The diagnosis and management of dyscalculia

Cognitive, affective and sociological predictors of school performance in mathematics

Mathematics is a key school subject for some of the most lucrative and economically important careers. Low mathematics performance in school is associated with low psychometric intelligence, family socioeconomic status (SES), specific mathematical abilities, and high mathematics anxiety. We used a sample of Hungarian schoolchildren (N = 102, mean age = 12.3 years) to directly compare the predictive power of general intelligence, specific mathematical abilities measured by the Pedagogical Examination of Dyscalculia (DPV), mathematics anxiety, and socioeconomic status for mathematics grades. Mathematics grades correlated with IQ, specific mathematic ability, mathematics anxiety, and a composite measure of family SES. The WISC-IV showcased a manifest correlation of 0.62 and a latent correlation of 0.78 with the DPV and high manifest (r=-0.53) and latent (r=-0.59) correlations with mathematics anxiety. IQ alone accounted for 52% of the variance in mathematics grades. IQ, specific mathematical ability, family SES and mathematics anxiety jointly accounted for 56% of the variance in grades, with a non-significant contribution of specific mathematical ability and family SES over IQ and a marginal contribution of mathematics anxiety. Our results show that psychometric intelligence is the most important predictor of mathematics grades, while family SES and specific mathematical abilities are only associated with grades to the extent they reflect psychometric intelligence. The results, however, confirmed a small role of mathematics anxiety over intelligence in predicting grades.

Performance on curriculum-based mathematics assessments in developmental dyscalculia: the effect of content domain and question format

Developmental Dyscalculia (DD) is characterised by persistent difficulties in learning mathematical skills, which usually becomes apparent in the early years of schooling. Traditionally, DD is known to affect children's arithmetic processing, whilst other domains of mathematics receive much less research attention. Nevertheless, contemporary diagnostic guidelines suggest that DD is linked to widespread and diverse difficulties, both within and outside of the domain of numbers. This study examined the performance (i.e., accuracy and number of questions attempted) of children on a curriculum-based mathematics assessment, considering the effect of content domains, question format (i.e., multiple-choice questions vs. constructed response questions) and test half. Participants were forty children aged 8 to 11 years old with DD (n = 20) and a carefully matched control group of typically developing children (n = 20) from primary schools in Northern Ireland. Results revealed that the DD group achieved significantly lower scores than the control group across all areas of the curriculum, and the magnitude of group differences was similar across all content domains. These findings indicate that performance in content domains other than in arithmetic may be equally informative in supporting the identification of children with DD. In addition, we found that using multiple-choice questions may support learners with DD in achieving the best outcome, and, thus, could be useful for assessing mathematics skills in dyscalculic children in classroom contexts. Nevertheless, constructed response questions may show the greatest sensitivity to identifying learners at risk, and could be the most useful in diagnostic settings.

AI-Enhanced Dyscalculia Screening: A Survey of Methods and Applications for Children

New forms of interaction made possible by developments in special educational technologies can now help students with dyscalculia. Artificial intelligence (AI) has emerged as a promising tool in recent decades, particularly between 2001 and 2010, offering avenues to enhance the quality of education for individuals with dyscalculia. Therefore, the implementation of AI becomes crucial in addressing the needs of students with dyscalculia. Content analysis techniques were used to examine the literature covering the influence of AI on dyscalculia and its potential to assist instructors in promoting education for individuals with dyscalculia. The study sought to create a foundation for a more inclusive dyscalculia education in the future through in-depth studies. AI integration has had a big impact on educational institutions as well as people who struggle with dyscalculia. This paper highlights the importance of AI in improving the educational outcomes of students affected by dyscalculia.

