Abstract |
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[eng] The learning of mathematics covers a variety of skills, such as comparing quantities, counting the number of items in a set, dealing with the numerical systems (i.e., writing and reading numbers), performing simple and complex calculations, or solving word problems. Typically, a majority of children are able to master these abilities, but an appreciable percentage of them does not and are then referenced as having developmental dyscalculia. It is clear that not being able to count efficiently, to understand the meaning of numbers, or to calculate as other children do, rapidly becomes a handicap during the development, not only at school but also in society in general, in the same way as not being able to read is. Despite the growing interest observed over these last few years, research on developmental dyscalculia or more general mathematical disability is actually much less advanced than research on dyslexia. It could be due to the complexity of the mathematics field. Several hypotheses have been proposed to account for this learning deficit, but the origin(s) of developmental dyscalculia remain(s) unclear. Research first focused on the role of the auxiliary cognitive functions not directly related to number processing. In particular, the different components of the working memory were extensively measured in children with mathematical difficulties. Other theories are based on potential weak spatial abilities, low speed of processing, or difficulties in retrieving information from long-term memory. More recently, Butterworth (1999b) proposes that humans are born with a capacity specialised for recognising and mentally manipulating numerosities. Unlike the previous hypotheses, he argues for ?a highly selective and specific deficit of a very basic capacity for understanding numbers, which leads to a range of difficulties in learning about number and arithmetic?. In the same vein, Dehaene (1997) speaks about the ?number sense? as the ability to represent and manipulate number magnitude nonverbally that could be impaired in developmental dyscalculia. In this thesis, we have focused on four main questions with respect to number development. First, we wanted to test whether or not difficulties encountered by mathematically disabled children are specific to the numerical domain. Children with mathematical disabilities manifesting poor calculation abilities were compared to control children of the same age during various tasks of retrieving information from long-term memory (Experiment 1). The second aim was to examine the integrity of the number magnitude representation in dyscalculia. We analysed potential differences in the slope of the numerical distance effect, which reflects the nature of analog magnitudes, in children with or without mathematical disabilities when they had to select the larger of two quantities presented in different formats (Experiment 2). These experiments are presented in Chapters 4 and 5. The two other questions are dedicated to the analysis of brain areas involved in number development using functional magnetic resonance imaging (fMRI). Our third objective was to examine age-related changes in frontal and parietal regions between children and adults during number comparison (Experiment 3). Finally, we conducted a second neuroimaging study to explore the potential neural correlates of dyscalculia. Cerebral activity of both children with pure dyscalculia and control children was analysed during a numerical and a non-numerical comparison tasks (Experiment 4). We also investigated whether or not these differences in brain activation were specific to number processing. These experiments are reported in Chapters 6 and 7. |