Mathematical modelling of the performance of a student in non-collaborative and non-presential learning

TL;DR

This paper develops a stochastic model to analyze how students understand online classes over multiple sessions, considering teacher quality and student affinity, with a focus on understanding session comprehension and convergence behavior.

Contribution

The paper introduces a novel non-Markovian stochastic model for student knowledge acquisition in online learning, including recursive formulas and convergence analysis.

Findings

Derived recursive expressions for session comprehension distribution

Analyzed convergence and speed of convergence of the model

Provided numerical examples illustrating model behavior

Abstract

In this paper we propose a model to study the appropriation of knowledge of one student in a non-collaborative online class. We formulate a stochastic model based on the quality of the teacher's class and the affinity of the student to understand the sessions, under the assumption that previous sessions have some influence in the understanding of the next sessions. This assumption implies that the process is not even a Markov process. This kind of situation appears in seminars and classes with many different sessions. We derive some recursive expressions for the distribution of the number of sessions that the student comprehends. Furthermore, we study the convergence of this distribution and study the speed of this convergence through some numerical examples.