaching practice, teacher training, early diagnosis as well as prevention and disorder-specific therapy. We conclude that the new interdisciplinary field of neuroeducation cannot be expected to provide direct innovative educational applications (e.g., teaching methods). Rather, the future potential of neuroscience lies in creating a deeper understanding of the underlying cognitive mechanisms and pathomechanisms of learning processes and learning disorders.

Development of magnitude processing in children with developmental dyscalculia: space, time, and number

Developmental dyscalculia (DD) is a learning disorder associated with impairments in a preverbal non-symbolic approximate number system (ANS) pertaining to areas in and around the intraparietal sulcus (IPS). The current study sought to enhance our understanding of the developmental trajectory of the ANS and symbolic number processing skills, thereby getting insight into whether a deficit in the ANS precedes or is preceded by impaired symbolic and exact number processing. Recent work has also suggested that humans are endowed with a shared magnitude system (beyond the number domain) in the brain. We therefore investigated whether children with DD demonstrated a general magnitude deficit, stemming from the proposed magnitude system, rather than a specific one limited to numerical quantity. Fourth graders with DD were compared to age-matched controls and a group of ability-matched second graders, on a range of magnitude processing tasks pertaining to space, time, and number. Children with DD displayed difficulties across all magnitude dimensions compared to age-matched peers and showed impaired ANS acuity compared to the younger, ability-matched control group, while exhibiting intact symbolic number processing. We conclude that (1) children with DD suffer from a general magnitude-processing deficit, (2) a shared magnitude system likely exists, and (3) a symbolic number-processing deficit in DD tends to be preceded by an ANS deficit.

Neurocognitive profiles of learning disabled children with neurofibromatosis type 1

Neurofibromatosis 1 (NF1) is a genetic condition generally associated with intellectual deficiency and learning disabilities. Although there have been groundbreaking advances in the understanding of the molecular, cellular, and neural systems underlying learning deficits associated to NF1 in animal models, much remains to be learned about the spectrum of neurocognitive phenotype associated with the NF1 clinical syndrome. In the present study, 32 children with NF1 ranging from 7 to 14 years were evaluated with neurocognitive tests dedicated to assess basic capacities which are involved in reading and mathematical achievement. Deficits in lexical and phonological strategies and poor number facts retrieval were found underlying reading and arithmetic disorders, respectively. Additionally, efficiencies in lexical/phonological strategies and mental arithmetic were significant predictors of individual differences in reading attainment and math. However, deficits in core numeric capacities were not found in the sample, suggesting that it is not responsible for calculation dysfluency. The estimated prevalence of Developmental Dyscalculia was 18.8%, and the male:female ratio was 5:1. On the other hand, the prevalence of Developmental Dyslexia was almost 3 times as high (50%), and no gender differences were found (male: female ratio = 1:1). This study offers new evidence to the neurocognitive phenotype of NF1 contributing to an in depth understanding of this condition, but also to possible treatments for the cognitive deficits associated with NF1.

Contributions from specific and general factors to unique deficits: two cases of mathematics learning difficulties

Mathematics learning difficulties are a highly comorbid and heterogeneous set of disorders linked to several dissociable mechanisms and endophenotypes. Two of these endophenotypes consist of primary deficits in number sense and verbal numerical representations. However, currently acknowledged endophenotypes are underspecified regarding the role of automatic vs. controlled information processing, and their description should be complemented. Two children with specific deficits in number sense and verbal numerical representations and normal or above-normal intelligence and preserved visuospatial cognition illustrate this point. Child H.V. exhibited deficits in number sense and fact retrieval. Child G.A. presented severe deficits in orally presented problems and transcoding tasks. A partial confirmation of the two endophenotypes that relate to the number sense and verbal processing was obtained, but a much more clear differentiation between the deficits presented by H.V. and G.A. can be reached by looking at differential impairments in modes of processing. H.V. is notably competent in the use of controlled processing but has problems with more automatic processes, such as nonsymbolic magnitude processing, speeded counting and fact retrieval. In contrast, G.A. can retrieve facts and process nonsymbolic magnitudes but exhibits severe impairment in recruiting executive functions and the concentration that is necessary to accomplish transcoding tasks and word problem solving. These results indicate that typical endophenotypes might be insufficient to describe accurately the deficits that are observed in children with mathematics learning abilities. However, by incorporating domain-specificity and modes of processing into the assessment of the endophenotypes, individual deficit profiles can be much more accurately described. This process calls for further specification of the endophenotypes in mathematics learning difficulties.

