Search

We delineate a developmental model of number representations. Notably, developmental dyscalculia (DD) is rarely associated with an all-or-none deficit in numerosity processing as would be expected if assuming abstract number representations. Finally, we suggest that the “generalist genes” view might be a plausible – though thus far speculative – explanatory framework for our model of how number representations develop.

Summary Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of school-level mathematical abilities in the context of otherwise normal academic achievement, with prevalence estimates in the order of 3–6% [1] . Behavioural studies show deficits in elementary numerical processing among individuals with pure DD [2,3], indicating that deficits in higher-level mathematical skills may stem from impaired representation and processing of basic numerical magnitude. Adult neuropsychological and neuroimaging research points to the intraparietal sulcus as a key region for the representation and processing of numerical magnitude [4]. This raises the possibility of a parietal dysfunction as a root cause of DD [5]. We show that, in children with pure DD, the right intraparietal sulcus is not modulated in response to numerical processing demands to the same degree as in typically developing children. This finding provides the first direct evidence for a specific impairment of parietal magnitude systems in DD during non-symbolic numerosity processing.

This article presents an analysis of a form of dysfunctional mathematical development. A child of normal intelligence was unable to acquire basic cardinal numerical skills, despite relatively intact ordinal number use. These findings provide evidence for an innate "cardinal/ordinal skills acquisition device" (COSAD). It is argued that if this COSAD is lacking, ordinal number use may be compensated for by linguistic logic and visual skills. Cardinal number skills, however, remain limited as these demand an innate internal representation of quantity, which cannot be compensated for. The findings are discussed in terms of different approaches to number development.

PLoS one 8(12), e83722 (2013). doi:10.1371/journal.pone.0083722, Published by PLoS [u.a.], Lawrence, Kan.

Behavioral characteristics of 140 children with developmental dyscalculia (DC) were evaluated using the Child Behavior Checklist. DC children demonstrated more behavior problems than normal children but significantly fewer problems than children psychiatrically referred. DC children had significantly more attentional problems although they had normal levels of anxiety/depression. Significantly higher scores on all syndrome scales were found for DC children who had attentional problems in the clinical range. When associated with dyslexia and a low verbal IQ, DC children had more attentional problems and externalizing syndromes. The implications of the behavioral characteristics of DC are discussed.

Developmental dyscalculia (DC) is a primary cognitive disorder of childhood manifested by disturbance of arithmetic ability. As an isolated learning disability (LD), it is usually treated by remedial education and not referred for further medical evaluation. We examined a group of 7 third-grade children with DC attending a mainstream school who had not progressed academically in spite of specie special education intervention. We were able to identify in all 7 children neurological conditions that had direct bearing on the children's cognitive disabilities and remedial programs. One child had petit mal seizures, another developmental Gerstmann syndrome, a third had dyslexia for numbers, and 4 children had attention deficit disorders without hyperactivity. Based on this experience, we suggest that the indications for medical of neurological assessment be broadened to include children who are not improving academically in spite of appropnatg professional intervention.

Number cognition is important both for the society and for the individual. The disorder of number cognition (developmental dyscalculia) can havemajor impact on individual life quality. Several children and adults experience problemswith one aspect of ‘arithmetic syntax’, the representation of place value structure. Here we provide the first cognitive neuroscience investigation of place value representation. Our study systematically contrasted semantic (the numerical distance effect) and syntactic (place value structure) violations in a mental addition verification task. Participants verified additions with fourdigit numbers. Semantic incongruencies elicited theN400 ERP effect. A centro-parietal (putative P600) effect to place-value violationswas not related to arithmetic syntax. Rather, this effect was an enlarged P3b reflecting different surprise values of place value vs. non-place value violations. This potential confound should be considered in numerical cognition experiments. The latency of the N400 and P3a effects were differentially affected byplace-value analysis. The amplitude of the P3a and that of a fronto-central positive effect (FP600) was sensitive to place value analysis and digit content. Results suggest that ERPs can index the syntactical analysis of multi-digit numbers. Both ERP and behavioral data confirmed thatmulti-digit numberswere decomposed into their constituent digits, rather than evaluated holistically. These findings enable the detailed investigation of place value representation in both normal and dyscalculic populations.

