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Developmental dyscalculia.

Developmental dyscalculia is a specific learning disability affecting the normal acquisition of arithmetic skills. Genetic, neurobiologic, and epidemiologic evidence indicates that dyscalculia, like other learning disabilities, is a brain-based disorder. However, poor teaching and environmental deprivation have also been implicated in its etiology. Because the neural network of both hemispheres comprises the substrate of normal arithmetic skills, dyscalculia can result from dysfunction of either hemisphere, although the left parietotemporal area is of particular significance. The prevalence of developmental dyscalculia is 5 to 6% in the school-aged population and is as common in girls as in boys. Dyscalculia can occur as a consequence of prematurity and low birthweight and is frequently encountered in a variety of neurologic disorders, such as attention-deficit hyperactivity disorder (ADHD), developmental language disorder, epilepsy, and fragile X syndrome. Developmental dyscalculia has proven to be a persisting learning disability, at least for the short term, in about half of affected preteen pupils. Educational interventions for dyscalculia range from rote learning of arithmetic facts to developing strategies for solving arithmetic exercises. The long-term prognosis of dyscalculia and the role of remediation in its outcome are yet to be determined.

Adolescent↗

Developmental dyscalculia.

Developmental dyscalculia is a specific learning disability affecting the acquisition of arithmetic skills in an otherwise-normal child. Although poor teaching, environmental deprivation, and low intelligence have been implicated in the etiology of developmental dyscalculia, current data indicate that this learning disability is a brain-based disorder with a familial-genetic predisposition. The neurologic substrate of developmental dyscalculia is thought to involve both hemispheres, particularly the left parietotemporal areas. Developmental dyscalculia is a common cognitive handicap; its prevalence in the school population is about 5-6%, a frequency similar to those of developmental dyslexia and attention-deficit-hyperactivity disorder. Unlike these, however, it is as common in females as in males. Developmental dyscalculia frequently is encountered in neurologic disorders, examples of which include attention-deficit-hyperactivity disorder, developmental language disorder, epilepsy, and fragile X syndrome. The long-term prognosis of developmental dyscalculia is unknown; it appears, however, to persist, at least for the short-term, in about half of affected preteen children. The consequences of developmental dyscalculia and its impact on education, employment, and psychologic well-being of affected individuals are unknown.

Brain Damage, Chronic↗

ADHD and dyscalculia: Evidence for independent familial transmission.

The familial relationship between dyscalculia and attention-deficit/hyperactivity disorder (ADHD) was assessed. We conducted a familial risk analysis using probands with and without ADHD of both genders and their first-degree relatives. Participants were assessed with structured diagnostic interviews and a cognitive test battery. We found elevated rates of ADHD in relatives of both ADHD proband groups, regardless of dyscalculia status, and elevated rates of dyscalculia in relatives of probands with dyscalculia, irrespective of ADHD status. There was no evidence for cosegregation or assortative mating. Our findings support the hypothesis that ADHD and dyscalculia are independently transmitted in families and are etiologically distinct. These results reinforce the current nosological approach to these disorders and underscore the need for separate identification and treatment strategies for children with both conditions.

Adolescent↗

Developmental dyscalculia: a prospective six-year follow-up.

To determine the natural history of developmental dyscalculia (DC) and factors impacting on its prognosis, we performed a prospective six-year longitudinal study. One hundred and forty children of normal intelligence diagnosed with DC in the fifth grade of elementary school were re-examined for dyscalculia three and six years later, in eighth (n=123) and eleventh (n=104; 41 males, 63 females) grades respectively. Mean age of the children in fifth grade was 11 years 1 month (SD 4 months), in eighth grade 14 years 2 months (SD 1 month), and in eleventh grade 17 years 2 months (SD 5 months). The assessment included standardized arithmetic, reading and writing tests, behavioural rating scales, information on socioeconomic status, educational interventions, and familial learning problems. Participants in eleventh grade were recategorized as having DC if their score on the arithmetic test was not more than the fifth centile for grade. At the six-year follow-up, 99/104 (95%) children diagnosed with dyscalculia in fifth grade were still performing poorly in arithmetic, scoring within the lowest quartile for their grade, and 42/104 (40%) were recategorized with DC. Chronicity of DC was associated with severity of the dyscalculia in fifth grade (p<0.05), lower IQ (p<0.01), inattention (p<0.01), and writing problems (p<0.01). Thus, DC is an enduring specific learning difficulty, persisting into late adolescence in almost half of affected individuals.

