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A long-standing debate concerns whether developmental dyscalculia is characterized by core deficits in processing nonsymbolic or symbolic numerical information as well as the role of domain-general difficulties. Heterogeneity in recruitment and diagnostic criteria make it difficult to disentangle this issue. Here, we selected children ( n = 58) with severely compromised mathematical skills (2 SD below average) but average domain-general skills from a large sample referred for clinical assessment of learning disabilities. From the same sample, we selected a control group of children ( n = 42) matched for IQ, age, and visuospatial memory but with average mathematical skills. Children with dyscalculia showed deficits in both symbolic and nonsymbolic number sense assessed with simple computerized tasks. Performance in the digit-comparison task and the numerosity match-to-sample task reliably separated children with developmental dyscalculia from controls in cross-validated logistic regression (area under the curve = .84). These results support a number-sense-deficit theory and highlight basic numerical abilities that could be targeted for early identification of at-risk children as well as for intervention.

The following analysis plan aims to test the effects of Calcularis, a math learning software, on numerical skills among 3rd and 4th grade Brazilian children with developmental dyscalculia.

A school-based study in South Africa

This review will address educators’ awareness of developmental dyscalculia, a specific learning disorder in Mathematics (SLDM). This review focuses on what we know globally about educators’ knowledge and awareness of dyscalculia.

Although researchers have debated whether a core deficit of nonsymbolic representation of magnitude underlies developmental dyscalculia (DD), research has mostly focused on numerosity processing. We probed the possibility of a general magnitude deficit in individuals with DD and asked whether sensitivity to size varied in contexts of depth ordering and size constancy. We measured full psychometric functions in size-discrimination tasks in 12 participants with DD and 13 control participants. Results showed that although people with DD exhibited veridical perceived magnitude, their sensitivity to size was clearly impaired. In contrast, when objects were embedded in depth cues allowing size-constancy computations, participants with DD demonstrated typical sensitivity to size. These results demonstrate a deficit in the perceptual resolutions of magnitude in DD. At the same time, the finding of an intact size constancy suggests that when magnitude perception is facilitated by implicit mandatory computations of size constancy, this deficit is no longer evident.

Abstract. Background: Poor numeracy and numerical learning problems are very common in our society and present serious obstacles in daily live, school or professional success. Accordingly, the goal of this study was to identify typical error patterns and problem solving strategies in children and adolescents with developmental dyscalculia (DD). Methods: We have examined 86 participants; half had a diagnosed DD (mean 15.5 years) and were compared to typically developing peers (mean 13.9 years). Numerical skills were tested by the standardized test battery BASIS-MATH 4–8. In addition, intelligence, alertness, spatial working memory, and math anxiety were assessed. Results: Results showed that subtractions, completion, and division are particularly challenging for DD. This applied notably to basic operations with large numbers, crossing tens/hundreds, but also simpler calculation problems. Item analyses revealed 10 calculation problems that differentiated best between groups. Moreover, DD used efficient calculation strategies to a lower extent. Discussion: In summary, basic numerical skills in DD, including those of lower difficulty levels, are clearly limited and even adolescents fail in such tasks. Moreover, we were able to identify 10 numerical tasks that would be particularly meaningful to implement in a DD-screener. Finally, our findings highlight the importance of considering individual problem-solving strategies when evaluating people with DD in a clinical, therapeutic or school setting.

Background Two hypotheses were tested regarding the characteristics of children with mathematical learning disabilities (MLD): (a) that children with MLD would have a 'core deficit' in basic number processing skills; and (b) that children with MLD would be at the end of a developmental continuum and have impairments in many cognitive skills. Methods From a large sample (N = 1,303) of typically developing children, we selected a group definable as having MLD. The children were given measures of basic number processing and domain-general constructs. Differences between the observed sample and a simulated population were estimated using Cohen's d and Bayes factors. Receiver operating characteristic curves were plotted, and the area under the curve was computed to ascertain the diagnostic power of measures. Results Results suggest that the differences between the MLD and control group can be defined along with general characteristics of the population rather than assuming single or multiple 'core deficits'. None of the measures of interest exceeded the diagnostic power that could be derived via simulation from the dimensional characteristics of the general population. Conclusions There is no evidence for core deficit(s) in MLD. We suggest that future research should focus on representative samples of typical populations and on carefully tested clinical samples confirming to the criteria of international diagnostic manuals. Clinical diagnoses require that MLD is persistent and resistant to intervention, so studies would deliver results less exposed to measurement fluctuations. Uniform diagnostic criteria would also allow for the easy cross-study comparison of samples overcoming a serious limitation of the current literature.

