International Journal of Education, Learning and Development Vol.3, No.9, pp.65-81, December 2015 Published by European Centre for Research Training and Development UK (www.eajournals.org) 65 ISSN 2054-6297(Print), ISSN 2054-6300(Online) Student’s Conceptual Difficulties With respect To the Notion of Random Variable Hamid AMRANI and Moncef ZAKI Interdisciplanary Laboratory of Research in Didactics of Sciences and Technology – Faculty of Sciences Dhar El Mahraz – Sidi Mohammed Ben Abdellah University, Fez, Morroco ABSTRACT: 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: Didactics of Mathematical Sciences, Random Variables, University, Formal and Intuitive Approaches, Conceptual Difficulties. INTRODUCTION AND PROBLEMATIC The teaching of the theory of probabilities is exempted at university from the beginning of the Bachelor of Science degree (BS degree) in the form of lectures (2 hours/week) and directed working sessions (2.5 hours/week), during all the first semester of the second year of the BS degree (15 weeks/semester). The definition of a probability is then systematically introduced in an axiomatic way, such as it is advocated by the official university programs. That generates thus from the start enormous conceptual difficulties for the students. The latter do not manage to easily establish a natural and intuitive link between the random situations of real life and the theory of probabilities (H. Steinbring, 1991). In addition, probabilistic modeling in terms of random variable, being closely related to the axiomatic definition of a probability, generates even more difficulties for the students at the time of treatments of the random variables. The probabilistic modeling in the BS degree cycle, through random variables defined on probabilized spaces, represents a fundamental basis in the course of the students, because the final objective is to make students acquire, at the conclusion of the BS degree, the mathematical tools for the treatment of forecasts, the estimate of parameters by confidence intervals, or the treatment of decision through the notion of statistical tests.