Abstract
In this thesis in didactics of mathematics, we study a possible transposition to the classroom of practices of researchers using mathematical modelling. We are focusing on the devolution to secondary pupils (11 years to 18 years) of the work of horizontal mathematization necessary to make a situation rooted in reality accessible to a mathematical treatment.We frame our work in the methodology of didactic engineering. We also include issues related to teaching practices and also we have some similarities with the approach of second-generation didactic engineering.Our epistemological analyses allowed us to identify invariant practices of researchers in life sciences concerning horizontal mathematization. We then relied on these analyses to characterize, develop and analyse a realistic fiction designed as an adaptation of a professional problem of modelling on the prediction of growth of a tree. We conducted our experiments in a training device of collaborative problem solving with an initial phase of questions and answers. We support the hypothesis that the characteristics of a realistic fiction designed as an adaptation of a professional problem of modelling with an initial phase of questions-answers between peers are likely to favour the devolution of horizontal mathematization to pupils.The didactic analyses of the collected data were conducted based on the results of the epistemological study. They highlighted the devolution to students of horizontal mathematization. In addition, some traces of transposition of the invariant practices identified in the epistemological study were attested. Relying on the framework of the didactic and ergonomic double approach and on a study of literature in mathematics education on possible obstacles to the teaching of mathematical modelling, we have made hypotheses on the obstacles and conditions about teaching practices related to the teaching of horizontal mathematization. We used the potential magnifying effect offered by the in-service teachers’ training device to emit and test hypotheses about potential internal levers within this device, in respect to a certain extent, to possible obstacles and conditions. The study of the general scope of our results concerning ordinary teaching practices is still to be done.