International audience; Developmental dyscalculia (DD) is a chronic condition that poses not only a barrier to employment and socio-emotional wellbeing but that also persists into adulthood. Thus, understanding the neuro-cognitive foundations of DD is relevant for both children and adults with DD. However, so far the vast majority of scientific research endeavours has been dedicated to the study of DD in children only. Consequently, our current understanding of DD in adulthood is rather patchy. The main aim of the present review is to summarize the scientific findings on DD in adults by focusing on its cognitive manifestations and neural substrates in adults. For instance, research on DD in adulthood suggests thatbeyond an outstanding deficiency in number processing-the processing of non-numerical magnitudes and domain-general skills seem to be also impaired in adults suffering from persistent DD. A secondary aim of this review is to delineate future lines of research that will provide us with a more elaborate understanding of the neurocognitive underpinnings of DD in adults (thus fostering the development of sensitive diagnostic marker tasks), and to formulate potential intervention areas targeting deficiencies frequently characterizing DD in adults.; Entwicklungsbedingte Rechenstörungen (‘developmental dyscalculia’ / DD) bleiben unbehandelt bis ins Erwachsenenalter bestehen und haben einen negativen Einfluss auf die Berufsmöglichkeiten (und somit auf das Einkommen) sowie die sozio-emotionale Gesundheit der Betroffenen. Daher ist ein besseres Verständnis der neurokognitiven Grundlagen von DD bei Erwachsenen äußerst relevant. Das Hauptziel der vorliegenden Überblicksarbeit ist die Darstellung der bisherigen wissenschaftlichen Befunde zu DD im Erwachsenenalter, wobei der Fokus auf den kognitiven und bildgebenden Studien liegt. Nach aktuellem Forschungsstand scheinen die kognitiven Defizite von Erwachsenen mit der Diagnose DD nicht auf Schwierigkeiten bezüglich der Zahlenverarbeitung im engeren Sinn beschränkt zu sein, sondern betreffen auch die Verarbeitung von nicht-numerischen Größen und domänen-übergreifende Fertigkeiten. Weitere Ziele der vorliegenden Arbeit sind die Skizzierung zukünftiger Forschungsfragen, die helfen sollen, (i) ein detaillierteres Verständnis der neurokognitiven Grundlagen von DD im Erwachsenenalter zu gewinnen (als Voraussetzung zur Entwicklung von sensitiven diagnostischen Instrumenten), und (ii) potentielle Interventionen zu definieren, die an den mit DD im Erwachsenenalter assoziierten kognitiven Defiziten ansetzen.

When a person with intellectual disabilities has communication and fine motor impairments, multiple choice tests (MCTs) are useful if they are designed to allow some corrections and to measure the ...

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.

Developmental dyscalculia (DD) is a developmental learning disability associated with deficits in processing numerical and mathematical information. Several studies demonstrated functional network alterations in DD. Yet, there are no studies, which examined the structural network integrity in DD. We compared whole-brain maps of volume based structural covariance between 19 (4 males) children with DD and 18 (4 males) typically developing children. We found elevated structural covariance in the DD group between the anterior intraparietal sulcus to the middle temporal and frontal gyrus (p < 0.05, corrected). A hippocampus subfield analysis showed higher structural covariance in the DD group for area CA3 to the parahippocampal and calcarine sulcus, angular gyrus and anterior part of the intraparietal sulcus as well as to the lingual gyrus. Lower structural covariance in this group was seen for the subiculum to orbitofrontal gyrus, anterior insula and middle frontal gyrus. In contrast, the primary motor cortex (control region) revealed no difference in structural covariance between groups. Our results extend functional magnetic resonance studies by revealing abnormal gray matter integrity in children with DD. These findings thus indicate that the pathophysiology of DD is mediated by both structural and functional abnormalities in a network involved in number processing and memory function., Journal of Neuroscience Research, 100 (2), ISSN:0360-4012, ISSN:1097-4547

Developmental dyscalculia (DD) is characterized by lower numerical and finger-related skills. Studies of enumeration among those DD that suggested core deficiency in pattern recognition, working memory or/and attention were mostly carried out in the visual modality. In our study, we examined visual (dots) enumeration of 1–10 stimuli and tactile (vibration) enumeration of 1–10 fingers among DD and matched-control adults. We used 800-ms stimuli exposure time of either random/non-neighboring or canonical/neighboring stimuli arrangements (visual/tactile). Compared to controls, those with DD responded faster in visual random enumeration and did not differ in reaction time (RT) of canonical stimuli arrangements. However, while the control group had near perfect accuracy in random stimuli arrangements of up to five stimuli, DD participants performed accurately for only up to four stimuli, and they were less accurate in the canonical stimuli arrangements in the counting range. In the tactile task, DD participants showed less accurate tactile enumeration only for neighboring arrangements, more profoundly for finger counting (FC) patterns. The longer exposure time in the visual task enabled us to explore pattern recognition effects when working memory and attention loads were low. We discuss possible modal-independent deficits in pattern recognition and working memory on enumeration performance among those with DD and the unique role of fingers in ordinal and cardinal representation of numbers.