Preliminary evidence for performance enhancement following parietal lobe stimulation in Developmental Dyscalculia

Nearly 7% of the population exhibit difficulties in dealing with numbers and performing arithmetic, a condition named Developmental Dyscalculia (DD), which significantly affects the educational and professional outcomes of these individuals, as it often persists into adulthood. Research has mainly focused on behavioral rehabilitation, while little is known about performance changes and neuroplasticity induced by the concurrent application of brain-behavioral approaches. It has been shown that numerical proficiency can be enhanced by applying a small-yet constant-current through the brain, a non-invasive technique named transcranial electrical stimulation (tES). Here we combined a numerical learning paradigm with transcranial direct current stimulation (tDCS) in two adults with DD to assess the potential benefits of this methodology to remediate their numerical difficulties. Subjects learned to associate artificial symbols to numerical quantities within the context of a trial and error paradigm, while tDCS was applied to the posterior parietal cortex (PPC). The first subject (DD1) received anodal stimulation to the right PPC and cathodal stimulation to the left PPC, which has been associated with numerical performance's improvements in healthy subjects. The second subject (DD2) received anodal stimulation to the left PPC and cathodal stimulation to the right PPC, which has been shown to impair numerical performance in healthy subjects. We examined two indices of numerical proficiency: (i) automaticity of number processing; and (ii) mapping of numbers onto space. Our results are opposite to previous findings with non-dyscalculic subjects. Only anodal stimulation to the left PPC improved both indices of numerical proficiency. These initial results represent an important step to inform the rehabilitation of developmental learning disabilities, and have relevant applications for basic and applied research in cognitive neuroscience, rehabilitation, and education.

Left fronto-parietal white matter correlates with individual differences in children's ability to solve additions and multiplications: a tractography study

Functional neuroimaging data have pointed to the activation of a fronto-parietal network during calculation tasks, the activity of which is modulated by arithmetic operation and arithmetical competence. As the cortical brain regions of this network are distant, it is crucial to investigate the white matter connections between them and to examine how these connections are related to different arithmetic operations and individual differences in arithmetical competence. By using diffusion tensor imaging (DTI) tractography in eighteen 12-year-olds, we tested whether white matter pathways connecting these distant regions were related to children's arithmetical competence and how this association was modulated by operation. For each child, we delineated the three subcomponents of the arcuate fasciculus, a bundle of pathways linking frontal and temporo-parietal regions that are commonly active during calculation tasks. Fractional anisotropy in the left anterior portion of the arcuate fasciculus was positively correlated with addition and multiplication, but not with subtraction and division, suggesting a specific role of this left anterior segment in the solution of those problems that are expected to be solved with fact retrieval. The observed correlation was not explained by age, intelligence and working memory. Follow-up control analyses using different types of reading measures revealed that the observed correlation only disappeared when measures that draw heavily on phonological processing, such as non-word reading, were controlled for, suggesting that the association between the left arcuate fasciculus-anterior and addition/multiplication reflects the involvement of phonological processing. These results are the first to demonstrate that individual differences in fronto-parietal white matter are associated with arithmetical competence in typically developing children of a very narrow age range and indicate that this association is modulated by arithmetic operation.

Diagnosing developmental dyscalculia on the basis of reliable single case FMRI methods: promises and limitations

FMRI-studies are mostly based on a group study approach, either analyzing one group or comparing multiple groups, or on approaches that correlate brain activation with clinically relevant criteria or behavioral measures. In this study we investigate the potential of fMRI-techniques focusing on individual differences in brain activation within a test-retest reliability context. We employ a single-case analysis approach, which contrasts dyscalculic children with a control group of typically developing children. In a second step, a support-vector machine analysis and cluster analysis techniques served to investigate similarities in multivariate brain activation patterns. Children were confronted with a non-symbolic number comparison and a non-symbolic exact calculation task during fMRI acquisition. Conventional second level group comparison analysis only showed small differences around the angular gyrus bilaterally and the left parieto-occipital sulcus. Analyses based on single-case statistical procedures revealed that developmental dyscalculia is characterized by individual differences predominantly in visual processing areas. Dyscalculic children seemed to compensate for relative under-activation in the primary visual cortex through an upregulation in higher visual areas. However, overlap in deviant activation was low for the dyscalculic children, indicating that developmental dyscalculia is a disorder characterized by heterogeneous brain activation differences. Using support vector machine analysis and cluster analysis, we tried to group dyscalculic and typically developing children according to brain activation. Fronto-parietal systems seem to qualify for a distinction between the two groups. However, this was only effective when reliable brain activations of both tasks were employed simultaneously. Results suggest that deficits in number representation in the visual-parietal cortex get compensated for through finger related aspects of number representation in fronto-parietal cortex. We conclude that dyscalculic children show large individual differences in brain activation patterns. Nonetheless, the majority of dyscalculic children can be differentiated from controls employing brain activation patterns when appropriate methods are used.

