Alcuni aspetti epistemologici dell'insegnamento della modellizzazione matematica:il caso di un modello deterministico e un modello probabilistico per uno stesso fenomeno

The aim of this paper is to help clarifying, in an educational perspective, some aspects of mathematical modeling. In order to do it, an example will be presented: it will concern the relationships between a deterministic model and a probabilistic model of the same phenomenon (the radioactive decay). In particular, a way will be suggested to overcome the rigid separation between deterministic and probabilistic models, which usually characterizes the teaching of the subject. From a mathematical point of view, it will be shown how it is possible to move, for the same phenomenon, from one kind of models to the other; then their features of flexible and non contradictory representations of reality will be put into evidence. Finally, connected to the same example, some relevant epistemological and educational aspects of the related activities that have involved university students and in-service teachers will be presented; some learning results and the potential of the subject will be put into evidence.