Arithmetical cognition is the result of enculturation. On a personal level of analysis, enculturation is a process of structured cultural learning that leads to the acquisition of evolutionarily recent, socio-culturally shaped arithmetical practices. On a sub-personal level, enculturation is realized by learning driven plasticity and learning driven bodily adaptability, which leads to the emergence of new neural circuitry and bodily action patterns. While learning driven plasticity in the case of arithmetical practices is not consistent with modularist theories of mental architecture, it can be enriched by the theory of neural reuse. According to neural reuse, cerebral regions are reused to contribute to multiple neural circuits in functionally constrained ways throughout ontogeny. By hypothesis, learning driven plasticity is complemented by learning driven bodily adaptability, which suggests that there is an interesting functional relationship between finger gnosis, finger counting, and arithmetical practices. The emerging perspective on enculturated arithmetical cognition will be complemented by considerations on associated developmental and acquired disorders, namely developmental dyscalculia and acquired acalculia. The upshot is that we need to take the cerebral, extra-cerebral bodily, and socio-cultural dimensions of enculturation into account in order to arrive at a better understanding of the phylogenetic and ontogenetic conditions of arithmetical cognition.

Animals including humans are endowed with a remarkable capacity to estimate rapidly the number of items in a scene. Some have questioned whether this ability reflects a genuine sense of number, or whether numerosity is derived indirectly from other covarying attributes, such as density and area. In previous work we have demonstrated that adult observers are more sensitive to changes in numerosity than to area or density, particularly changes that leave numerosity constant, pointing to a spontaneous sensitivity to numerosity, not attributable to area and density. Here we extend this line of research with a novel technique where participants reproduce the size and density of a dot-array. They were given no explicit instructions of what to match, but could regulate freely all combinations of area and density by trackpad. If the task is mediated by matching separately area and texture-density, the errors in the two attributes have to be independent. Contrarily to this prediction, we found that errors in area and density were negatively correlated, suggesting that subjects matched numerosity, rather than area and density. We employed this technique to investigate processing of number in adolescents with typical and low math abilities (dyscalculia). Interestingly, we found that dyscalculics also reproduced numerosity rather than area or density. However, compared to typicals, dyscalculics had longer reaction times, a tendency to rely also on area, and their performance did not improve over sessions. Taken together, the data demonstrate that numerosity emerges as the most spontaneous and sensitive dimension, supporting the existence of a dedicated number sense and confirm numerosity atypicalities in dyscalculia.

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

Developmental dyscalculia (DD) is a neurodevelopmental disorder specific to arithmetic learning even with normal intelligence and age-appropriate education. Difficulties often persist from childhood through adulthood. Underlying neurobiological mechanisms of DD, however, are poorly understood. This study aimed to identify possible structural connectivity alterations in DD. We evaluated 10 children with pure DD (11.3 plus-or-minus sign 0.7 years) and 16 typically developing (TD) peers (11.2 plus-or-minus sign 0.6 years) using diffusion tensor imaging. We first assessed white matter microstructure with tract-based spatial statistics. Then we used probabilistic tractography to evaluate tract lengths and probabilistic connectivity maps in specific regions. At whole brain level, we found no significant microstructural differences in white matter between children with DD and TD peers. Also, seed-based connectivity probabilities did not differ between groups. However, we did find significant differences in regions-of-interest tracts which had previously been related to math ability in children. The major findings of our study were reduced white matter coherence and shorter tract lengths of the left superior longitudinal/arcuate fasciculus and left anterior thalamic radiation in the DD group. Furthermore, lower white matter coherence and shorter pathways corresponded with the lower math performance as a result of the correlation analyses. These results from regional analyses indicate that learning, memory and language-related pathways in the left hemisphere might underlie DD. Keywords: Mathematical learning disability, diffusion tensor imaging, superior longitudinal fasciculus, anterior thalamic radiation, probabilistic tractography, tract-based spatial statistics

Non-invasive brain stimulation (NIBS) has been highlighted as a powerful tool to promote neuroplasticity, and an attractive approach to support cognitive remediation. Here we provide a systematic review of 26 papers using NIBS to ameliorate cognitive dysfunctions in three prevalent neurodevelopmental disorders: Attention-Deficit/Hyperactivity Disorder (ADHD), Developmental Dyslexia and Developmental Dyscalculia. An overview of the state of research shows a predominance of studies using repetitive transcranial magnetic stimulation (rTMS) and transcranial direct current stimulation (tDCS) techniques, and an unequal distribution among clinical conditions. Regarding the utility of NIBS, the results are promising but also ambiguous. Twenty-three papers reported beneficial effects, but many of these effects were found only once or were only partially replicated and some studies even reported detrimental effects. Furthermore, most studies differed in at least one core aspect, the NIBS applied, the questionnaires and cognitive tests conducted, or the age group investigated, and sample sizes were mostly small. Hence, further studies are needed to rigorously examine the potential of NIBS in the remediation of cognitive functions. Finally, we discuss potential caveats and future directions. We reason that if adequately addressing these challenges NIBS can be feasible, with potential benefits in treating neurodevelopmental disorders.