Number sense deficits in children with developmental dyscalculia, dyslexia, co-occurring disorder and their typically developing peers

The aim of this study was to explore a number sense deficits in children with developmental dyscalculia, dyslexia, co-occurring disorder and their typically developing peers. A non-symbolic quantity comparison task was used in this study to examine whether children with dyscalculia have number sense deficits. Children aged 10-11 years old from nine primary schools in Taif city, Saudi Arabia, were selected to participate in this study. The children were divided into the dyscalculia group (n = 62), the dyslexia group (n = 60), and co-occurring disorder group (n = 65), and the typically developing peers group (n = 100).4 groups (dyscalculia, dyslexia, co-occurring disorder and typically developing peers group) × 2 stimulus ratio (6:7; 8:12). There were significant differences in non-symbolic quantity comparison tasks between children with dyslexia, co-occurring disorder, and typically developing peers. These results indicate that children with dyscalculia do have number sense deficiencies, but number sense deficiencies are not specific to children with dyscalculia.

Mathematics Skills in Epilepsy: A Systematic Review and Meta-Analysis

Mathematics incorporates a broad range of skills, which includes basic early numeracy skills, such as subitizing and basic counting to more advanced secondary skills including mathematics calculation and reasoning. The aim of this review was to undertake a detailed investigation of the severity and pattern of early numeracy and secondary mathematics skills in people with epilepsy. Searches were guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement. Twenty adult studies and 67 child studies were included in this review. Overall, meta-analyses revealed significant moderate impairments across all mathematics outcomes in both adults (g= -0.676), and children (g= -0.593) with epilepsy. Deficits were also observed for specific mathematics outcomes. For adults, impairments were found for mathematics reasoning (g= -0.736). However, two studies found that mathematics calculation was not significantly impaired, and an insufficient number of studies examined early numeracy skills in adults. In children with epilepsy, significant impairments were observed for each mathematics outcome: early numeracy (g= -0.383), calculation (g= -0.762), and reasoning (g= -0.572). The gravity of impairments also differed according to the site of seizure focus for children and adults, suggesting that mathematics outcomes were differentially vulnerable to the location of seizure focus.

Exploration heuristics decrease during youth

Deciding between exploring new avenues and exploiting known choices is central to learning, and this exploration-exploitation trade-off changes during development. Exploration is not a unitary concept, and humans deploy multiple distinct mechanisms, but little is known about their specific emergence during development. Using a previously validated task in adults, changes in exploration mechanisms were investigated between childhood (8-9 y/o, N = 26; 16 females), early (12-13 y/o, N = 38; 21 females), and late adolescence (16-17 y/o, N = 33; 19 females) in ethnically and socially diverse schools from disadvantaged areas. We find an increased usage of a computationally light exploration heuristic in younger groups, effectively accommodating their limited neurocognitive resources. Moreover, this heuristic was associated with self-reported, attention-deficit/hyperactivity disorder symptoms in this population-based sample. This study enriches our mechanistic understanding about how exploration strategies mature during development.

Relationship of Exclusion From Physical Education and Bullying in Students With Specific Developmental Disorder of Scholastic Skills

Objectives: This study aimed to analyze the relationships among exclusion from PE, gender, and bullying in adolescents with specific developmental disorder of scholastic skills (SDDSS) aged 11, 13, and 15 years in Czechia.

Methods: In total, the final research sample consisted of 13,953 students (49.4% boys) from the 2013/2014 Health Behaviour in School-aged Children survey. Chi-square tests and regression models stratified by presence of SDDSS diagnosis were used to assess the relationships between non-involvement in PA and bullying.

Results: Students diagnosed with SDDSS (12.4% of the sample) were more likely to be excluded from physical education (PE) than students without this diagnosis. This exclusion was associated with higher odds of bullying victimization and perpetration. Our findings further showed that male gender plays a significant role for bullying perpetration for both groups (with and without SDDSS) investigated in the present study.

Conclusion: Higher likelihood of aggressive behavior occurs in students who are excluded from PE, including students with SDDSS.