Adolescent↗

Dyscalculia and dyslexia after right hemisphere injury in infancy.

OBJECTIVE: To use the findings from neuropsychological evaluation and functional magnetic resonance imaging (fMRI) to assess interhemispheric reorganization of function after early unilateral brain injury. DESIGN AND METHODS: The study focused on one case of early brain injury that resulted in both dyscalculia and dyslexia. Brain injury was studied using both structural and fMRI. Intellectual function was evaluated using the Wechsler Intelligence Scale for Children, Third Edition, while visuospatial skills were assessed using the Block Design subtest of the Wechsler Intelligence Scale for Children, Third Edition, and Judgment of Line Orientation subtest. The Selective Reminding Test and the Recurring Figures Test were used to evaluate memory and orientation; language and speech skills were evaluated using the Boston Naming Test, Controlled Oral Word Association, Gates-MacGinitie Reading Test, and color naming. Various methods were used to study arithmetic skills, including the Wide Range Achievement Test-Revised and the Peabody Individual Achievement Test. The control group for fMRI consisted of nine normal subjects. SETTING: Neuropsychological laboratory in primary care hospital. PATIENT: A 17-year-old boy who had sustained a closed head injury associated with a partially depressed, right parietal skull fracture, and right temporal hemorrhage in a motor vehicle crash at age 7 months (November 9, 1977). Subsequent social behavior was normal, but the patient had difficulty throughout school in mathematics and spelling and was characterized as having a "short attention span." INTERVENTION: None. MAIN OUTCOME MEASURES: Standardized tests of arithmetic and reading supplemented by an assessment of calculation and quantitative skills. While performing calculations, fMRI disclosed predominantly left hemisphere activation involving the frontal and posterior parietal regions, whereas this task produced bilateral activation of the supramarginal gyrus in seven of nine normal subjects. RESULTS: Neuropsychological findings confirmed the presence of dyscalculia and dyslexia despite normal intellectual functioning. Visuospatial skills ranged from the low normal to average level. The fMRI findings were consistent with early interhemispheric transfer of visuospatial skills normally committed to the right parietal area to the left parietal region. The patient's dyscalculia and reading ability raise a question of acquired left parietal dysfunction as a consequence of the competition between verbal and visuospatial functions for left hemisphere representation. CONCLUSION: Interhemispheric reorganization of function may be bidirectional rather than a feature unique to the left hemisphere substrate for language.

Adolescent↗

A systematic procedure for identifying and classifying children with dyscalculia among primary school children in India.

This paper describes the procedures adopted by two independent studies in India for identifying and classifying children with dyscalculia in primary schools. For determining the presence of dyscalculia both inclusionary and exclusionary criteria were used. When other possible causes of arithmetic failure had been excluded, figures for dyscalculia came out as 5.98% (15 cases out of 251) in one study and 5.54% (78 out of 1408) in the second. It was found in the latter study that 40 out of the 78 (51.27%) also had reading and writing problems. The findings are discussed in the light of previous studies.

Child↗

Developmental dyscalculia and basic numerical capacities: a study of 8-9-year-old students.

Thirty-one 8- and 9-year-old children selected for dyscalculia, reading difficulties or both, were compared to controls on a range of basic number processing tasks. Children with dyscalculia only had impaired performance on the tasks despite high-average performance on tests of IQ, vocabulary and working memory tasks. Children with reading disability were mildly impaired only on tasks that involved articulation, while children with both disorders showed a pattern of numerical disability similar to that of the dyscalculic group, with no special features consequent on their reading or language deficits. We conclude that dyscalculia is the result of specific disabilities in basic numerical processing, rather than the consequence of deficits in other cognitive abilities.