Number cognition is important both for the society and for the individual. The disorder of number cognition (developmental dyscalculia) can have major impact on individual life quality. Several children and adults experience problems with one aspect of ‘arithmetic syntax’, the representation of place value structure. Here we provide the first cognitive neuroscience investigation of place value representation. Our study systematically contrasted semantic (the numerical distance effect) and syntactic (place value structure) violations in a mental addition verification task. Participants verified additions with four-digit numbers. Semantic incongruencies elicited the N400 ERP effect. A centro-parietal (putative P600) effect to place-value violations was not related to arithmetic syntax. Rather, this effect was an enlarged P3b reflecting different surprise values of place value vs. non-place value violations. This potential confound should be considered in numerical cognition experiments. The latency of the N400 and P3a effects were differentially affected by place-value analysis. The amplitude of the P3a and that of a fronto-central positive effect (FP600) was sensitive to place value analysis and digit content. Results suggest that ERPs can index the syntactical analysis of multi-digit numbers. Both ERP and behavioral data confirmed that multi-digit numbers were decomposed into their constituent digits, rather than evaluated holistically. These findings enable the detailed investigation of place value representation in both normal and dyscalculic populations.

Background Functional magnetic resonance imaging (fMRI) studies investigating the neural mechanisms underlying developmental dyscalculia are scarce and results are thus far inconclusive. Main aim of the present study is to investigate the neural correlates of nonsymbolic number magnitude processing in children with and without dyscalculia. Methods 18 children (9 with dyscalculia) were asked to solve a non-symbolic number magnitude comparison task (finger patterns) during brain scanning. For the spatial control task identical stimuli were employed, instructions varying only (judgment of palm rotation). This design enabled us to present identical stimuli with identical visual processing requirements in the experimental and the control task. Moreover, because numerical and spatial processing relies on parietal brain regions, task-specific contrasts are expected to reveal true number-specific activations. Results Behavioral results during scanning reveal that despite comparable (almost at ceiling) performance levels, task-specific activations were stronger in dyscalculic children in inferior parietal cortices bilaterally (intraparietal sulcus, supramarginal gyrus, extending to left angular gyrus). Interestingly, fMRI signal strengths reflected a group × task interaction: relative to baseline, controls produced significant deactivations in (intra)parietal regions bilaterally in response to number but not spatial processing, while the opposite pattern emerged in dyscalculics. Moreover, beta weights in response to number processing differed significantly between groups in left – but not right – (intra)parietal regions (becoming even positive in dyscalculic children). Conclusion Overall, findings are suggestive of (a) less consistent neural activity in right (intra)parietal regions upon processing nonsymbolic number magnitudes; and (b) compensatory neural activity in left (intra)parietal regions in developmental dyscalculia.

Developmental dyscalculia (DD) is a specific learning disability affecting the acquisition of mathematical skills in children with otherwise normal general intelligence. The goal of the present study was to examine cerebral mechanisms underlying DD. Eighteen children with DD aged 11.2 ± 1.3 years and twenty age-matched typically achieving schoolchildren were investigated using functional magnetic resonance imaging (fMRI) during trials testing approximate and exact mathematical calculation, as well as magnitude comparison. Children with DD showed greater inter-individual variability and had weaker activation in almost the entire neuronal network for approximate calculation including the intraparietal sulcus, and the middle and inferior frontal gyrus of both hemispheres. In particular, the left intraparietal sulcus, the left inferior frontal gyrus and the right middle frontal gyrus seem to play crucial roles in correct approximate calculation, since brain activation correlated with accuracy rate in these regions. In contrast, no differences between groups could be found for exact calculation and magnitude comparison. In general, fMRI revealed similar parietal and prefrontal activation patterns in DD children compared to controls for all conditions. In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers.

A case study of developmental dyscalculia is presented in which there is impairment of number processing. When reading and writing arabic numbers the syntactic component of the number is processed accurately but lexical processing results in incorrect digit selection. When reading arabic numbers the allocation of lexical items into syntactic frames is particularly poor for digits in the units position. Lexical allocation is unaffected by stimulus length. Despite poor short term memory, word reading is not impaired except for the reading of numeral words for which there is a category specific deficit. Reading errors to numeral words are more frequent than to arabic numbers but the nature of the errors is comparable. This reading deficit coexists with good phonological reading skills. The results are discussed in relation to models derived from studies of the acquired dyscalculias.