Heterogeneity of Dyscalculia Risk Dependent on the Type of Number Line Estimation Task and the Number Magnitude

An ability that is impaired in developmental dyscalculia (DD) is related to number line estimation (NLE). However, due to variability in NLE task performance, group differences do not exemplify the real difficulty level observed in the DD population. Thirty-two of the fifty-two participants posing dyscalculia risk (DR) (mean age = 9.88) experienced difficulties in mathematics. All the children performed two number-to-position tasks and two tasks requiring a verbal estimation of a number indicated on a line, utilizing the ranges 0–100 and 0–1000. The results showed that the estimation error in the verbal task was greater in the DR group than in the typically developed (TD) group for the 0–1000 range. In the number-to-position task, group differences were found for both ranges and the variability within both groups was smaller than it was in the verbal tasks. Analyses of each of the 26 numerical magnitudes revealed a more comprehensive pattern. The majority of the group effects were related to the 0–1000 line. Therefore, considerable data variability, especially in the DD group, suggests this issue must be analyzed carefully in the case of other mathematical capacities. It also critically questions some well-established phenomena and norms in experimental and diagnostic practices.

Discerning Developmental Dyscalculia and Neurodevelopmental Models of Numerical Cognition in a Disadvantaged Educational Context

Developmental Dyscalculia (DD) signifies a failure in representing quantities, which impairs the performance of basic math operations and schooling achievement during childhood. The lack of specificity in assessment measures and respective cut-offs are the most challenging factors to identify children with DD, particularly in disadvantaged educational contexts. This research is focused on a numerical cognition battery for children, designed to diagnose DD through 12 subtests. The aims of the present study were twofold: to examine the prevalence of DD in a country with generally low educational attainment, by comparing z-scores and percentiles, and to test three neurodevelopmental models of numerical cognition based on performance in this battery. Participants were 304 Brazilian school children aged 7–12 years of both sexes (143 girls), assessed by the Zareki-R. Performances on subtests and the total score increase with age without gender differences. The prevalence of DD was 4.6% using the fifth percentile and increased to 7.4% via z-score (in total 22 out of 304 children were diagnosed with DD). We suggest that a minus 1.5 standard deviation in the total score of the Zareki-R is a useful criterion in the clinical or educational context. Nevertheless, a percentile ≤ 5 seems more suitable for research purposes, especially in developing countries because the socioeconomic environment or/and educational background are strong confounder factors to diagnosis. The four-factor structure, based on von Aster and Shalev’s model of numerical cognition (Number Sense, Number Comprehension, Number Production and Calculation), was the best model, with significant correlations ranging from 0.89 to 0.97 at the 0.001 level.

Foundational Number Sense Training Gains Are Predicted by Hippocampal-Parietal Circuits

The development of mathematical skills in early childhood relies on number sense, the foundational ability to discriminate among quantities. Number sense in early childhood is predictive of academic and professional success, and deficits in number sense are thought to underlie lifelong impairments in mathematical abilities. Despite its importance, the brain circuit mechanisms that support number sense learning remain poorly understood. Here, we designed a theoretically motivated training program to determine brain circuit mechanisms underlying foundational number sense learning in female and male elementary school-age children (7-10 years). Our 4 week integrative number sense training program gradually strengthened the understanding of the relations between symbolic (Arabic numerals) and nonsymbolic (sets of items) representations of quantity. We found that our number sense training program improved symbolic quantity discrimination ability in children across a wide range of math abilities including children with learning difficulties. Crucially, the strength of pretraining functional connectivity between the hippocampus and intraparietal sulcus, brain regions implicated in associative learning and quantity discrimination, respectively, predicted individual differences in number sense learning across typically developing children and children with learning difficulties. Reverse meta-analysis of interregional coactivations across 14,371 fMRI studies and 89 cognitive functions confirmed a reliable role for hippocampal-intraparietal sulcus circuits in learning. Our study identifies a canonical hippocampal-parietal circuit for learning that plays a foundational role in children's cognitive skill acquisition. Findings provide important insights into neurobiological circuit markers of individual differences in children's learning and delineate a robust target for effective cognitive interventions.SIGNIFICANCE STATEMENT Mathematical skill development relies on number sense, the ability to discriminate among quantities. Here, we develop a theoretically motivated training program and investigate brain circuits that predict number sense learning in children during a period important for acquisition of foundational cognitive skills. Our integrated number sense training program was effective in children across a wide a range of math abilities, including children with learning difficulties. We identify hippocampal-parietal circuits that predict individual differences in learning gains. Our study identifies a brain circuit critical for the acquisition of foundational cognitive skills, which will be useful for developing effective interventions to remediate learning disabilities.

