Mathematical Expectation: Conceptual Difficulties Among Students

Abstract

In this paper, we are interested in the introductory teaching of the notion of Mathematical expectation, also known as the expected value. Our research hypothesis is that teaching based on a formal approach may be a didactic failure. The long-term observations of a reduced number of students made it possible to identify various difficulties and conceptual obstacles around the interpretation and the implementation of this notion. The difficulties that obstruct the availability of this object are due mainly to conceptual confusion between the notion of expected value and the notion of probability, others are due to erroneous representations. A quantitative analysis of students' productions showed that the relevance of the formal approach to the interpretation of expected value had no effect on its validity, compared to the intuitive approach which had an impact on its validity. These results thus encourage the adoption of a dialectic: formalism / intuition in the introduction of probabilistic formalism. Received: 7 February 2024 / Accepted: 29 May 2024 / Published: 5 July 2024