Nonverbal learning disabilities (NVLD), a clinical condition still little reported in Brazil, are characterized by damages in the visual spatial domains, visual motor integration, fine motor skills, math skills and social and emotional difficulties. Developmental Dyscalculia (DD) is a neurodevelopmental disorder that affects basic arithmetic skills acquisition, including storage and recovery of arithmetic facts, calculation fluency and precision and number sense domain. Although both are persistent Math learning disorder/disability, they cause different damages. The objective of this case report is to describe, compare and analyze the neuropsychological profile of two Brazilian children with similar complaints but distinct diagnosis.

International audience; Around 20% of the population exhibits moderate to severe numerical disabilities [1, 2, 3], and a further percentage loses its numerical competence during the lifespan as a result of stroke or degenerative diseases [4]. In this work, we investigated the feasibility of using noninvasive stimulation to the parietal lobe during numerical learning to selectively improve numerical abilities. We used transcranial direct current stimulation (TDCS), a method that can selectively inhibit or excitate neuronal populations by modulating GABAergic (anodal stimulation) and glutamatergic (cathodal stimulation) activity [5, 6]. We trained subjects for 6 days with artificial numerical symbols, during which we applied concurrent TDCS to the parietal lobes. The polarity of the brain stimulation specifically enhanced or impaired the acquisition of automatic number processing and the mapping of number into space, both important indices of numerical proficiency [7, 8, 9]. The improvement was still present 6 months after the training. Control tasks revealed that the effect of brain stimulation was specific to the representation of artificial numerical symbols. The specificity and longevity of TDCS on numerical abilities establishes TDCS as a realistic tool for intervention in cases of atypical numerical development or loss of numerical abilities because of stroke or degenerative illnesses.

SYNOPSISFour patients with ‘developmental dyscalculia’ are described who were initially identified on the basis of clinical tests, reports of longstanding and severe difficulties in arithmetic, and psychological test results. Descriptive psychological testing indicated (1) that the arithmetical deficits could not be accounted for on the basis of a generally low level of intellectual functioning; (2) that of the four basic arithmetical processes that of multiplication was relatively more deficient; (3) that this relative deficiency in multiplication stemmed from a faulty grasp of basic multiplication tables; that this was a real difficulty, experienced subjectively by the patient, and one that could not be accounted for simply by carelessness; and finally, that the degree of difficulty experienced varied with the multiplication table involved. Two kinds of attempt were made to improve arithmetical functioning. The first involved brief remedial coaching programmes directed at the basic multiplication tables: relatively little success was obtained with this method. The second kind of attempt involved methods of bypassing the necessity for learning multiplication tables: some success was obtained with these methods. The discussion concentrates on some of the features which may provide possibly useful cues for identifying ‘developmental dyscalculia’: these are classified in terms of: (1) pattern of deficit displayed; (2) qualitative features of arithmetical performance; and (3) response to remedial teaching. Some suggestions are made concerning further lines of investigation.

The most common characteristic of children with mathematical disorders is a difficulty in retrieving basic arithmetic facts. Different hypotheses about the underlying cause and the specificity of this deficit have been postulated. Some of them are general (such as low speed-of-processing or difficulties in retrieving semantic information from long- term memory), others are more specific (such as problems with material requiring verbal routines or a deficit in represent- ing or accessing arithmetic facts). To clarify this, children with poor arithmetic facts abilities (PoorAF) and control chil- dren of the same age performed five computerized tasks requiring the retrieval of information from long-term memory such as the product of multiplication facts, words semantically related to a target, objects functionally associated with a target, countries corresponding to a capital city presented as target, and the final word of incomplete French proverbs. In addition, a perceptual task was used as a measure of children's processing speed. It was found that children with PoorAF were significantly slower than control children only in the arithmetic retrieval task. These findings support the hypothesis of a specific numerical deficit altering the retrieval of the arithmetic network from long-term memory.