Math Fluency during Primary School

Math fluency is the ability to solve arithmetic facts quickly and accurately (i.e., addition and subtraction problems up to 20, and multiplication and division problems from the multiplication table). Curricula in primary school devote a significant period of time for learning and retrieval of arithmetic facts. Recently, a new computerized tool to assess math fluency—the BGU-MF (Ben-Gurion University Math Fluency) test—was developed and found to be a reliable and valid tool for adults. In the current study, we examine the performance of first to sixth-grade children in math fluency using the BGU-MF. The results present the performance of MF during childhood and emphasize that it continues to develop during primary school. Importantly, proficiency of MF differed by operations, and the automaticity of math facts was acquired in different grades. Moreover, we found that the BGU-MF is a reliable and valid tool not only for adults but also for children during primary school. Our study has educational implications for the teaching, practice, and retrieval of arithmetic facts.

The Cognitive Profile of Math Difficulties: A Meta-Analysis Based on Clinical Criteria

Math difficulties (MD) manifest across various domain-specific and domain-general abilities. However, the existing cognitive profile of MD is incomplete and thus not applicable in typical settings such as schools or clinics. So far, no review has applied inclusion criteria according to DSM or ICD, summarized domain-specific abilities or examined the validity of response time scores for MD identification. Based upon stringent clinical criteria, the current meta-analysis included 34 studies which compared cognitive performances of a group with MD (n = 680) and a group without MD (n = 1565). Criteria according to DSM and ICD were applied to identify MD (percentile rank ≤ 16, age range 8-12 years, no comorbidities/low IQ). Effect sizes for 22 abilities were estimated and separated by their level and type of scoring (AC = accuracy, RT = response time). A cognitive profile of MD was identified, characterized by distinct weaknesses in: (a) computation (calculation [AC], fact retrieval [AC]), (b) number sense (quantity processing [AC], quantity-number linking [RT], numerical relations [AC]), and (c) visual-spatial short-term storage [AC]. No particular strength was found. Severity of MD, group differences in reading performance and IQ did not significantly moderate the results. Further analyses revealed that (a) effects are larger when dealing with numbers or number words than with quantities, (b) MD is not accompanied by any weakness in abilities typically assigned to reading, and (c) weaknesses in visual-spatial short-term storage emphasize the notion that number and space are interlinked. The need for high-quality studies investigating domain-general abilities is discussed.

Domain-General Cognitive Skills in Children with Mathematical Difficulties and Dyscalculia: A Systematic Review of the Literature

Mathematical performance implies a series of numerical and mathematical skills (both innate and derived from formal training) as well as certain general cognitive abilities that, if inadequate, can have a cascading effect on mathematics learning. These latter skills were the focus of the present systematic review. Method: The reviewing process was conducted according to the PRISMA statement. We included 46 studies comparing school-aged children’s performance with and without math difficulties in the following cognitive domains: processing speed, phonological awareness, short- and long-term memory, executive functions, and attention. Results: The results showed that some general cognitive domains were compromised in children with mathematical difficulties (i.e., executive functions, attention, and processing speed). Conclusions: These cognitive functions should be evaluated during the diagnostic process in order to better understand the child’s profile and propose individually tailored interventions. However, further studies should investigate the role of skills that have been poorly investigated to date (e.g., long-term memory and phonological awareness).

Boosting Numerical Cognition in Children and Adolescents with Mathematical Learning Disabilities by a Brain-Based Intervention: A Study Protocol for a Randomized, Sham-Controlled Clinical Trial

Numbers are everywhere, and supporting difficulties in numerical cognition (e.g., mathematical learning disability (MLD)) in a timely, effective manner is critical for their daily use. To date, only low-efficacy cognitive-based interventions are available. The extensive data on the neurobiology of MLD have increased interest in brain-directed approaches. The overarching goal of this study protocol is to provide the scientific foundation for devising brain-based and evidence-based treatments in children and adolescents with MLD. In this double-blind, between-subject, sham-controlled, randomized clinical trial, transcranial random noise stimulation (tRNS) plus cognitive training will be delivered to participants. Arithmetic, neuropsychological, psychological, and electrophysiological measures will be collected at baseline (T0), at the end of the interventions (T1), one week (T2) and three months later (T3). We expect that tRNS plus cognitive training will significantly improve arithmetic measures at T1 and at each follow-up (T2, T3) compared with placebo and that such improvements will correlate robustly and positively with changes in the neuropsychological, psychological, and electrophysiological measures. We firmly believe that this clinical trial will produce reliable and positive results to accelerate the validation of brain-based treatments for MLD that have the potential to impact quality of life.

