Demonstration through absurd: a thorn in teaching and learning mathematics - a case study in Mali

Abstract

The present work has as a theme " Demonstration through absurd: a thorn in teaching and learning mathematics: a case study in Mali “To achieve this, we conducted a review of the literature that focused on work around reasoning by the absurd and the institutional study of demonstration by the absurd. The problem relates to the role that demonstration by the absurd plays in classroom practices and in school textbooks and its absence in the curricula. The research questions are worded as follows: In Mali, is demonstration by the absurd considered to be beyond the capacities of the secondary school student? Regarding a statement, does the future teacher recognize the need for a demonstration by the absurd or can he transform it in such a way that a demonstration by the absurd is necessary? The mathematical study of the demonstration by the absurd, allowed us to analyze this method of demonstration as reference knowledge and to make its logical interpretation. The classification of the problems made by the first author in his thesis, allowed us to choose the didactic variables. The experimental part includes the choice and a priori analysis of three problems proposed to student teachers at the École Normale Supérieure in Bamako, the handing over of items in one session, the a posteriori analysis of the productions. The student teachers were put in a situation of problem solving by the method of the demonstration by the absurd to eventually know their relation to the demonstration by the absurd. A posteriori analysis allowed us to see confirmation that the demonstration by the absurd poses difficulties for secondary school teachers.