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Forms of mathematical thought. (Modalites de la pensee mathematique d’eleves de douze ans devant des problemes de pavages.) (French)
Educ. Stud. Math. 27, No. 2, 165-189 (1994).
The main part of this paper consists in an analysis of the activities of twelve years old students solving problems of polygonal tilings and improving on this occasion their knowledge of plane geometry. The analysis, bearing principally on the thinking processes of the students, results in a presentation of these processes in two principal categories: those which belong to that may be called the instantaneous thinking and result mainly in the perception of some simple structures or in some swift "conjectures", and those which are of a more discursive nature and appear mainly in the drawing activities and in the argumentation of the proofs. This paper contains also a comparison of the above mentioned teaching with the analogous one organized on the same theme (tilings of the plane) by D. van Hiele, and analysed in her Ph. D. (1957). (orig.) - Le present article est d’abord une analyse d’un enseignement dans lequel des eleves de douze ans ont traite des problemes de pavages polygonaux et progresse a cette occasion dans leur apprentissage de la geometric plane. L’analyse, qui a porte principalement sur les processus de pensee des eleves, aboutit a rassembler ces processus en deux categories principales; ceux qui relevant d’une pensee dite instantance et qui se manifestent surtout part des constats ou des "conjectures" rapides, et ceux qui sont plutot discursifs et apparaissent principalement dans les activites de dessin et l’argumentation des preuves. Cet article contient aussi une comparaison de l’einseignement mentionne ci-dessus avec celui realise par D. van Hiele sur le meme theme et analyse dans sa these de doctorat (1957). (orig.)
Classification: C33
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