Shared Developmental Trajectories for Fractional Reasoning and Fine Motor Ability in 4 and 5 Year Olds

We investigated preschool-aged children's understanding of early fractional tasks and how that performance correlates with fine motor skills and use of gestures while counting. Participants were 33 preschoolers aged 4 to 5 in two Southeastern public elementary schools. Children were tested individually in an interview-like setting. Mathematics tasks were presented in a paper and pencil format and the Grooved Pegboard test assessed fine motor skills. Finally, utilization of gestures was evaluated by taking a behavioral rating of the child's hand morphology, accuracy of gestures, and synchrony of gestures and spoken word while performing a counting task. Results indicate that performance on fractional reasoning tasks significantly predicts both fine motor ability and accuracy of gestures.

Efficacy of a Computer-Based Learning Program in Children With Developmental Dyscalculia. What Influences Individual Responsiveness?

This study presents the evaluation of a computer-based learning program for children with developmental dyscalculia and focuses on factors affecting individual responsiveness. The adaptive training program Calcularis 2.0 has been developed according to current neuro-cognitive theory of numerical cognition. It aims to automatize number representations, supports the formation and access to the mental number line and trains arithmetic operations as well as arithmetic fact knowledge in expanding number ranges. Sixty-seven children with developmental dyscalculia from second to fifth grade (mean age 8.96 years) were randomly assigned to one of two groups (Calcularis group, waiting control group). Training duration comprised a minimum of 42 training sessions à 20 min within a maximum period of 13 weeks. Compared to the waiting control group, children of the Calcularis group demonstrated a higher benefit in arithmetic operations and number line estimation. These improvements were shown to be stable after a 3-months post training interval. In addition, this study examines which predictors accounted for training improvements. Results indicate that this self-directed training was especially beneficial for children with low math anxiety scores and without an additional reading and/or spelling disorder. In conclusion, Calcularis 2.0 supports children with developmental dyscalculia to improve their arithmetical abilities and their mental number line representation. However, it is relevant to further adapt the setting to the individual circumstances.

The Diagnosis and Treatment of Dyscalculia

BACKGROUND

3-7% of all children, adolescents, and adults suffer from dyscalculia. Severe, persistent difficulty performing arithmetical calculations leads to marked impairment in school, at work, and in everyday life and elevates the risk of comorbid mental disorders. The state of the evidence underlying various methods of diagnosing and treating this condition is unclear.

METHODS

Systematic literature searches were carried out from April 2015 to June 2016 in the PsycInfo, PSYNDEX, MEDLINE, ProQuest, ERIC, Cochrane Library, ICTRP, and MathEduc databases. The main search terms on dyscalculia were the German terms "Rechenstörung," "Rechenschwäche," and "Dyskalkulie" and the English terms "dyscalculia," "math disorder, and "math disability." The data from the retrieved studies were evaluated in a meta-analysis, and corresponding recommendations on the diagnosis and treatment of dyscalculia were jointly issued by the 20 societies and associations that participated in the creation of this guideline.

RESULTS

The diagnosis of dyscalculia should only be made if the person in question displays below-average mathematical performance when seen in the context of relevant information from the individual history, test findings, clinical examination, and further psychosocial assessment. The treatment should be directed toward the individual mathematical problem areas. The mean effect size found across all intervention trials was 0.52 (95% confidence interval [0.42; 0.62]). Treatment should be initiated early on in the primary-school years and carried out by trained specialists in an individual setting; comorbid symptoms and disorders should also receive attention. Persons with dyscalculia are at elevated risk of having dyslexia as well (odds ratio [OR]: 12.25); the same holds for attention deficit/hyperactivity disorder and for other mental disorders, both internalizing (such as anxiety and depression) and externalizing (e.g., disorders characterized by aggression and rule-breaking).