Neural connectivity patterns underlying symbolic number processing indicate mathematical achievement in children

In early childhood, humans learn culturally specific symbols for number that allow them entry into the world of complex numerical thinking. Yet little is known about how the brain supports the development of the uniquely human symbolic number system. Here, we use functional magnetic resonance imaging along with an effective connectivity analysis to investigate the neural substrates for symbolic number processing in young children. We hypothesized that, as children solidify the mapping between symbols and underlying magnitudes, important developmental changes occur in the neural communication between the right parietal region, important for the representation of non-symbolic numerical magnitudes, and other brain regions known to be critical for processing numerical symbols. To test this hypothesis, we scanned children between 4 and 6 years of age while they performed a magnitude comparison task with Arabic numerals (numerical, symbolic), dot arrays (numerical, non-symbolic), and lines (non-numerical). We then identified the right parietal seed region that showed greater blood-oxygen-level-dependent signal in the numerical versus the non-numerical conditions. A psychophysiological interaction method was used to find patterns of effective connectivity arising from this parietal seed region specific to symbolic compared to non-symbolic number processing. Two brain regions, the left supramarginal gyrus and the right precentral gyrus, showed significant effective connectivity from the right parietal cortex. Moreover, the degree of this effective connectivity to the left supramarginal gyrus was correlated with age, and the degree of the connectivity to the right precentral gyrus predicted performance on a standardized symbolic math test. These findings suggest that effective connectivity underlying symbolic number processing may be critical as children master the associations between numerical symbols and magnitudes, and that these connectivity patterns may serve as an important indicator of mathematical achievement.

Brain structure, number magnitude processing, and math proficiency in 6- to 7-year-old children born prematurely: a voxel-based morphometry study

The aim of the present voxel-based morphometry study was to examine the link between brain structure and number skills in a group of 6-7-year-old children born prematurely, which are considered to be an at-risk population for mathematical learning disabilities. Therefore, gray and white matter density values were extracted from brain areas previously reported to be relevant for number processing in developing brain systems and, thereafter, correlated with response time results tapping semantic number knowledge [i.e. numerical distance effect (NDE) derived from a number comparison task] as well as with general math proficiency (as indexed by a standardized calculation test). Behavioral results disclosed a significant NDE, thus indicating well-established number magnitude representations for one-digit numerals in our study group. Significant positive correlations between gray matter and NDE emerged in parietal regions (including the right anterior inferior and the left superior parietal lobe) and in the right superior temporal gyrus. Moreover, white matter and NDE were negatively correlated in the right anterior inferior parietal lobe and the right inferior frontal gyrus. Overall, our results are novel insofar as they show that in 6-7-year-old children born prematurely, individual differences in gray and white matter structures are associated with numerical skills. Importantly, in our study group the observed link between brain structure and behavioral performance emerges only regarding an experimental task tapping semantic number knowledge, whereas general math proficiency does not seem to be related to individual differences in brain structure in our study group.

