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

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.