Mathematical Expectation: Conceptual Difficulties Among Students

Abdelouahed  El Maroufi; Marouane  Moukhliss; Abdelhak  Eseghir; Hamid  El Amrani; Moncef  Zaki; Mohamed  Latifi

doi:10.36941/jesr-2024-0104

Authors

Abdelouahed El Maroufi Laboratory of Applied Sciences and Didactic (LaSAD), Ecole Normale Supérieure, Abdelmalek Essaadi University, Tetouan, Morocco
Marouane Moukhliss Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morocco
Abdelhak Eseghir Laboratory of Stochastic and Deterministic Modelling (LaMSD), Mohamed First University, Oujda, Morocco 4Center of Training Education’ Inspectors, Rabat, Morocco
Hamid El Amrani Faculty of Legal Economic and Social Sciences, Abdelmalek Essaadi University, Tetouan, Morocco
Moncef Zaki Interdisciplinary Research Laboratory in Didactics of Science and Technology (LIRDST), Faculty of Sciences Dhar El Mahraz, Sidi Mohammed Ben Abdellah University, Fez, Morocco
Mohamed Latifi Laboratory of Analysis, Modeling and Simulation (LAMS), Faculty of Sciences Ben M'sik, Hassan II University, Casablanca, Morocco; Interdisciplinary Research Laboratory in Didactics of Science and Technology (LIRDST), Faculty of Sciences Dhar El Mahraz, Sidi Mohammed Ben Abdellah University, Fez, Morocco

DOI:

https://doi.org/10.36941/jesr-2024-0104

Keywords:

expected value, probability distribution, formal approach, intuitive approach

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