Residual number processing in dyscalculia

Developmental dyscalculia – a congenital learning disability in understanding numerical concepts – is typically associated with parietal lobe abnormality. However, people with dyscalculia often retain some residual numerical abilities, reported in studies that otherwise focused on abnormalities in the dyscalculic brain. Here we took a different perspective by focusing on brain regions that support residual number processing in dyscalculia. All participants accurately performed semantic and categorical colour-decision tasks with numerical and non-numerical stimuli, with adults with dyscalculia performing slower than controls in the number semantic tasks only. Structural imaging showed less grey-matter volume in the right parietal cortex in people with dyscalculia relative to controls. Functional MRI showed that accurate number semantic judgements were maintained by parietal and inferior frontal activations that were common to adults with dyscalculia and controls, with higher activation for participants with dyscalculia than controls in the right superior frontal cortex and the left inferior frontal sulcus. Enhanced activation in these frontal areas was driven by people with dyscalculia who made faster rather than slower numerical decisions; however, activation could not be accounted for by response times per se, because it was greater for fast relative to slow dyscalculics but not greater for fast controls relative to slow dyscalculics. In conclusion, our results reveal two frontal brain regions that support efficient number processing in dyscalculia.

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Dyscalculics (DD) show congenital number impairment due to parietal abnormalities.

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However DD often show residual number skills which have not been studied before.

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We studied the brain networks supporting residual skills and individual differences

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DD: reduced parietal grey-matter, accurate but slower than controls in number tasks

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Faster DD responses over-activated two frontal areas

Fractionating the neural correlates of individual working memory components underlying arithmetic problem solving skills in children

Baddeley and Hitch's multi-component working memory (WM) model has played an enduring and influential role in our understanding of cognitive abilities. Very little is known, however, about the neural basis of this multi-component WM model and the differential role each component plays in mediating arithmetic problem solving abilities in children. Here, we investigate the neural basis of the central executive (CE), phonological (PL) and visuo-spatial (VS) components of WM during a demanding mental arithmetic task in 7-9 year old children (N=74). The VS component was the strongest predictor of math ability in children and was associated with increased arithmetic complexity-related responses in left dorsolateral and right ventrolateral prefrontal cortices as well as bilateral intra-parietal sulcus and supramarginal gyrus in posterior parietal cortex. Critically, VS, CE and PL abilities were associated with largely distinct patterns of brain response. Overlap between VS and CE components was observed in left supramarginal gyrus and no overlap was observed between VS and PL components. Our findings point to a central role of visuo-spatial WM during arithmetic problem-solving in young grade-school children and highlight the usefulness of the multi-component Baddeley and Hitch WM model in fractionating the neural correlates of arithmetic problem solving during development.

Visuo-spatial working memory is an important source of domain-general vulnerability in the development of arithmetic cognition

The study of developmental disorders can provide a unique window into the role of domain-general cognitive abilities and neural systems in typical and atypical development. Mathematical disabilities (MD) are characterized by marked difficulty in mathematical cognition in the presence of preserved intelligence and verbal ability. Although studies of MD have most often focused on the role of core deficits in numerical processing, domain-general cognitive abilities, in particular working memory (WM), have also been implicated. Here we identify specific WM components that are impaired in children with MD and then examine their role in arithmetic problem solving. Compared to typically developing (TD) children, the MD group demonstrated lower arithmetic performance and lower visuo-spatial working memory (VSWM) scores with preserved abilities on the phonological and central executive components of WM. Whole brain analysis revealed that, during arithmetic problem solving, left posterior parietal cortex, bilateral dorsolateral and ventrolateral prefrontal cortex, cingulate gyrus and precuneus, and fusiform gyrus responses were positively correlated with VSWM ability in TD children, but not in the MD group. Additional analyses using a priori posterior parietal cortex regions previously implicated in WM tasks, demonstrated a convergent pattern of results during arithmetic problem solving. These results suggest that MD is characterized by a common locus of arithmetic and VSWM deficits at both the cognitive and functional neuroanatomical levels. Unlike TD children, children with MD do not use VSWM resources appropriately during arithmetic problem solving. This work advances our understanding of VSWM as an important domain-general cognitive process in both typical and atypical mathematical skill development.

Design and evaluation of the computer-based training program Calcularis for enhancing numerical cognition

This article presents the design and a first pilot evaluation of the computer-based training program Calcularis for children with developmental dyscalculia (DD) or difficulties in learning mathematics. The program has been designed according to insights on the typical and atypical development of mathematical abilities. The learning process is supported through multimodal cues, which encode different properties of numbers. To offer optimal learning conditions, a user model completes the program and allows flexible adaptation to a child's individual learning and knowledge profile. Thirty-two children with difficulties in learning mathematics completed the 6–12-weeks computer training. The children played the game for 20 min per day for 5 days a week. The training effects were evaluated using neuropsychological tests. Generally, children benefited significantly from the training regarding number representation and arithmetic operations. Furthermore, children liked to play with the program and reported that the training improved their mathematical abilities.