Brain↗

Automatic activation of internal magnitudes: a study of developmental dyscalculia.

The association between Arabic numerals and the representations of magnitude in adult developmental dyscalculia was examined. University students compared physical size, vertical positioning (height), or grayness (different shades of gray) of 2 Arabic numerals. The numerical values could produce a Stroop-like numerical congruity effect (NCE; 3-5 vs. 3-5). The dyscalculia group did not show NCE in the grayness task, and their physical comparisons produced a significantly smaller NCE compared with that produced by the control group. Whereas previous research suggested that Arabic numerals activate representations of magnitude automatically, the results of this study indicate that this is not the case because (a) people with developmental dyscalculia require attention to associate internal representations of magnitude with Arabic numerals, and (b) activation of internal magnitudes depends on context (task).

Adolescent↗

Attentional function as measured by a Continuous Performance Task in children with dyscalculia.

This study determined whether or not students with dyscalculia had difficulty with attention as measured by the Conners' Computerized Continuous Performance Test (CPT). Fifty-six control subjects and 27 subjects with dyscalculia were administered the CPT. Performance was measured using percent omission errors, percent commission errors, mean response time, SE of response times (SE-RT), and a calculated overall attention index (CPT Index). Compared with controls, subjects with dyscalculia had higher CPT Index scores, made more omission errors, and had more inconsistent response times (SE-RT). Multiple regression analysis of arithmetic scores showed that SE-RT and percent commission errors were the only CPT measures that contributed to the arithmetic scores. Problems with attention, as measured by the Conners' CPT, were associated with lower arithmetic achievement scores. Students who have difficulties in arithmetic may have more attentional problems than other children, and students with attentional difficulties may be at risk for difficulties in arithmetic.

Attention↗

Developmental dyscalculia: prevalence and demographic features.

One hundred and forty-three 11-year-old children with development dyscalculia, from a cohort of 3029 students, were studied to determine demographic features and prevalence of this primary cognitive disorder. They were evaluated for gender, IQ, linguistic and perceptual skills, symptoms of attention-deficit hyperactivity disorder (ADHD), socio-economic status and associated learned disabilities. The IQs of the 140 children (75 girls and 65 boys) retained in the study group (three were excluded because of low IQs) ranged from 80 to 129 (mean 98.2, SD 9.9). 26 per cent of the children had symptoms of ADHD, and 17 per cent had dyslexia. Their socio-economic status was significantly lower than that of the rest of the cohort, and 42 per cent had first-degree relatives with learning disabilities. The prevalence of dyscalculia in the original cohort was 6.5 per cent, similar to that of dyslexia and ADHD. However, unlike these other learning disabilities, dyscalculia affected the two sexes in about the same proportions.

Child↗

Regional metabolism: associations with dyscalculia in Alzheimer's disease.

OBJECTIVES: The ability to calculate, which is an important aspect of social daily living, is commonly impaired in patients with Alzheimer's disease even early in the course of the disease. Dyscalculia is often accompanied by focal brain damage, and has been argued to be an independent sign localised around the left temporoparietal region. However, the region most responsible for dyscalculia in Alzheimer's disease has not been determined. The relation between calculation ability and regional cerebral glucose metabolism in Alzheimer's disease was therefore examined. METHODS: The calculation ability, In 91 patients with probable Alzheimer's disease of minimal to moderate severity, was assessed using the arithmetic subtest of the Wechsler adult intelligence scale-revised and the performance correlated with regional cerebral glucose metabolism determined by "F-fluorodeoxyglucose and PET. RESULTS: Regional glucose metabolism in the left inferior parietal lobule and in the left inferior temporal gyrus was significantly correlated with the calculation performance irrespective of age, sex, education, and severity of disease. CONCLUSIONS: The results suggest that dysfunction of the left inferior parietal lobule and the left inferior temporal gyrus plays an important part in producing dyscalculia in patients with Alzheimer's disease.