Developmental dyscalculia (DD) is a specific learning disability affecting the development of numerical and arithmetical skills. The origin of DD is typically attributed to the suboptimal functioning of key regions within the dorsal visual stream (parietal cortex) which support numerical cognition. While DD individuals are often impaired in visual numerosity perception, the extent to which they also show a wider range of visual dysfunctions is poorly documented. In the current study we measured sensitivity to global motion (translational and flow), 2D static form (Glass patterns) and 3D structure from motion in adults with DD and control subjects. While sensitivity to global motion was comparable across groups, thresholds for static form and structure from motion were higher in the DD compared to the control group, irrespective of associated reading impairments. Glass pattern sensitivity predicted numerical abilities, and this relation could not be explained by recently reported differences in visual crowding. Since global form sensitivity has often been considered an index of ventral stream function, our findings could indicate a cortical dysfunction extending beyond the dorsal visual stream. Alternatively, they would fit with a role of parietal cortex in form perception under challenging conditions requiring multiple element integration.

Children with developmental dyscalculia (DD) differ from typically developing (TD) children regarding brain activation. While arithmetic training reduces fronto-temporo-parietal activation related to domain-general processes in TD children, we do not know whether these findings also hold for children with DD. Since children with DD are one main target group for intervention and remediation, it is essential to know how arithmetic training that improves arithmetic performance induces brain activation changes in these children. In a within-participant design, a group of 20 children with DD underwent two weeks of training in simple and complex multiplication. Brain activation was measured using functional near-infrared spectroscopy (fNIRS) before and after training to assess training-related changes. Two weeks of training led to increased temporo-parietal activation for trained versus untrained simple multiplication. For both trained and untrained complex multiplication, widespread increases in activation were observed in frontal, parietal, and temporo-parietal cortices. Interestingly, training-specific activation increases were observed only in the bilateral parietal cortex, but not in the other regions. These brain activation changes were more robust in younger children. We conclude that in contradiction to the training-related brain activation decreases seen in studies of TD children, children with DD showed improved behavioral performance along with increased brain activation. Therefore, using neuroimaging techniques such as fNIRS on children with DD provided valuable insights about strategy changes and the neural networks involved in mental arithmetic.

Developmental dyscalculia (DD) is a learning disability affecting the acquisition of numerical-arithmetical skills. Affected people show persistent deficits in number processing, which are associated with aberrant brain activation and structure. Reduced gray matter has been reported in DD for the parietal cortex including the intraparietal sulcus (IPS), but also the frontal and occipito-temporal cortex. Furthermore, dyscalculics show white matter differences for instance in the inferior (ILF) and superior longitudinal fasciculus (SLF). However, the longitudinal development of these structural differences is unknown. Therefore, our goal was to investigate the developmental trajectory of gray and white matter in children with and without DD. In this longitudinal study, neuropsychological measures and T1-weighted structural images were collected twice with an interval of 4 years from 13 children with DD (8.2–10.4 years) and 10 typically developing (TD) children (8.0–10.4 years). Voxel-wise estimation of gray and white matter volumes was assessed using voxel-based morphometry for longitudinal data. The present findings reveal for the first time that DD children show persistently reduced gray and white matter volumes over development. Reduced gray matter was found in the bilateral inferior parietal lobes including the IPS, supramarginal gyri, left precuneus, cuneus, right superior occipital gyrus, bilateral inferior and middle temporal gyri, and insula. White matter volumes were reduced in the bilateral ILF and SLF, inferior fronto-occipital fasciculus (IFOF), corticospinal tracts, and right anterior thalamic radiation (ATR). Behaviorally, children with DD performed significantly worse in various numerical tasks at baseline and follow-up, corroborating persistent deficits in number processing. The present results are in line with the literature showing that children with DD have reduced gray and white matter volumes in the numerical network. Our study further sheds light on the trajectory of brain development, revealing that these known structural differences in the long association fibers and the adjacent regions of the temporal- and frontoparietal cortex persist in dyscalculic children from childhood into adolescence. In conclusion, our results underscore that DD is a persistent learning disorder accompanied by deficits in number processing and reduced gray and white matter volumes in number related brain areas., Frontiers in Human Neuroscience, 14, ISSN:1662-5161

This study investigated the hypothesis that developmental dyscalculia is part of the behavioural phenotype of Down syndrome. One hundred and fifty-one individuals with Down syndrome across three ag...

