Mathematical modelling of student’s cumulative learning
Vol. 14 No. 28 (2022), Natural Sciences and Engineering
Vol. 14 No. 28 (2022)

Mathematical modelling of student’s cumulative learning

Natural Sciences and Engineering
https://doi.org/10.21640/ns.v14i28.2947
Published 2022-04-08
Alma Rocío Sagaceta Mejía
Iberoamerican University, Mexico City
https://orcid.org/0000-0001-8265-3379
Julián Alberto Fresán Figueroa
Autonomous Metropolitan University, Cuajimalpa Unit
https://orcid.org/0000-0002-9834-8157
Ehyter Matías Martín González
University of Guanajuato
https://orcid.org/0000-0003-3824-699X
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Keywords

modelo estocástico
aprendizaje
proceso no-markoviano
calidad de un curso
modelos matemáticos
procesos de aprendizaje
cursos
calidad educativa
sesiones
distribución
convergencia
educación
formación
cadenas de Markov
aprendizaje exitoso
enseñanza stochastic model
learning
non-markovian process
quality of a course
mathematical models
learning processes
courses
educational quality
sessions
distribution
convergence
education
formation
Markov chains
successful learning
teaching

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). https://doi.org/10.21640/ns.v14i28.2947
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Abstract

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.

https://doi.org/10.21640/ns.v14i28.2947
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