CONCLUSION

Symptom-specific interventions involving the training of specific mathematical content yield the best results. There is still a need for high-quality intervention trials and for suitable tests and learning programs for older adolescents and adults.

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.

Developmental Dyscalculia and Automatic Magnitudes Processing: Investigating Interference Effects between Area and Perimeter

The relationship between numbers and other magnitudes has been extensively investigated in the scientific literature. Here, the objectives were to examine whether two continuous magnitudes, area and perimeter, are automatically processed and whether adults with developmental dyscalculia (DD) are deficient in their ability to automatically process one or both of these magnitudes. Fifty-seven students (30 with DD and 27 with typical development) performed a novel Stroop-like task requiring estimation of one aspect (area or perimeter) while ignoring the other. In order to track possible changes in automaticity due to practice, we measured performance after initial and continuous exposure to stimuli. Similar to previous findings, current results show a significant group × congruency interaction, evident beyond exposure level or magnitude type. That is, the DD group systematically showed larger Stroop effects. However, analysis of each exposure period showed that during initial exposure to stimuli the DD group showed larger Stroop effects in the perimeter and not in the area task. In contrast, during continuous exposure to stimuli no triple interaction was evident. It is concluded that both magnitudes are automatically processed. Nevertheless, individuals with DD are deficient in inhibiting irrelevant magnitude information in general and, specifically, struggle to inhibit salient area information after initial exposure to a perimeter comparison task. Accordingly, the findings support the assumption that DD involves a deficiency in multiple cognitive components, which include domain-specific and domain-general cognitive functions.

Perfil de niños con déficits en la cognición numérica

La presente investigación tuvo como objetivo caracterizar el perfil neurocognitivo de niños en relación a las habilidades cuantitativas, intelectuales, de memoria operativa y sus aspectos emocionales. La muestra fue de 42 niños de edad escolar de 8 a 10 años, divididos en dos grupos: con dificultades en aritmética (CDA=21) y sin dificultades en aritmética (SDA=21). Los niños fueron evaluados a través de pruebas cognitivas y escalas de comportamiento, que analizaron variables como: rendimiento escolar, razonamiento abstracto, memoria operativa, cognición numérica, ansiedad y estrés. El perfil de los niños CDA se caracterizó por dificultades en el rendimiento escolar de forma general. Fueron encontrados síntomas de estrés compatibles con fases de alerta y resistencia, baja capacidad de memoria operativa y de cognición numérica, específicamente de procesamiento numérico y cálculo.

The Origin of Mathematics and Number Sense in the Cerebellum: with Implications for Finger Counting and Dyscalculia

Background

Mathematicians and scientists have struggled to adequately describe the ultimate foundations of mathematics. Nobel laureates Albert Einstein and Eugene Wigner were perplexed by this issue, with Wigner concluding that the workability of mathematics in the real world is a mystery we cannot explain. In response to this classic enigma, the major purpose of this article is to provide a theoretical model of the ultimate origin of mathematics and “number sense” (as defined by S. Dehaene) that is proposed to involve the learning of inverse dynamics models through the collaboration of the cerebellum and the cerebral cortex (but prominently cerebellum-driven). This model is based upon (1) the modern definition of mathematics as the “science of patterns,” (2) cerebellar sequence (pattern) detection, and (3) findings that the manipulation of numbers is automated in the cerebellum. This cerebro-cerebellar approach does not necessarily conflict with mathematics or number sense models that focus on brain functions associated with especially the intraparietal sulcus region of the cerebral cortex. A direct corollary purpose of this article is to offer a cerebellar inner speech explanation for difficulty in developing “number sense” in developmental dyscalculia.

