In this article, we are interested in an introductory teaching of the probabilistic formalism at university level, in particular around the notion of random variable. Our research hypothesis is that a teaching based on a formal approach, even if it is intended for second year students of the Bachelor of Science degree, can be doomed to a didactic failure. Our study with a small number of students, but over a long duration of observations, has allowed to raise various conceptual difficulties and obstacles around the definition and production of random variable examples. The difficulties that impede the availability of this object are mainly due to conceptual confusions between the concept of random variable and the notions of image universe, random experiment, or law of probabilities. A quantitative analysis of the productions of students showed that the relevance of the formal approach was without effect on the production of example, whereas that of the intuitive approach had an effect on the validity of the production of example of random variable. These results encourage thus the adoption of a dialectical formalism/intuition in the introduction of the probabilistic formalism; such an approach of teaching would seem to be a priori quite in favor of a good apprehension by the students.
Keywords: Conceptual Difficulties, Didactics of Mathematical Sciences, Formal and Intuitive Approaches, Random Variables, University