Developmental dyscalculia: a dysconnection syndrome?

Numerical understanding is important for everyday life. For children with developmental dyscalculia (DD), numbers and magnitudes present profound problems which are thought to be based upon neuronal impairments of key regions for numerical understanding. The aim of the present study was to investigate possible differences in white matter fibre integrity between children with DD and controls using diffusion tensor imaging. White matter integrity and behavioural measures were evaluated in 15 children with developmental dyscalculia aged around 10 years and 15 matched controls. The main finding, obtained by a whole brain group comparison, revealed reduced fractional anisotropy in the superior longitudinal fasciculus in children with developmental dyscalculia. In addition, a region of interest analysis exhibited prominent deficits in fibres of the superior longitudinal fasciculus adjacent to the intraparietal sulcus, which is thought to be the core region for number processing. To conclude, our results outline deficient fibre projection between parietal, temporal and frontal regions in children with developmental dyscalculia, and therefore raise the question of whether dyscalculia can be seen as a dysconnection syndrome. Since the superior longitudinal fasciculus is involved in the integration and control of distributed brain processes, the present results highlight the importance of considering broader domain-general mechanisms in the diagnosis and therapy of dyscalculia.

Numerical Transcoding Proficiency in 10-Year-Old Schoolchildren is Associated with Gray Matter Inter-Individual Differences: A Voxel-Based Morphometry Study

Are individual differences in numerical performance sustained by variations in gray matter volume in schoolchildren? To our knowledge, this challenging question for neuroeducation has not yet been investigated in typical development. We used the Voxel-Based Morphometry method to search for possible structural brain differences between two groups of 10-year-old schoolchildren (N = 22) whose performance differed only in numerical transcoding between analog and symbolic systems. The results indicated that children with low numerical proficiency have less gray matter volume in the parietal (particularly in the left intraparietal sulcus and the bilateral angular gyri) and occipito-temporal areas. All the identified regions have previously been shown to be functionally involved in transcoding between analog and symbolic numerical systems. Our data contribute to a better understanding of the intertwined relationships between mathematics learning and brain structure in healthy schoolchildren.

A common variant in myosin-18B contributes to mathematical abilities in children with dyslexia and intraparietal sulcus variability in adults

The ability to perform mathematical tasks is required in everyday life. Although heritability estimates suggest a genetic contribution, no previous study has conclusively identified a genetic risk variant for mathematical performance. Research has shown that the prevalence of mathematical disabilities is increased in children with dyslexia. We therefore correlated genome-wide data of 200 German children with spelling disability, with available quantitative data on mathematic ability. Replication of the top findings in additional dyslexia samples revealed that rs133885 was a genome-wide significant marker for mathematical abilities (P(comb) = 7.71 × 10(-10), n = 699), with an effect size of 4.87%. This association was also found in a sample from the general population (P = 0.048, n = 1080), albeit with a lower effect size. The identified variant encodes an amino-acid substitution in MYO18B, a protein with as yet unknown functions in the brain. As areas of the parietal cortex, in particular the intraparietal sulcus (IPS), are involved in numerical processing in humans, we investigated whether rs133885 was associated with IPS morphology using structural magnetic resonance imaging data from 79 neuropsychiatrically healthy adults. Carriers of the MYO18B risk-genotype displayed a significantly lower depth of the right IPS. This validates the identified association between rs133885 and mathematical disability at the level of a specific intermediate phenotype.

Early risk predictors for impaired numerical skills in 5-year-old children born before 32 weeks of gestation

AIM

To unravel risk predictors for impaired numerical skills at 5 years of age in a population-based cohort of very preterm infants.

METHODS

Between January 2003 and August 2006, we prospectively enrolled all infants born in Tyrol with <32 weeks of gestation. A total of 161 of 223 preterm infants (participation rate 72.2%) had a detailed examination at 5 years of age including cognitive assessment (Hannover-Wechsler Intelligence Test for preschool children, third edition (HAWIVA-III) or Snijders-Oomen Nonverbal Intelligence Test (SON-R)). In 135 children, numerical abilities were assessed with the dyscalculia test TEDI-MATH. The association between pre- and postnatal factors and impaired numerical skills was analyzed by means of logistic regression analysis.