Aged↗

Developmental dyscalculia: prevalence and prognosis.

The prevalence of developmental dyscalculia (DC) in the school population ranges from 3-6 %, a frequency similar to that of developmental dyslexia and ADHD. These studies fulfilled the criteria for an adequate prevalence study, i.e., were population based, using standardized measures to evaluate arithmetic function. Although the variation in prevalence is within a narrow range, the differences are probably due to which definition of dyscalculia was used, the age the diagnosis was made and the instrument chosen to test for DC. The relative predominance of girls with DC may reflect a greater vulnerability to environmental influences alone or in addition to a biological predisposition. DC is not only encountered as a specific learning disability but also in diverse neurological disorders, examples of which include ADHD, developmental language disorder, epilepsy, treated phenylketonuria and Fragile X syndrome. Although the long-term prognosis of DC is as yet unknown, current data indicate that DC is a stable learning disability persisting, at least for the short term, in about half of affected children. The long-term consequences of DC and its impact on education, employment and psychological well-being have yet to be determined.

Adolescent↗

Dyscalculia and elements of the developmental Gerstmann syndrome in school children.

Fourteen (14) dyscalculic school children were drawn from a larger population of learning-disabled children. The subjects were divided into two groups, those with normal-or-better reading ability and those with dyslexia equal in degree to their dyscalculia. Both groups showed a variety of behavioral deficits in addition to those comprising Gerstmann's syndrome and were notably poor in auditory and visual discrimination and motor coordination. Good readers showed severely-impaired ability to make right-left discriminations, while the poor readers were average in this ability. Poor readers showed marked impairment of word fluency and hand writing, while good readers were average in this regard. The dyscalculia and reading deficits reported here appear unrelated to central-language impairment. Subjects with all four elements of the developmental Gerstmann's syndrome did not constitute an homogeneous behavioral group and were found among samples of both good and poor readers. The pattern of behavioral deficits shown by these subjects suggests cerebral impairment rather than slow maturation as a probable etiology. While the DGS is not useful as a behavioral description, its value as a possible localizing neurological sign cannot yet be ruled out.

Adolescent↗

Persistence of developmental dyscalculia: what counts? Results from a 3-year prospective follow-up study.

OBJECTIVE: To study the natural history of developmental dyscalculia (DC), a specific learning disability affecting approximately 5% of the normal school age population and to identify factors that contribute to persistence. STUDY DESIGN: Of a cohort of 3029 fourth-grade students, 185 children were classified as having DC; 140 participated in phase 1 in which they underwent IQ testing; arithmetic, reading, and writing evaluations; and an assessment for attention-deficit/hyperactivity disorder over a 3-year period. Three years later (phase 2), 88% of the children (123 of 140) were retested. RESULTS: The arithmetic scores of 95% of the 123 children with DC fell within the lowest quartile for their class. At phase 2, 47% (57 of 123) of the children were reclassified as having persistent DC, scoring in the lowest 5% for their age group (13 to 14 years old). Factors significantly associated with persistence of DC in a multivariate model were severity of the arithmetic disorder and arithmetic problems in siblings of the probands. Factors that were not associated with persistence included socioeconomic status, gender, the presence of another learning disability, and educational interventions. CONCLUSIONS: The outcome of DC is similar to that of other learning disabilities, with a persisting course in almost half of affected children; the remainder continue to perform poorly in arithmetic. The ultimate outcome of children with dyscalculia and the effect on education, employment, and psychologic well-being have yet to be determined.

Adolescent↗

Understanding dissociations in dyscalculia: a brain imaging study of the impact of number size on the cerebral networks for exact and approximate calculation.