Introduction Typically, humans place themselves at a preferred distance from others. This distance is known to characterize human spatial behavior. Here, we focused on neurocognitive conditions that may affect interpersonal distances. The current study investigated whether neurocognitive deficiencies in numerical and spatial knowledge may affect social perception and modulate personal space. Method In an event‐related potential (ERP) study, university students with developmental dyscalculia (DD) and typically developing control participants were given a computerized version of the comfortable interpersonal distance task, in which participants were instructed to press the spacebar when they began to feel uncomfortable by the approach of a virtual protagonist. Results Results showed that students with deficiencies in numerical and spatial skills (i.e., DD) demonstrated reduced variability in their preferred distance from an approaching friend. Importantly, DD showed decreased amplitude of the N1 wave in the friend condition. Conclusion These results suggest that people coping with deficiencies in spatial cognition have a less efficient allocation of spatial attention in the service of processing personal distances. Accordingly, the study highlights the fundamental role of spatial neurocognition in organizing social space., We found that even this seemingly resilient group of young adults with dyscalculia who are enrolled in university display abnormal neuro‐physiological functioning suggestive of a less efficient allocation of spatial attention in the service of processing distances in everyday activities. This deficient attention mechanism leads to abnormal choices of preferred distance from others, mainly from friends, which may have an effect on reciprocal social behavior.

Deficits in numerical magnitude perception characterize the mathematics learning disability developmental dyscalculia (DD), but recent studies suggest the relation stems from inhibitory control demands from incongruent visual cues in the nonsymbolic number comparison task. This study investigated the relation among magnitude perception during differing congruency conditions, executive function, and mathematics achievement measured longitudinally in children (n = 448) from ages 4 to 13. This relation was investigated across achievement groups and as it related to mathematics across the full range of achievement. Only performance on incongruent trials related to achievement. Findings indicate that executive function in a numerical context, beyond magnitude perception or executive function in a non-numerical context, relates to DD and mathematics across a wide range of achievement.

It has been suggested that a core deficit of the “number sense” may underlie dyscalculia. We test this idea by measuring perceptual adaptation and discrimination thresholds for numerosity and object size in a group of dyscalculic and typical preadolescents (N = 71, mean age 12). We confirmed that numerosity discrimination thresholds are higher in developmental dyscalculia, while size thresholds are not affected. However, dyscalculics adapted to numerosity in a similar way to typicals. This suggests that although numerosity thresholds are selectively higher in dyscalculia, the mechanisms for perceiving numerosity are otherwise similar, suggesting that have a similar, but perhaps noisier, number sense.

© 2017 APA, all rights reserved). A negative correlation between math anxiety and mathematics performance is frequently reported. Thus, some may assume that high levels of mathematics anxiety are associated with poor mathematical understanding. However, no previous research has clearly measured the association between mathematics anxiety and mathematical learning disability. To fill this gap, here we investigated the comorbidity of developmental dyscalculia (a selective, serious deficit in mathematical performance) and mathematics anxiety in a sample of 1,757 primary school (8- to 9-year-old) and secondary school (12- to 13-year-old) children. We found that children with developmental dyscalculia were twice as likely to have high mathematics anxiety as were children with typical mathematics performance. More girls had comorbid mathematics anxiety and developmental dyscalculia than did boys. However, 77% of children with high mathematics anxiety had typical or high mathematics performance. Our findings suggest that cognitive and emotional mathematics problems largely dissociate and call into question the assumption that high mathematics anxiety is exclusively linked to poor mathematics performance. Different intervention methods need to be developed to prevent and treat emotional and cognitive blocks of mathematical development. (PsycINFO Database Record

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).

Children with Cerebral Palsy (CP) often perform poorly in mathematics. It is not yet clear to what extent mathematics difficulties in this clinical condition are similar to those observed in developmental dyscalculia. To better elucidate this issue, we conducted an exploratory cross-sectional study with a sample of children and adolescents with congenital brain injuries and educational history of problems in Mathematics. Fifty students aged 7–15 years, of both genders (28 males) participated in the study, 31 with typical development (TD) and 19 of whom diagnosed with spastic CP. Nine had hemiplegia and ten diplegia. Assessment procedures included a neuropsychological battery covering numerical cognition (ZAREKI-R) and working memory (AWMA) skills, and a computerized task for comparing non-symbolic magnitudes as a measure of number sense. Despite average intelligence coefficient, participants with CP underperformed the TD in five of the 12 ZAREKI-R subtests, as well as in the number sense and working memory tasks. scores were lower among hemiplegic children compared to diplegic, numerical cognition was impaired in all CP group, unveiling a dyscalculia secondary to neurodevelopmental impairments. Therefore, we can consider that mathematical learning difficulties in CP as being heterogeneous and associated with the immaturity of neuropsychological functions, with consequences for the development of numerical cognition.

Objective People suffering from developmental dyscalculia (DD) are known to have impairment in numerical abilities and have been found to have weaker processing of countable magnitudes. However, not much research was done on their abilities to process noncountable magnitudes. An example of noncountable magnitude is conceptual size (e.g., mouse is small and elephant is big). Recently, we found that adults process conceptual size automatically. The current study examined automatic processing of conceptual size in students with DD and developmental dyslexia. Method Conceptual and physical sizes were manipulated orthogonally to create congruent (e.g., a physically small apple compared to a physically large violin) and incongruent (e.g., a physically large apple compared to a physically small violin) conditions. Participants were presented with 2 objects and had to choose the larger one. Each trial began with an instruction to respond to the physical or to the conceptual dimension. Results Control and the dyslexic groups presented automatic processing of both conceptual and physical sizes. The dyscalculic group presented automatic processing of physical size but not automaticity of processing conceptual size. Conclusion Our results fit with previous findings of weaker magnitude representation in those with DD, specifically regarding noncountable magnitudes, and support theories of a shared neurocognitive substrate for different types of magnitudes. (PsycINFO Database Record

