Processing Ordinality and Quantity: The Case of Developmental Dyscalculia

In contrast to quantity processing, up to date, the nature of ordinality has received little attention from researchers despite the fact that both quantity and ordinality are embodied in numerical information. Here we ask if there are two separate core systems that lie at the foundations of numerical cognition: (1) the traditionally and well accepted numerical magnitude system but also (2) core system for representing ordinal information. We report two novel experiments of ordinal processing that explored the relation between ordinal and numerical information processing in typically developing adults and adults with developmental dyscalculia (DD). Participants made “ordered” or “non-ordered” judgments about 3 groups of dots (non-symbolic numerical stimuli; in Experiment 1) and 3 numbers (symbolic task: Experiment 2). In contrast to previous findings and arguments about quantity deficit in DD participants, when quantity and ordinality are dissociated (as in the current tasks), DD participants exhibited a normal ratio effect in the non-symbolic ordinal task. They did not show, however, the ordinality effect. Ordinality effect in DD appeared only when area and density were randomized, but only in the descending direction. In the symbolic task, the ordinality effect was modulated by ratio and direction in both groups. These findings suggest that there might be two separate cognitive representations of ordinal and quantity information and that linguistic knowledge may facilitate estimation of ordinal information

Developmental dyscalculia: a dysconnection syndrome?

Numerical understanding is important for everyday life. For children with developmental dyscalculia (DD), numbers and magnitudes present profound problems which are thought to be based upon neuronal impairments of key regions for numerical understanding. The aim of the present study was to investigate possible differences in white matter fibre integrity between children with DD and controls using diffusion tensor imaging. White matter integrity and behavioural measures were evaluated in 15 children with developmental dyscalculia aged around 10 years and 15 matched controls. The main finding, obtained by a whole brain group comparison, revealed reduced fractional anisotropy in the superior longitudinal fasciculus in children with developmental dyscalculia. In addition, a region of interest analysis exhibited prominent deficits in fibres of the superior longitudinal fasciculus adjacent to the intraparietal sulcus, which is thought to be the core region for number processing. To conclude, our results outline deficient fibre projection between parietal, temporal and frontal regions in children with developmental dyscalculia, and therefore raise the question of whether dyscalculia can be seen as a dysconnection syndrome. Since the superior longitudinal fasciculus is involved in the integration and control of distributed brain processes, the present results highlight the importance of considering broader domain-general mechanisms in the diagnosis and therapy of dyscalculia

A numerical model of birch pollen emission and dispersion in the atmosphere. Description of the emission module

A birch pollen emission model is described and its main features are discussed. The development of the model is based on a double-threshold temperature sum model that describes the propagation of the flowering season and naturally links to the thermal time models to predict the onset and duration of flowering. For the flowering season, the emission model considers ambient humidity and precipitation rate, both of which suppress the pollen release, as well as wind speed and turbulence intensity, which promote it. These dependencies are qualitatively evaluated using the aerobiological observations. Reflecting the probabilistic character of the flowering of an individual tree in a population, the model introduces relaxation functions at the start and end of the season. The physical basis of the suggested birch pollen emission model is compared with another comprehensive emission module reported in literature. The emission model has been implemented in the SILAM dispersion modelling system, the results of which are evaluated in a companion paper

Structural and functional brain anatomy in children with developmental dyscalculia: what counts?

