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 theor

Development of a Possible General Magnitude System for Number and Space

There is strong evidence for a link between numerical and spatial processing. However, whether this association is based on a common general magnitude system is far from conclusive and the impact of development is not yet known. Hence, the present study aimed to investigate the association between discrete non-symbolic number processing (comparison of dot arrays) and continuous spatial processing (comparison of angle sizes) in children between the third and sixth grade (N = 367). Present findings suggest that the processing of comparisons of number of dots or angle are related to each other, but with angle processing developing earlier and being more easily comparable than discrete number representations for children of this age range. Accordingly, results favor the existence of a more complex underlying magnitude system consisting of dissociated but closely interacting representations for continuous and discrete magnitudes

Developmental dyscalculia in adults: Current issues and open questions for future research.

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 that – beyond 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

Impaired neural networks for approximate calculation in dyscalculic children: a functional MRI study

BACKGROUND: 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. METHODS: 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. RESULTS: 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. CONCLUSION: In conclusion, there is evidence for a deficient recruitment of neural resources in children with DD when processing analog magnitudes of numbers

Does It Count? Pre-School Children’s Spontaneous Focusing on Numerosity and Their Development of Arithmetical Skills at School

BACKGROUND Children's spontaneous focusing on numerosity (SFON) is related to numerical skills. This study aimed to examine (1) the developmental trajectory of SFON and (2) the interrelations between SFON and early numerical skills at pre-school as well as their influence on arithmetical skills at school. METHOD Overall, 1868 German pre-school children were repeatedly assessed until second grade. Nonverbal intelligence, visual attention, visuospatial working memory, SFON and numerical skills were assessed at age five (M = 63 months, Time 1) and age six (M = 72 months, Time 2), and arithmetic was assessed at second grade (M = 95 months, Time 3). RESULTS SFON increased significantly during pre-school. Path analyses revealed interrelations between SFON and several numerical skills, except number knowledge. Magnitude estimation and basic calculation skills (Time 1 and Time 2), and to a small degree number knowledge (Time 2), contributed directly to arithmetic in second grade. The connection between SFON and arithmetic was fully mediated by magnitude estimation and calculation skills at pre-school. CONCLUSION Our results indicate that SFON first and foremost influences deeper understanding of numerical concepts at pre-school and-in contrast to previous findings -affects only indirectly children's arithmetical development at school

Taking a Closer Look: The Relationship between Pre-School Domain General Cognition and School Mathematics Achievement When Controlling for Intelligence

Intelligence, as well as working memory and attention, affect the acquisition of mathematical competencies. This paper aimed to examine the influence of working memory and attention when taking different mathematical skills into account as a function of children's intellectual ability. Overall, intelligence, working memory, attention and numerical skills were assessed twice in 1868 German pre-school children (t1, t2) and again at 2nd grade (t3). We defined three intellectual ability groups based on the results of intellectual assessment at t1 and t2. Group comparisons revealed significant differences between the three intellectual ability groups. Over time, children with low intellectual ability showed the lowest achievement in domain-general and numerical and mathematical skills compared to children of average intellectual ability. The highest achievement on the aforementioned variables was found for children of high intellectual ability. Additionally, path modelling revealed that, depending on the intellectual ability, different models of varying complexity could be generated. These models differed with regard to the relevance of the predictors (t2) and the future mathematical skills (t3). Causes and conclusions of these findings are discussed

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

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

Number Processing and Calculation in Brazilian Children Aged 7-12 Years

Numerical cognition is based on two components - number processing and calculation. Its development is influenced by biological, cognitive, educational, and cultural factors. The objectives of the present study were to: i) assess number processing and calculation in Brazilian children aged 7-12 years from public schools using the Zareki-R (Battery of neuropsychological tests for number processing and calculation in children, Revised; von Aster & Dellatolas, 2006) in order to obtain normative data for Portuguese speakers; ii) identify how environment, age, and gender influences the development of these mathematical skills; iii) investigate the construct validity of the Zareki-R by the contrast with the Arithmetic subtest of WISC-III. The sample included 172 children, both genders, divided in two groups: urban (N = 119) and rural (N = 53) assessed by the Zareki-R. Rural children presented lower scores in one aspect of number processing; children aged 7-8 years demonstrated an inferior global score than older; boys presented a superior performance in both number processing and calculation. Construct validity of Zareki-R was demonstrated by high to moderate correlations with Arithmetic subtest of WISC-III. The Zareki-R therefore is a suitable instrument to assess the development of mathematical skills, which is influenced by factors such as environment, age, and gende