Computer_aided simulation of random experiments at the interface of probability and statistics

Abstract

     This article focuses on the use and role of computer simulation of random experiments in secondary education, taking the case of France as an example. Indeed, one of the essential aspects of the teaching of probability in secondary schools is the place given to modelling. Linking a real random experiment with probability theory leads to questioning the modelling in terms of process. Moreover, the use of technological tools (computer, calculator), which are increasingly present in mathematics teaching, leads to the question of modelling reality via the simulation of random experiments. The transition from random experiments to their simulation is an important issue in the teaching of statistics, as it allows students to access "statistical thinking". The mathematical workspace of simulation conceals a fundamental ambiguity which is the coexistence of two different domains: that of probability, of course, but also that of statistics, which intervene in turn in the problem-solving process. This ambiguity is likely to create confusion in students between what is observational and what is theoretical, but once clearly explained it can be used to introduce probabilistic concepts, based on their analogy with already known statistical concepts.