Calculia is considered to be the ability of performing arithmetic operations. Problems in acquiring arithmetic skills can be described as difficulties in counting as well as developmental dyscalculia. The most comman difficulties in counting are: difficulties in logic, difficulties in planning, perseverance of inappropriate (responses) procedures and poor understanding of arithmetic operations. The aim of the research is to determine the influence of executive functions on the acquisition of mathematical skills and the appearance of dyscalculia at junior schoolchildren. It is operation analized in the following way: - the determination of the relationship between the ability levels of planning and forming of concepts (as elements of executive functioning) and mastering of mathematical skills of junior schoolchildren - the determination of the relationship between the elements of executive systems (abilities of planning, flexibility of attention and mental rigidity) at children with difficulties in mastering mathematical skills. Following tests of neuropsychological test battery were used. The examined variables: planning; perseverance; mental rigidity. WCST- WISCONSIN CARD SORTING TEST - used for evaluation, is the best-known test for the discovery of perseverance and mental rigidity. Control variables are: sex, age and deviant intellect quotient. In accordance with the set goal of the research to determine the influence of the examined characteristic of EF and their influence on the acquisition of mathematical skills and the appearance of difficulties in it, we concluded that the influence existed and that the role of EF in the acquisition of mathematical skills at junior primary schoolchildren was considerable. The assertion was based on the results which, at children with calculation difficulties, show low efficiency and high connection of the examined cognitive characteristics of EF (p lt 0,01). At children who do not show calculation difficulties, the examined characteristics of EF show high efficiency without any statistically important connection (p>0,01).

The clinical profile termed developmental dyscalculia (DD) is a fundamental disability affecting children already prior to arithmetic schooling, but the formal diagnosis is often only made during school years. The manifold associated deficits depend on age, education, developmental stage, and task requirements. Despite a large body of studies, the underlying mechanisms remain dubious. Conflicting findings have stimulated opposing theories, each presenting enough empirical support to remain a possible alternative. A so far unresolved question concerns the debate whether a putative innate number sense is required for successful arithmetic achievement as opposed to a pure reliance on domain-general cognitive factors. Here, we outline that the controversy arises due to ambiguous conceptualizations of the number sense. It is common practice to use early number competence as a proxy for innate magnitude processing, even though it requires knowledge of the number system. Therefore, such findings reflect the degree to which quantity is successfully transferred into symbols rather than informing about quantity representation per se. To solve this issue, we propose a three-factor account and incorporate it into the partly overlapping suggestions in the literature regarding the etiology of different DD profiles. The proposed view on DD is especially beneficial because it is applicable to more complex theories identifying a conglomerate of deficits as underlying cause of DD.

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

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

Two hypotheses have been proposed about the etiology of neurodevelopmental learning disorders, such as dyslexia and dyscalculia: representation impairments and disrupted access to representations. We implemented a multi-method brain imaging approach to directly investigate these representation and access hypotheses in dyscalculia, a highly prevalent but understudied neurodevelopmental disorder in learning to calculate. We combined several magnetic resonance imaging methods and analyses, including univariate and multivariate analyses, functional and structural connectivity. Our sample comprised 24 adults with dyscalculia and 24 carefully matched controls. Results showed a clear deficit in the non-symbolic magnitude representations in parietal, temporal and frontal regions, as well as hyper-connectivity in visual brain regions in adults with dyscalculia. Dyscalculia in adults was thereby related to both impaired number representations and altered connectivity in the brain. We conclude that dyscalculia is related to impaired number representations as well as altered access to these representations.

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 a 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.

Background Math anxiety, defined as a negative affective response to mathematics, is known to have deleterious effects on math performance in the general population. However, the assumption that math anxiety is directly related to math performance, has not yet been validated. Thus, our primary objective was to investigate the effects of math anxiety on numerical processing in children with specific deficits in the acquisition of math skills (Developmental Dyscalculia; DD) by using a novel affective priming task as an indirect measure. Methods Participants (12 children with DD and 11 typically-developing peers) completed a novel priming task in which an arithmetic equation was preceded by one of four types of priming words (positive, neutral, negative or related to mathematics). Children were required to indicate whether the equation (simple math facts based on addition, subtraction, multiplication or division) was true or false. Typically, people respond to target stimuli more quickly after presentation of an affectively-related prime than after one that is unrelated affectively. Result Participants with DD responded faster to targets that were preceded by both negative primes and math-related primes. A reversed pattern was present in the control group. Conclusion These results reveal a direct link between emotions, arithmetic and low achievement in math. It is also suggested that arithmetic-affective priming might be used as an indirect measure of math anxiety.