Mathematical modelling of student’s cumulative learning

Supplementary Files



modelo estocástico
proceso no-markoviano
calidad de un curso
modelos matemáticos
procesos de aprendizaje
calidad educativa
cadenas de Markov
aprendizaje exitoso
enseñanza stochastic model
non-markovian process
quality of a course
mathematical models
learning processes
educational quality
Markov chains
successful learning

How to Cite

Sagaceta Mejía, A. R., Fresán Figueroa, J. A., & Martín González, E. M. (2022). Mathematical modelling of student’s cumulative learning. Nova Scientia, 14(28).


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.


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