Abstract

SAGACETA MEJIA, Alma Rocío; FRESAN FIGUEROA, Julián Alberto  and  MARTIN GONZALEZ, Ehyter Matías. Mathematical modelling of student’s cumulative learning. Nova scientia [online]. 2022, vol.14, n.28, 00008.  Epub Aug 01, 2022. ISSN 2007-0705.  https://doi.org/10.21640/ns.v14i28.2947.

In this paper we propose a model to study the learning process of one student during a course. 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. The afore mentioned assumption implies that the process is not a Markov process. 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 illustrate its speed of convergence through some numerical examples. Finally, we apply these results to propose a methodology to estimate the quality of this kind of courses.

Keywords : stochastic model; learning; non-markovian process; quality of a course; mathematical models; learning processes; courses; educational quality; sessions; distribution; convergence; education; formation.

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