The Pedagogical Assessment of Dyscalculia (PAD) is a special educational testing method. It is the renewed version of the Dekany–Juhasz method devised by the team of dyscalculia experts from ELTE GYOSZI (Special Educational Service of Eotvos Lorand University). It is also based on the findings of current neuropsychological researches. The concept of PAD is based on the assumption that the numeric and other non-mathematical-specific systems (partial abilities) which is a part of calculation may indicate dysfunction in different ways and on different levels. The tasks in the test are aligned with the developmental stages matching the given age of the child. By relying on the method of error analysis and on the use of objective criteria, the overall results indicate those typical mistakes which are indicative of the dyscalculia. It also provides eventuality for further inspections of other partial abilities and the cognitive compensatory strategies. The individual tests may provide the possibility of differentiating between the developmental dyscalculia (serious learning disability) and learning difficulties and other possible issues. As a result of this it becomes possible to create an individual development plan (therapy).

This review reconciles past findings on numerical processing with key assumptions of the most predominant model of arithmetic in the literature, the Triple Code Model (TCM). This is implemented by reporting diverse findings in the literature ranging from behavioral studies on basic arithmetic operations over neuroimaging studies on numerical processing to developmental studies concerned with arithmetic acquisition, with a special focus on developmental dyscalculia (DD). We evaluate whether these studies corroborate the model and discuss possible reasons for contradictory findings. A separate section is dedicated to the transfer of TCM to arithmetic development and to alternative accounts focusing on developmental questions of numerical processing. We conclude with recommendations for future directions of arithmetic research, raising questions that require answers in models of healthy as well as abnormal mathematical development. What this paper adds This review assesses the leading model in the field of arithmetic processing (Triple Code Model) by presenting knowledge from interdisciplinary research. It assesses the observed contradictory findings and integrates the resulting opposing viewpoints. The focus is on the development of arithmetic expertise as well as abnormal mathematical development. The original aspect of this article is that it points to a gap in research on these topics and provides possible solutions for future models.

Symbolic and non-symbolic magnitude representations, measured by digit or dot comparison tasks, are assumed to underlie the development of arithmetic skills. The comparison distance effect (CDE) has been suggested as a hallmark of the preciseness of mental magnitude representations. It implies that two magnitudes are harder to discriminate when the numerical distance between them is small, and may therefore differ in children with mathematical difficulties (MD), i.e. low mathematical achievement or dyscalculia. However, empirical findings on the CDE in children with MD are heterogeneous, and only few studies assess both symbolic and non-symbolic skills. This meta-analysis therefore integrates 44 symbolic and 48 non-symbolic response time (RT) outcomes reported in nineteen studies (N=1630 subjects, aged 6-14 years). Independent of age, children with MD show significantly longer mean RTs than typically achieving controls, particularly on symbolic (Hedges' g=0.75; 95% CI [0.51; 0.99]), but to a significantly lower extent also on non-symbolic (g=0.24; 95% CI [0.13; 0.36]) tasks. However, no group differences were found for the CDE. Extending recent work, these meta-analytical findings on children with MD corroborate the diagnostic importance of magnitude comparison speed in symbolic tasks. By contrast, the validity of CDE measures in assessing MD is questioned. ispartof: Research in Developmental Disabilities vol:64 pages:152-167 ispartof: location:United States status: published

The acquisition of numerical competency is regarded as imperative for quality of life and economic well-being. Many children have significant mathematical learning difficulties known as dyscalculia. The aim of this research was to systematically review the available literature for interventions with children presenting with dyscalculia in primary schools, in order to provide an evidence base of filtered information assessed for methodological rigour and coherence. The study evaluated literature from 2004 to 2014 that reported on interventions for primary school children presenting with dyscalculia. Specific databases were accessed to highlight literature for inclusion in the study. The studies were assessed at title, abstract and full text levels for quality based on the inclusion and exclusion criteria. The findings provide a base of effective interventions that can be used in the school setting for individual development with a holistic focus and present various methods of instruction for childr...

A popular suggestion states that an evolutionarily grounded analogue magnitude representation, also called an approximate number system (ANS) or ‘number sense’ underlies human mathematical knowledge. During recent years many studies aimed to train the ANS with the intention of transferring improvements to symbolic arithmetic. Methods: We critically evaluated all published studies that aimed to train the ANS. We also carried out a citation analysis of the training studies. Results: There is no conclusive evidence that specific ANS training improves symbolic arithmetic. The citation analysis demonstrates that highly controversial results often get cited in support of specific claims without discussion of controversies. Conclusions: We suggest ways to run future training studies so that clear evidence can be collected and also suggest that data should be discussed in considering both supporting and contrary evidence and arguments.