Results

It is argued that during infancy the cerebellum learns (1) a first tier of internal models for a primitive physics that constitutes the foundations of visual-spatial working memory, and (2) a second (and more abstract) tier of internal models based on (1) that learns “number” and relationships among dimensions across the primitive physics of the first tier. Within this context it is further argued that difficulty in the early development of the second tier of abstraction (and “number sense”) is based on the more demanding attentional requirements imposed on cerebellar inner speech executive control during the learning of cerebellar inverse dynamics models. Finally, it is argued that finger counting improves (does not originate) “number sense” by extending focus of attention in executive control of silent cerebellar inner speech.

Discussion

It is suggested that (1) the origin of mathematics has historically been an enigma only because it is learned below the level of conscious awareness in cerebellar internal models, (2) understandings of the development of “number sense” and developmental dyscalculia can be advanced by first understanding the ultimate foundations of number and mathematics do not simply originate in the cerebral cortex, but rather in cerebro-cerebellar collaboration (predominately driven by the cerebellum).

Conclusion

It is concluded that difficulty with “number sense” results from the extended demands on executive control in learning inverse dynamics models associated with cerebellar inner speech related to the second tier of abstraction (numbers) of the infant’s primitive physics.

Transcranial random noise stimulation and cognitive training to improve learning and cognition of the atypically developing brain: A pilot study

Learning disabilities that affect about 10% of human population are linked to atypical neurodevelopment, but predominantly treated by behavioural interventions. Behavioural interventions alone have shown little efficacy, indicating limited success in modulating neuroplasticity, especially in brains with neural atypicalities. Even in healthy adults, weeks of cognitive training alone led to inconsistent generalisable training gains, or "transfer effects" to non-trained materials. Meanwhile, transcranial random noise stimulation (tRNS), a painless and more direct neuromodulation method was shown to further promote cognitive training and transfer effects in healthy adults without harmful effects. It is unknown whether tRNS on the atypically developing brain might promote greater learning and transfer outcomes than training alone. Here, we show that tRNS over the bilateral dorsolateral prefrontal cortices (dlPFCs) improved learning and performance of children with mathematical learning disabilities (MLD) during arithmetic training compared to those who received sham (placebo) tRNS. Training gains correlated positively with improvement on a standardized mathematical diagnostic test, and this effect was strengthened by tRNS. These findings mirror those in healthy adults, and encourage replications using larger cohorts. Overall, this study offers insights into the concept of combining tRNS and cognitive training for improving learning and cognition of children with learning disabilities.

Evaluation of a Computer-Based Training Program for Enhancing Arithmetic Skills and Spatial Number Representation in Primary School Children

Calcularis is a computer-based training program which focuses on basic numerical skills, spatial representation of numbers and arithmetic operations. The program includes a user model allowing flexible adaptation to the child's individual knowledge and learning profile. The study design to evaluate the training comprises three conditions (Calcularis group, waiting control group, spelling training group). One hundred and thirty-eight children from second to fifth grade participated in the study. Training duration comprised a minimum of 24 training sessions of 20 min within a time period of 6-8 weeks. Compared to the group without training (waiting control group) and the group with an alternative training (spelling training group), the children of the Calcularis group demonstrated a higher benefit in subtraction and number line estimation with medium to large effect sizes. Therefore, Calcularis can be used effectively to support children in arithmetic performance and spatial number representation.

Lack of replication for the myosin-18B association with mathematical ability in independent cohorts

Twin studies indicate that dyscalculia (or mathematical disability) is caused partly by a genetic component, which is yet to be understood at the molecular level. Recently, a coding variant (rs133885) in the myosin-18B gene was shown to be associated with mathematical abilities with a specific effect among children with dyslexia. This association represents one of the most significant genetic associations reported to date for mathematical abilities and the only one reaching genome-wide statistical significance. We conducted a replication study in different cohorts to assess the effect of rs133885 maths-related measures. The study was conducted primarily using the Avon Longitudinal Study of Parents and Children (ALSPAC), (N = 3819). We tested additional cohorts including the York Cohort, the Specific Language Impairment Consortium (SLIC) cohort and the Raine Cohort, and stratified them for a definition of dyslexia whenever possible. We did not observe any associations between rs133885 in myosin-18B and mathematical abilities among individuals with dyslexia or in the general population. Our results suggest that the myosin-18B variant is unlikely to be a main factor contributing to mathematical abilities.

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.

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.