Calculation ability represents an extremely complex cognitive process. It has been understood to be associated with and depend upon multifactor abilities, including verbal, spatial, memory, and executive functions (Ardila et al., 1998). The complexity of numerical processing may refer to the difficulties investigating its disorder: Developmental Dyscalculia (DD). The underlying deficits, which cause DD, remain unanswered but various factors have been proposed. These can be classified into two models: Domain general or domain specific factors. An involvement of domain specificity in the development of DD results from infant and non-human primate studies (McCrink and Wynn, 2004; Nieder, 2005). It has been argued that the core aspect of numerical cognition is an innate “number sense”, which is a short-hand term for our ability to quickly understand, approximate and manipulate numerical quantities (Dehaene, 1997). The core deficit hypothesis proposes that an impaired system leads to deficits in number sense what is the cause of a least some types of DD. This ‘number sense’ is located in the parietal lobe and therefore, children with DD should exhibit a dysfunction of this region. On the other hand, domain general factors, as attention or working memory, which stand for an involvement of the executive system in calculation, are not in the focus of investigations about the underlying deficits of DD. The main goal of this thesis was to evaluate the neural network of children with DD in respect of a domain general approach. In Study A, entitled “Optimized Voxel Based Morphometry in Children with Developmental Dyscalculia” we investigated dyscalculic children compared to control children by use of voxel-based morphometry. This method reveals anatomical differences between groups and is independent of cognitive functions. Results show decreased grey matter volume in the right IPS. If it is assumed that the right IPS exclusively serves as a region that represents a core analog representation of number this finding would contribute to the domain specific hypotheses, described above. But there were additional clusters at the bilateral middle frontal gyrus, the left inferior 5 frontal gyrus and bilateral anterior cingulum which refer to possible domain general impairments of the attentional and the working memory system, which might have a negative effect on the acquisition of number representation and number processing capacities. In Study B, entitled “Dysfunctional Neural Network of Spatial Working Memory Contributes to Developmental Dyscalculia” special interest has been addressed to neural functions of a domain general factor, spatial working memory. Functional magnetic resonance imaging (fMRI) was used to examine children with and without DD with a spatial working memory paradigm. We found reduced activation in working memory relevant brain areas, such as the right IPS, the right inferior frontal lobe and in the right insula in children with DD when compared to control group. Decreased activation in the right IPS of children with DD during a spatial working memory task may indicate that more domain general factors such as working memory influence the acquisition of arithmetic competencies and the development of a mental number line. Therefore, our data support the general domain hypothesis and we conclude, that poor spatial working memory capacity in DD influences the formation of a core understanding of numerical information and the development of a ‘mental number line’

Optimized voxel-based morphometry in children with developmental dyscalculia.

Developmental dyscalculia (DD) is a specific learning disability affecting the normal acquisition of arithmetic skills. Current studies estimate that 3-6% of the school population is affected by DD. Genetic, neurobiological, and epidemiologic evidence indicates that dyscalculia is a brain-based disorder. Imaging studies suggest the involvement of parietal and prefrontal cortices in arithmetic tasks. The aim of the present study was to analyze if children with DD show structural differences in parietal, frontal, and cingulate areas compared to typically achieving children. Magnetic resonance imaging was obtained from 12 children with DD aged 9.3+/-0.2 years and 12 age-matched control children without any learning disabilities on a 1.5 T whole-body scanner. Voxel-based morphometry analysis with an optimization of spatial segmentation and normalization procedures was applied to compare the two groups in order to find differences in cerebral gray and white matter. Compared to controls, children with DD show significantly reduced gray matter volume in the right intraparietal sulcus (IPS), the anterior cingulum, the left inferior frontal gyrus, and the bilateral middle frontal gyri. White matter comparison demonstrates clusters with significantly less volume in the left frontal lobe and in the right parahippocampal gyrus in dyscalculic children. The decreased gray and white matter volumes in the frontoparietal network might be the neurological substrate of impaired arithmetic processing skills. The white matter volume decrease in parahippocampal areas may have influence on fact retrieval and spatial memory processing

Optimized voxel-based morphometry in children with developmental dyscalculia.

Developmental dyscalculia (DD) is a specific learning disability affecting the normal acquisition of arithmetic skills. Current studies estimate that 3-6% of the school population is affected by DD. Genetic, neurobiological, and epidemiologic evidence indicates that dyscalculia is a brain-based disorder. Imaging studies suggest the involvement of parietal and prefrontal cortices in arithmetic tasks. The aim of the present study was to analyze if children with DD show structural differences in parietal, frontal, and cingulate areas compared to typically achieving children. Magnetic resonance imaging was obtained from 12 children with DD aged 9.3+/-0.2 years and 12 age-matched control children without any learning disabilities on a 1.5 T whole-body scanner. Voxel-based morphometry analysis with an optimization of spatial segmentation and normalization procedures was applied to compare the two groups in order to find differences in cerebral gray and white matter. Compared to controls, children with DD show significantly reduced gray matter volume in the right intraparietal sulcus (IPS), the anterior cingulum, the left inferior frontal gyrus, and the bilateral middle frontal gyri. White matter comparison demonstrates clusters with significantly less volume in the left frontal lobe and in the right parahippocampal gyrus in dyscalculic children. The decreased gray and white matter volumes in the frontoparietal network might be the neurological substrate of impaired arithmetic processing skills. The white matter volume decrease in parahippocampal areas may have influence on fact retrieval and spatial memory processing

Dysfunctional neural network of spatial working memory contributes to developmental dyscalculia.

