Une situation ouverte en mathématiques : rapports dialectiques entre Théorie - Expérimentation - Contingence - Christine Del Notaro (Recherches en Éducation)
This article departs from the results of a research (Del Notaro, on 2010) and suggests describing some phenomena observed in the contingency of the practice of primary teachers, in mathematics. The observation of the effective practices allowed us to bring to light a phenomenon in our doctoral thesis, which we named the saturation of the environment (“saturation du milieu”). We show how this phenomenon constrains the practices and present the way we proceeded and which contributed to bring an end of the confusion. The set up device is to be envisaged as an interaction of knowledge between the experimenter and the pupils: sets of tasks (“jeux de tâches”). We explain besides, how, by an effect of didactic transposition, an apparently opened situation is confined when found in an exercise book for the teachers instead of circulating between the various worlds for which it is nevertheless intended: first of all, the “noosphere” from which it arises, then, that of the school for whom it was conceived, then that of the training which tries to exploit it and finally, that of the research which uses it with the pupils and analyses the effects.