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UNE INGENIERIE DIDACTIQUE POUR L'APPRENTISSAGE DU THEOREME DE THALES AU COLLEGE

Abstract : The basic aim of this research is - firstly - to define the external and internal functionalities to Mathematics of the Thales theorem in order to know - secondly - if they are conveyed through History in present teaching and if they are transmittable within an engineering at a secondary school level. After an epistemological research aiming at studying the evolution of the bearing on the statement and after connected prooves in History since Greek Antiquity, we have defined difficulties met by pupils in the recognition of geometrical configurations linked to this theorem and its application. This has more particularly permitted to show the part played by the archetypal and prototypical figures linked to the Thales theorem and the mistakes occuring as soon as the figures proposed to pupils stray from them. These mistakes have particularly allowed to define pathogen figures, the figures which have been - wrongly - admitted unable to form the subject of an application of the theorem being qualified of pathological ones. The actual teaching of this theorem has been analysed too and a certain number of deficiences have been shown such as the weak level of problematicalisation of the activities supposed to induce the theorem and the open approach characterizing them. From these whole researches a didactic engineering has been formed. It aims at justifying the introduction of this theorem by means of calculation problems - calculation of inaccessible distance measures in the meso-space - on the one hand at organizing the needed relations between the meso-space and the micro-space on the other hand. This didactic building up, which took in consideration the main difficulty in passing to irrational statements as well, has been experienced and little by little made subtle.
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Eric Laguerre. UNE INGENIERIE DIDACTIQUE POUR L'APPRENTISSAGE DU THEOREME DE THALES AU COLLEGE. Education. Université Paris-Diderot - Paris VII, 2005. Français. ⟨tel-00337891⟩

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