A theoretical-experimental model for research into epistemological obstacles

Introduction: In the theory of situations of G. Brousseau and in general of the French school, the study of the epistemological obstacles has had a secondary role. Initially the study of the obstacles was tied to questions of an ergonomic nature. How can we distinguish in the shortest possible time the didactic and/or epistemological obstacles relative to the specific content to be taught? The previous modelling such as that of Dourux-Brousseau derived from the works of Bachelard, allow us to recognise if a notion is an obstacle. That model however does not provide strong a-priori deductive instruments for the analysis of obstacles. In the model of Douroux-Brousseau the research instruments were substantially of a didactic type. Previously, other research instruments for epistemological obstacles have been distinguished of historical type without any consideration of the obstacles of didactic type. The approach followed by me is closely tied to an investigation of linguistic/communicative type. The instruments of analisi were semiotic in nature. In the elaboration of the model time after time the instruments of investigation necessary for the "falsification" of the model were indicated. Sometimes of experiemental type and sometimes of theoretical/experimental type. The topic used in the model is that of the Postulate of Eudoxus-Archimedes. The postulate of Eudoxus-Archimedes is an item of knowledge that constitutes an obstacle to the preliminary introduction of the Hypereals and may be an obstacle to non standard analysis.