" l'observation dans les traitements figuraux de geometrie en classe de sixieme "
Institution:
Université Louis Pasteur (Strasbourg) (1971-2008)Disciplines:
Directors:
Abstract EN:
After studying forty years of school books of the french first form, we can notice that observation is given a very important place in geometry. Observation, whether it's interventionist, or suggestive, or conspicuous, is never neutral. While studying six different french first forms, we were confronted to the question of the pupils attitude towards the problems of geometry, attitude where the mere observation can be in the process of solution. The pupils have two distinct attitudes in front of a mathematical figure to study. Those two attidudes are often opposed : one attitude is intuitive and handling ( a perceptive and heuristic apprehension of figures) the other one is deductive or being the result of a calculus ( the discursive and operating interpretation ). Whether adopting a perceptive geometry, or a deductive geometry, it's necessary to develop what we call a " geometry of implying observation " leading the pupil to apprehend the same concepts but under different tights, and having taken time to observe before apprehending them. Indeed, it's not what we see that provoke the apprehension of the figure, but what we know beforehand ( hypo, thesis, knowledge of some properties, schemas. . . ). That's why we suggest develop- ping the conversion of the representations of the discursive registre to the figural registre. If this conversion time leading from the figure to the elaboration of the text of a gaping construction program m is necessary for the exploration of a figure, then it also points out the importance of the training of the different figural treatments which give the geometrical figures their heuristic importance. At the very moment where we want that our pupils are at the heart of the process of learning, it's our duty to give them the ways and means to be actor of their observation.
Abstract FR:
L'etude, a travers quarante ans de manuels scolaires de sixieme, permet de remarquer la place donnee a l'observation en geometrie. Tantot dirigiste, tantot suggeree ou ostensive, l'observation n'est jamais neutre. Notre recherche aupres des eleves de sixieme nous a menee a une interro, gation sur l'attitude des eleves confrontes a des problemes de geometrie ou l'observation premiere de la figure peut jouer un role dans le processus de resolution. Une figure a etudier fait l'objet de deux attitudes souvent contraires : l'une intuitive et manipulatoire ( l'apprehension perceptive et heuristique des formes ) et l'autre deductive ou relevant d'un calcul ( l'interpretation discursive et operatoire ). Entre une geometrie perceptive et une geometrie deductive, il est necessaire de developper ce que nous appelons une geometrie de l'obser, vation impliquante amenant l'eleve a prendre en compte les memes concepts sous diverses formes, en ayant pris le temps d'observer avant de faire. Ce n'est pas ce qu'on voit qui commande l'apprehension de la figure, mais ce qu'on en sait avant ( hypotheses, connaissances des proprietes, schemes. . . ). Si le temps de conversion figure -*- texte, que nous proposons, d'un programme de construction lacunaire se revele un temps necessaire pour l'exploration d'une figure, cela met en evidence la necessite et l'importance d'un apprentissage des differents traitements figuraux qui donnent aux figures geometriques leur role heuristique. A l'heure ou nous voulons que nos eleves soient au coeur de l'apprentissage, donnons leur les moyens d'etre acteur de leur observation.