The underlying neural mechanisms of developmental dyscalculia (DD) are still far from being clearly understood. Even the behavioral processes that generate or influence this heterogeneous disorder are a matter of controversy. To date, the few studies examining functional brain activation in children with DD mainly focus on number and counting related tasks, whereas studies on more general cognitive domains that are involved in arithmetical development, such as working memory are virtually absent. There are several studies showing a close relationship between DD and spatial working memory [Camos, V. (2008). Low working memory capacity impedes both efficiency and learning of number transcoding in children. Journal of Experimental Child Psychology, 99(1), 37-57; McLean, J. F., & Hitch, G. J. (1999). Working memory impairments in children with specific arithmetic learning difficulties. Journal of Experimental Child Psychology, 74(3), 240-260; Rosselli, M., Matute, E., Pinto, N., & Ardila, A. (2006). Memory abilities in children with subtypes of dyscalculia. Developmental Neuropsychology, 30(3), 801-818; Siegel, L. S., & Ryan, E. B. (1989). The development of working memory in normally achieving and subtypes of learning disabled children. Child Development, 60(4), 973-980]. The relationship between these two mechanisms is still matter of debate, but this study follows the assumption that poor spatial working memory capacity may hinder the acquisition of spatial number representations in children with DD [Geary, D. C. (1993). Mathematical disabilities: Cognitive, neuropsychological, and genetic components. Psychological Bulletin, 114(2), 345-362; von Aster, M., & Shalev, R. S. (2007). Number development and developmental dyscalculia. Developmental Medicine and Child Neurology, 49(11), 868-873]. Using functional MRI the current study compares brain activity associated with spatial working memory processes in 8-10-year-old children with DD and normally achieving controls. Both groups showed significant spatial working memory related activity in a network including occipital and parietal regions. Children with DD showed weaker neural activation compared to the control group during a spatial working memory task in the right intraparietal sulcus (IPS), the right insula and the right inferior frontal lobe. Performance tests outside the scanner showed impaired working memory proficiency in children with DD. Bringing behavioral performance and neural activity together we found significant correlations of right IPS activity with performance on the verbal digit span forward and the spatial Corsi Block Tapping test. Our findings demonstrate for the first time an involvement of spatial working memory processes in the neural underpinnings of DD. These poor spatial working memory processes may inhibit the formation of spatial number representations (mental numberline) as well as the storage and retrieval of arithmetical facts

Mental number line training in children with developmental dyscalculia

Developmental dyscalculia (DD) is a specific learning disability that affects the acquisition of mathematical skills in children with normal intelligence and age-appropriate school education (prevalence 3-6%). One essential step in the development of mathematical understanding is the formation and automated access to a spatial representation of numbers. Many children with DD show a deficient development of such a mental number line. The present study aimed to develop a computer-based training program to improve the construction and access to the mental number line. Sixteen children with DD aged 8-10 years and 16 matched control children completed the 5-week computer training. All children played the game 15 min a day for 5 days a week. The efficiency of the training was evaluated by means of neuropsychological tests and functional magnetic resonance imaging (fMRI) during a number line task. In general, children with and without DD showed a benefit from the training indicated by (a) improved spatial representation of numbers and (b) the number of correctly solved arithmetical problems. Regarding group differences in brain activation, children with DD showed less activation in bilateral parietal regions, which reflects neuronal dysfunction in pivotal regions for number processing. Both groups showed reduced recruitment of relevant brain regions for number processing after the training which can be attributed to automatization of cognitive processes necessary for mathematical reasoning. Moreover, results point to a partial remediation of deficient brain activation in dyscalculics after consolidation of acquired and refined number representation. To conclude, the present study represents the first attempt to evaluate a custom-designed training program in a group of dyscalculic children and results indicate that the training leads to an improved spatial representation of the mental number line and a modulation of neural activation, which both facilitate processing of numerical tasks