Neuropsychological studies have revealed different subtypes of dyscalculia, including dissociations between exact calculation and approximation abilities, and an impact of number size on performance. To understand the origins of these effects, we measured cerebral activity with functional MRI at 3 Tesla and event-related potentials while healthy volunteers performed exact and approximate calculation tasks with small and large numbers. Bilateral intraparietal, precentral, dorsolateral and superior prefrontal regions showed greater activation during approximation, while the left inferior prefrontal cortex and the bilateral angular regions were more activated during exact calculation. Increasing number size during exact calculation led to increased activation in the same bilateral intraparietal regions as during approximation, as well the left inferior and superior frontal gyri. Event-related potentials gave access to the temporal dynamics of calculation processes, showing that effects of task and of number size could be found as early as 200-300 ms following problem presentation. Altogether, the results reveal two cerebral networks for number processing. Rote arithmetic operations with small numbers have a greater reliance on left-lateralized regions, presumably encoding numbers in verbal format. Approximation and exact calculation with large numbers, however, put heavier emphasis on the left and right parietal cortices, which may encode numbers in a non-verbal quantity format. Subtypes of dyscalculia can be explained by lesions disproportionately affecting only one of these networks.

Adult↗

Principles underlying the design of "The Number Race", an adaptive computer game for remediation of dyscalculia.

BACKGROUND: Adaptive game software has been successful in remediation of dyslexia. Here we describe the cognitive and algorithmic principles underlying the development of similar software for dyscalculia. Our software is based on current understanding of the cerebral representation of number and the hypotheses that dyscalculia is due to a "core deficit" in number sense or in the link between number sense and symbolic number representations. METHODS: "The Number Race" software trains children on an entertaining numerical comparison task, by presenting problems adapted to the performance level of the individual child. We report full mathematical specifications of the algorithm used, which relies on an internal model of the child's knowledge in a multidimensional "learning space" consisting of three difficulty dimensions: numerical distance, response deadline, and conceptual complexity (from non-symbolic numerosity processing to increasingly complex symbolic operations). RESULTS: The performance of the software was evaluated both by mathematical simulations and by five weeks of use by nine children with mathematical learning difficulties. The results indicate that the software adapts well to varying levels of initial knowledge and learning speeds. Feedback from children, parents and teachers was positive. A companion article describes the evolution of number sense and arithmetic scores before and after training. CONCLUSION: The software, open-source and freely available online, is designed for learning disabled children aged 5-8, and may also be useful for general instruction of normal preschool children. The learning algorithm reported is highly general, and may be applied in other domains.

Journal Article↗

An open trial assessment of "The Number Race", an adaptive computer game for remediation of dyscalculia.

BACKGROUND: In a companion article, we described the development and evaluation of software designed to remediate dyscalculia. This software is based on the hypothesis that dyscalculia is due to a "core deficit" in number sense or in its access via symbolic information. Here we review the evidence for this hypothesis, and present results from an initial open-trial test of the software in a sample of nine 7-9 year old children with mathematical difficulties. METHODS: Children completed adaptive training on numerical comparison for half an hour a day, four days a week over a period of five-weeks. They were tested before and after intervention on their performance in core numerical tasks: counting, transcoding, base-10 comprehension, enumeration, addition, subtraction, and symbolic and non-symbolic numerical comparison. RESULTS: Children showed specific increases in performance on core number sense tasks. Speed of subitizing and numerical comparison increased by several hundred msec. Subtraction accuracy increased by an average of 23%. Performance on addition and base-10 comprehension tasks did not improve over the period of the study. CONCLUSION: Initial open-trial testing showed promising results, and suggested that the software was successful in increasing number sense over the short period of the study. However these results need to be followed up with larger, controlled studies. The issues of transfer to higher-level tasks, and of the best developmental time window for intervention also need to be addressed.

Journal Article↗

Developmental cognitive neuropsychology of number processing and calculation: varieties of developmental dyscalculia.

This article provides a brief overview about the current state of cognitive developmental neuropsychology of developmental dyscalculia (DD) as well as results from a Zurich study that investigates different subtypes of DD according to various aspects of numerical abilities that are impaired or preserved. The differential effects of impairments of one particular numerical area on the development of other numerical abilities are highlighted in the case of a 17 year old boy with severe DD and Developmental Gerstmann Syndrome. A comprehensive model of developmental dynamics of number processing and calculation abilities will be proposed in the last section with respect to the development of intelligence theory.

Adolescent↗