RESULTS

Dyscalculia test showed delayed numerical skills (TEDI-MATH Sum T-score <40) in 27 of 135 children tested (20.0%). In half of the children tested, delayed numerical abilities were related to lower IQ scores. Smoking in pregnancy, intracerebral haemorrhage and chronic lung disease were predictive of delayed numerical skills at 5 years of age in the multivariate analysis.

CONCLUSION

This study identified risk predictors for impaired numerical skills in preterm infants. Our data support the role of both pre- and perinatal factors in the evolution of mathematical deficits.

Interventions Supporting Children’s Mathematics School Success

In today’s society, mathematics is one of the most important competencies imparted in school. To improve children’s mathematical skills, existing interventions and trainings in mathematical learning address different proficiency levels and age groups, take place in different settings, can focus on a single task or a set of different tasks, be applied for different durations, and address different types of numerical content. However, when such trainings are evaluated, this often happens only insufficiently. In this review, we derive and apply four evaluation criteria in a meta-analysis of mathematical intervention literature: (i) evaluation with the actual target group, (ii) evaluation in comparison to a performance-matched control group, (iii) evaluation in comparison to a comparable alternative intervention, and (iv) separate evaluation of subcomponents in the case of multi-componential approaches. Based on these criteria, we review current intervention approaches, paying particular attention to how they were evaluated. A meta-analysis on 39 effect sizes extracted from 37 studies revealed a reliable impact of three of the above-proposed evaluation criteria on the reported efficacy of an intervention. In contrast, sample and methodological characteristics like grade level of participants or training duration were not associated with effect sizes. These data indicate that the reported efficacy of an intervention in mathematical learning may depend not only on the type of intervention conducted, but also on the thoroughness of the evaluation procedure.

An electrophysiological investigation of non-symbolic magnitude processing: numerical distance effects in children with and without mathematical learning disabilities

INTRODUCTION

The aim of the present study was to probe electrophysiological effects of non-symbolic numerical processing in 20 children with mathematical learning disabilities (mean age = 99.2 months) compared to a group of 20 typically developing matched controls (mean age = 98.4 months).

METHODS

EEG data were obtained while children were tested with a standard non-symbolic numerical comparison paradigm that allowed us to investigate the effects of numerical distance manipulations for different set sizes, i.e., the classical subitizing, counting and estimation ranges. Effects of numerical distance manipulations on event-related potential (ERP) amplitudes as well as activation patterns of underlying current sources were analyzed.

RESULTS

In typically developing children, the amplitudes of a late parietal positive-going ERP component showed systematic numerical distance effects that did not depend on set size. For the group of children with mathematical learning disabilities, ERP distance effects were found only for stimuli within the subitizing range. Current source density analysis of distance-related group effects suggested that areas in right inferior parietal regions are involved in the generation of the parietal ERP amplitude differences.

CONCLUSION

Our results suggest that right inferior parietal regions are recruited differentially by controls compared to children with mathematical learning disabilities in response to non-symbolic numerical magnitude processing tasks, but only for stimuli with set sizes that exceed the subitizing range.

Symbolic and non symbolic numerical representation in adults with and without developmental dyscalculia

Background

The question whether Developmental Dyscalculia (DD; a deficit in the ability to process numerical information) is the result of deficiencies in the non symbolic numerical representation system (e.g., a group of dots) or in the symbolic numerical representation system (e.g., Arabic numerals) has been debated in scientific literature. It is accepted that the non symbolic system is divided into two different ranges, the subitizing range (i.e., quantities from 1-4) which is processed automatically and quickly, and the counting range (i.e., quantities larger than 4) which is an attention demanding procedure and is therefore processed serially and slowly. However, so far no study has tested the automaticity of symbolic and non symbolic representation in DD participants separately for the subitizing and the counting ranges.

Methods

DD and control participants undergo a novel version of the Stroop task, i.e., the Enumeration Stroop. They were presented with a random series of between one and nine written digits, and were asked to name either the relevant written digit (in the symbolic task) or the relevant quantity of digits (in the non symbolic task) while ignoring the irrelevant aspect.

Result

DD participants, unlike the control group, didn't show any congruency effect in the subitizing range of the non symbolic task.

