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

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Employing rationally designed model systems with precise atom-by-atom particle size control, we demonstrate by means of combining noninvasive in situ indirect nano-plasmonic sensing and ex situ scanning transmission electron microscopy that monomodal size-selected platinum cluster catalysts on different supports exhibit remarkable intrinsic sintering resistance even under reaction conditions. The observed stability is related to suppression of Oftwald ripening by elimination of its main driving force via size-selection. This study thus constitutes a general blueprint for the rational design of sintering resistant catalyst systems and for efficient experimental strategies to determine sintering mechanisms. Moreover, this is the first systematic experimental investigation of sintering processes in nanoparticle systems with an initially perfectly monomodal size distribution under ambient conditions