SITUATIONS D'INITIATION AU RAISONNEMENT DÉDUCTIF |
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| Authors: | Gilbert Arsac Michel Mante |
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| Institution: | (1) CNRS-IRPEACS, équipe COAST, Ecole Normale Supérieure de Lyon et Université Lyon I, France;(2) Institut Universitaire de Formation des maîtres, Lyon, France |
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| Abstract: | We examine classroom situations which allow the learning of rules of mathematical reasoning. Drawing on an epistemological analysis and G. Brousseau's theory of situations, we define a priori theoretical characteristics which such situations must possess. We then use this analysis, and hypotheses about the cognitive functioning of pupils of this age, to establish learning situations for the rule of the excluded middle, and for the use of the figure in geometry. We report the results of experimentation with two of thses situations and show that, through the study of a mathematical problem, debate about these rules can be generated amongst students aged twelve to thirteen. We explain why, in our opinion, for epistemological reasons linked to the two particular rules concerned, it is necessary for the teacher to conclude the debate, and we examine our cognitive hypotheses against the actual results of experimentation. |
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