Conclusion

These findings suggest that DD may be impaired in the ability to process symbolic numerical information or in the ability to automatically associate the two systems (i.e., the symbolic vs. the non symbolic). Additionally DD have deficiencies in the non symbolic counting range.

The diagnosis and management of dyscalculia

BACKGROUND

Dyscalculia is defined as difficulty acquiring basic arithmetic skills that is not explained by low intelligence or inadequate schooling. About 5% of children in primary schools are affected. Dyscalculia does not improve without treatment.

METHODS

In this article, we selectively review publications on dyscalculia from multiple disciplines (medicine, psychology, neuroscience, education/special education).

RESULTS

Many children and adolescents with dyscalculia have associated cognitive dysfunction (e.g., impairment of working memory and visuospatial skills), and 20% to 60% of those affected have comorbid disorders such as dyslexia or attention deficit disorder. The few interventional studies that have been published to date document the efficacy of pedagogic-therapeutic interventions directed toward specific problem areas. The treatment is tailored to the individual patient's cognitive functional profile and severity of manifestations. Psychotherapy and/or medication are sometimes necessary as well.

CONCLUSION

The early identification and treatment of dyscalculia are very important in view of its frequent association with mental disorders. Sufferers need a thorough, neuropsychologically oriented diagnostic evaluation that takes account of the complexity of dyscalculia and its multiple phenotypes and can thus provide a basis for the planning of effective treatment.

Math Self-Assessment, but Not Negative Feelings, Predicts Mathematics Performance of Elementary School Children

Mathematics anxiety has been associated to performance in school mathematics. The association between math anxiety and psychosocial competencies as well as their specific contribution to explain school mathematics performance are still unclear. In the present study, the impact of sociodemographic factors, psychosocial competencies, and math anxiety on mathematics and spelling performance was examined in school children with and without mathematics difficulties. The specific contributions of psychosocial competencies (i.e., general anxiety and attentional deficits with hyperactivity) and math anxiety (i.e., self-assessment in mathematics) to school mathematics performance were found to be statistically independent from each other. Moreover, psychosocial competencies—but not math anxiety—were related also to spelling performance. These results suggest that psychosocial competencies are more related to general mechanisms of emotional regulation and emotional response towards academic performance, while mathematics anxiety is related to the specific cognitive aspect of self-assessment in mathematics.

Nature and culture of finger counting: diversity and representational effects of an embodied cognitive tool

Studies like the one conducted by Domahs et al. (2010, in Cognition) corroborate that finger counting habits affect how numbers are processed, and legitimize the assumption that this effect is culturally modulated. The degree of cultural diversity in finger counting, however, has been grossly underestimated in the field at large, which, in turn, has restricted research questions and designs. In this paper, we demonstrate that fingers as a tool for counting are not only naturally available, but are also-and crucially so-culturally encoded. To substantiate this, we outline the variability in finger counting and illustrate each of its types with instances from the literature. We argue that the different types of finger counting all constitute distinct representational systems, and we use their properties-dimensionality, dimensional representation, base and sub-base values, extendibility and extent, sign count, and regularity-to devise a typology of such systems. This allows us to explore representational effects, that is, the cognitive implications these properties may have, for instance, for the efficiency of information encoding and representation, ease of learning and mastering the system, or memory retrieval and cognitive load. We then highlight the ambivalent consequences arising from structural inconsistencies between finger counting and other modes of number representation like verbal or notational systems, and we discuss how this informs questions on the evolution and development of counting systems. Based on these analyses, we suggest some directions for future research in the field of embodied cognition that would profit substantially from taking into account the cultural diversity in finger counting.

Neurokognitive Grundlagen der typischen und atypischen Zahlenverarbeitung

Zusammenfassung: Numerische Kenntnisse bilden ein wichtiges Fundament für die schulische und berufliche Entwicklung. Viele Kinder leiden jedoch unter großen Schwierigkeiten beim Erlernen numerischer Kompetenzen und werden oft mit einer «entwicklungsbedingten Dyskalkulie» diagnostiziert. Eine wachsende Anzahl von Studien mit Hilfe bildgebender Verfahren zeigt nun, dass spezifische Regionen im Gehirn von Kindern mit Dyskalkulie einen atypischen Entwicklungsverlauf beim Erlernen basisnumerischer Kompetenzen – wie dem Vergleichen numerischer Mengen – aufweisen. Diese Studien deuten somit auf eine domänenspezifische Ursache der Rechenschwäche hin. In der vorliegenden Übersichtsarbeit möchten wir die Befunde zur typischen und atypischen Gehirnentwicklung der Zahlenverarbeitung von einer neurowissenschaftlichen Perspektive diskutieren. Weiters werden wichtige Implikationen für Diagnostik und Intervention besprochen.