Sex chromosome aneuploidies (SCA) are associated with an increased risk for specific learning disorders (SLD). Individuals with Klinefelter Syndrome (KS) show an increased incidence of developmental dyslexia and individuals with Turner Syndrome (TS) are often affected by developmental dyscalculia. Accordingly, KS frequently coincides with verbal deficits, and TS with visual-spatial impairments. Though neurocognitive profiles of KS and TS are well-established, little is known about the neurobiology underling learning in SCA. This review summarizes current structural and functional magnetic resonance imaging (MRI) studies in KS and TS related to literacy and mathematical skills. It includes studies that focus on correlates between brain anatomy and cognition in SCA and on functional brain responses during learning-related tasks and at rest. We highlight important neural circuits that are related to domain-specific skills of literacy and mathematics. We discuss how identifying neuroendophenotypes of learning in SCA might contribute to developing a novel framework for SLD that accounts for potential genetic effects on learning, and from the X and Y chromosomes specifically. Future research directions are considered to establish clear brain-behavior relationships that might ultimately improve the treatment of SLD in SCA across development.

Developmental dyscalculia (DD) is a developmental learning disability that manifests as a persistent difficulty in comprehending even the most basic numeric and arithmetic concepts, despite normal intelligence and schooling opportunities. Given the predominant use of numbers in modern society, this condition can pose major challenges in the sufferer's everyday life, both in personal and professional development. Since, to date, we still lack a universally recognized and psychometrically driven definition of DD, its diagnosis has been applied to a wide variety of cognitive profiles. In this chapter, we review the behavioral and neural characterization of DD as well as the different neurocognitive and etiologic accounts of this neurodevelopmental disorder. We underline the multicomponential nature of this heterogeneous disability: different aspects of mathematical competence can be affected by both the suboptimal recruitment of general cognitive functions supporting mathematical cognition (such as attention, memory, and cognitive control) and specific deficits in mastering numeric concepts and operations. Accordingly, both intervention paradigms focused on core numeric abilities and more comprehensive protocols targeting multiple neurocognitive systems have provided evidence for effective positive outcomes.

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., Postprints der Universität Potsdam : Humanwissenschaftliche Reihe, 650

Developmental dyscalculia refers to the arithmetic difficulties, computing capacity significantly lower than its intelligence, age and education level should be at current levels at a young age. Based on many published literature, this paper collated and analyzed the influential factors of dyscalculia, including genetic inheritance, cognitive factors, environment, education and individual emotional factors, which may explain the causes of dyscalculia. Through systematic analysis and comparison, we summarized the results and combined them with our thinking to show you some efficient methods for interventions of dyscalculia and put forward the outlook to provide a more detailed review for future researches by pointing out their advantages and disadvantages of existing methods.

Studies in children with AD(H)D without mathematical learning disability (MLD) as well as studies on the effects of methylphenidate on arithmetic have shown that most deficits in mathematics and most error types commonly described as specific to developmental dyscalculia (e. g., finger-counting, fact-retrieval deficit, complex counting, difficulties with carry/borrow procedures, self-corrections) cannot be classified as such and should thus not be used for the differential diagnosis of primary dyscalculia and secondary MLD. This article proposes using the overall score in the dyscalculia test Basis-Math 4-8 (Moser Opitz et al., 2010) as well as implausible subtraction errors as a marker for dyscalculia and the number of self-corrections made during the test as a cognitive marker for attention deficits. Hierarchical cluster analyses were calculated in a sample of 51 clinically referred children with normal IQ and suspicion of MLD, using IQ, years of schooling, overall score of the Basis-Math 4–8 and number of self-corrections in this test as variables. The results revealed a subgroup with primary dyscalculia as well as three subgroups with secondary MLD (two with attention deficit hyperactivity disorder, one with depression and one small subgroup with high IQ). In conclusion, the Basis-Math 4–8 (Moser Opitz et al., 2010) can offer substantial information for the differential diagnosis of dyscalculia and secondary deficits in mathematics due to attention problems and enable optimization of treatment decisions for the different groups.

Developmental dyscalculia is a specific learning disability that is described as a heterogeneous and persistent cognitive disorder. Given the need to detect and intervene as early as possible to minimise its effects, teachers' knowledge about symptoms, characteristics and effective intervention strategies in dyscalculia is essential. Given the lack of research about this topic and measures to evaluate teachers' knowledge, this study aims to present a literature-based measure to evaluate knowledge about developmental dyscalculia and to investigate the predictors of this type of knowledge. Data were collected from a sample of 175 primary school teachers. The measure presented adequate psychometric properties. Teachers' personal characteristics such as age and gender did not predict their knowledge about dyscalculia. Being a Special Education teacher predicted a higher knowledge of intervention strategies in dyscalculia and having heard about dyscalculia predicted higher knowledge about not only intervention strategies but also dyscalculia characteristics. The data are discussed, and suggestions for further studies are presented., Financial support by the [grant number UID/FIL/00683/2013., This work was supported by the Portuguese Foundation for Science and Technology (FCT) through national funds and co-financed by FEDER through COMPETE 2020, by the grant with the reference [POCI-01-0145-FEDER-007562] (strategic project UID/CE/00317/2013) and by the [grant number UID/FIL/00683/2013]. The last author is also supported by the FCT [grant number SFRH/BPD/102549/2014].