Time-Resolved and Spatio-Temporal Analysis of Complex Cognitive Processes and their Role in Disorders like Developmental Dyscalculia

The aim of this article is to report on the importance and challenges of a time-resolved and spatio-temporal analysis of fMRI data from complex cognitive processes and associated disorders using a study on developmental dyscalculia (DD). Participants underwent fMRI while judging the incorrectness of multiplication results, and the data were analyzed using a sequence of methods, each of which progressively provided more a detailed picture of the spatio-temporal aspect of this disease. Healthy subjects and subjects with DD performed alike behaviorally though they exhibited parietal disparities using traditional voxel-based group analyses. Further and more detailed differences, however, surfaced with a time-resolved examination of the neural responses during the experiment. While performing inter-group comparisons, a third group of subjects with dyslexia (DL) but with no arithmetic difficulties was included to test the specificity of the analysis and strengthen the statistical base with overall fifty-eight subjects. Surprisingly, the analysis showed a functional dissimilarity during an initial reading phase for the group of dyslexic but otherwise normal subjects, with respect to controls, even though only numerical digits and no alphabetic characters were presented. Thus our results suggest that time-resolved multi-variate analysis of complex experimental paradigms has the ability to yield powerful new clinical insights about abnormal brain function. Similarly, a detailed compilation of aberrations in the functional cascade may have much greater potential to delineate the core processing problems in mental disorders.

The neuroethics of non-invasive brain stimulation

Transcranial direct current stimulation (TDCS) is a brain stimulation tool that is portable, painless, inexpensive, apparently safe, and with potential long-term efficacy. Recent results obtained from TDCS experiments offer exciting possibilities for the enhancement and treatment of normal or impaired abilities, respectively. We discuss new neuroethical problems that have emerged from the usage of TDCS, and also focus on one of the most likely future applications of TDCS: enhancing learning and cognition in children with typical and atypical development.

The role of finger representations and saccades for number processing: an FMRI study in children

A possible functional role of finger representations for the development of early numerical cognition has been the subject of recent debate; however, until now, only behavioral studies have directly supported this view. Working from recent models of number processing, we focused on the neural networks involved in numerical tasks and their relationship to the areas underlying finger representations and saccades in children aged 6–12 years. We were able to differentiate three parietal circuits that were related to distinct aspects of number processing. Abstract magnitude processing was subserved by an association area also activated by saccades and visually guided finger movements. Addition processes led to activation in an area only engaged during saccade encoding, whereas counting processes resulted in the activation of an area only activated during visually guided finger movements, namely in the anterior intraparietal sulcus. Apart from this area, a large network of specifically finger-related brain areas including the ventral precentral sulcus, supplementary motor area, dorso-lateral prefrontal cortex, insula, thalamus, midbrain, and cerebellum was activated during (particularly non-symbolic) exact addition but not during magnitude comparison. Moreover, a finger-related activation cluster in the right ventral precentral sulcus was only present during non-symbolic addition and magnitude comparison, but not during symbolic number processing tasks. We conclude that finger counting may critically mediate the step from non-symbolic to symbolic and exact number processing via somatosensory integration processes and therefore represents an important example of embodied cognition.

A hand full of numbers: a role for offloading in arithmetics learning?

Finger counting has been associated to arithmetic learning in children. We examined children with (n = 14) and without (n = 84) mathematics learning difficulties with ages between 8 and 11 years. Deficits in finger gnosia were found in association to mathematical difficulties. Finger gnosia was particularly relevant for the performance in word problems requiring active manipulation of small magnitudes in the range between 1 and 10. Moreover, the deficits in finger gnosia could not be attributed to a shortage in working memory capacity but rather to a specific inability to use fingers to transiently represent magnitudes, tagging to be counted objects, and reducing the cognitive load necessary to solve arithmetic problems. Since finger gnosia was more related to symbolic than to non-symbolic magnitude processing, finger-related representation of magnitude seems to be an important link for learning the mapping of analog onto discrete symbolic magnitudes.