Considerable recent work suggests that mathematical abilities in children correlate with the ability to estimate numerosity. Does math correlate only with numerosity estimation, or also with other similar tasks? We measured discrimination thresholds of school-age (6- to 12.5-years-old) children in 3 tasks: numerosity of patterns of relatively sparse, segregatable items (24 dots); numerosity of very dense textured patterns (250 dots); and discrimination of direction of motion. Thresholds in all tasks improved with age, but at different rates, implying the action of different mechanisms: In particular, in young children, thresholds were lower for sparse than textured patterns (the opposite of adults), suggesting earlier maturation of numerosity mechanisms. Importantly, numerosity thresholds for sparse stimuli correlated strongly with math skills, even after controlling for the influence of age, gender and nonverbal IQ. However, neither motion-direction discrimination nor numerosity discrimination of texture patterns showed a significant correlation with math abilities. These results provide further evidence that numerosity and texture-density are perceived by independent neural mechanisms, which develop at different rates; and importantly, only numerosity mechanisms are related to math. As developmental dyscalculia is characterized by a profound deficit in discriminating numerosity, it is fundamental to understand the mechanism behind the discrimination. (PsycINFO Database Record

Developmental dyscalculia (DD), a pervasive learning difficulty, affects 5-6% of the population. The current study sought to identify the underlying deficits by contrasting third graders (10-year o ...

Different number-specific and general cognitive markers have been claimed to underlie preschoolers' math ability. It is unclear, however, whether similar/different cognitive markers, or combinations of them, are associated with different patterns of emerging math abilities (i.e., different patterns of strength and weakness). To examine this question, 103 preschoolers (40-60 months of age) completed six math tasks (count sequence, object counting, give a number, naming numbers, ordinal relations, and arithmetic), three number-specific markers of math ability (dot enumeration, magnitude comparison, and spontaneous focusing on numerosity), and four general markers (working memory, response inhibition, attention, and vocabulary). A three-step latent profile modeling procedure identified five math ability profiles that differed in their patterns of math strengths and weaknesses; specifically, the profiles were characterized by (a) excellent math ability on all math tasks, (b) good arithmetic ability, (c) good math ability but relatively poor count sequence recitation ability, (d) average ability on all math tasks, and (e) poor ability on all math tasks. After controlling for age, only dot enumeration and spontaneous focusing on numerosity were associated with the math ability profiles, whereas vocabulary was also marginally significant, and these markers were differentially associated with different profiles; that is, different cognitive markers were associated with different patterns of strengths and weaknesses in math abilities. Findings are discussed in terms of their implications for the development of math cognition.

There has been a continuous debate on different criteria on assessment of mathematical learning disability (MLD). Originally, MLD was defined as an unexpected failure to acquire basic mathematics skills despite normal intelligence, adequate schooling, and absence of neurological or psychiatric disorders. This approach, based on a discrepancy between the intelligence and the academic skills, has been largely criticized. One of the strongest candidates to replace this approach has been the response-to-intervention (RTI) instruction model, where the focus has been in the student’s learning in optimal learning conditions, for example, when participating in an evidence-based intervention program. However, the RTI approach does not sufficiently take into account the individual factors that affect the responsiveness to a mathematical intervention and does not have effective algorithms for differential diagnosis of specific MLD and low attainment in mathematics. Therefore, a third alternative in assessment has focused on cognitive patterns of strengths and weaknesses (PSW). The PSW model offers several theoretical and empirical advances to the previous models. However, there is also strong evidence supporting a view that severe forms of MLD would stem from a core deficit that is independent of the comorbid, but individually varying, cognitive disorders. The selected approach also has direct implications for educational policy and practice in classrooms.

In this chapter, we review the genetic foundations of developmental dyscalculia. We begin by briefly reviewing the clinical epidemiology of dyscalculia. Next, we review evidence for genetic susceptibility from familial aggregation and heritability estimates. Evidence for genetic susceptibility is substantial but associated with some limitations. Familial aggregation studies do not distinguish genetic from environmental influences. As heritability does not identify specific genes, it applies only at the population, not at the individual level. Current molecular genetic methods are helping to identify specific genes implicated in dyscalculia. We discuss evidence from genome-wide association studies on dyscalculia and on its comorbidities, mainly dyslexia, autism, and specific language impairment. The number of such studies is small but growing. So far, some candidate genes have been identified, but none of them has yet been confirmed in independent studies. Developmental dyscalculia is a heterogeneous phenotype. Future advances depend, among other things, on improvements in phenotype characterization and identification of families with clear phenotypic segregation.