Mathematical Model for Adaptive Technology in E-learning Systems

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Nataliia Barchenko 1,* Volodymyr Tolbatov 1 Tetiana Lavryk 1 Viktor Obodiak 1 Igor Shelehov 1 Andrii Tolbatov 2 Sergiy Gnatyuk 3 Olena Tolbatova 3

1. Sumy State University, Department of Computer Science, 2, Rymskogo-Korsakova st., Sumy, 40007, Ukraine

2. Sumy National Agrarian University, Department of Cybernetics and Informatics, 160, Gerasim Kondratiev st., Sumy, 40000, Ukraine

3. National Aviation University, Kyiv, Ukraine

* Corresponding author.


Received: 23 Nov. 2021 / Revised: 10 Jan. 2022 / Accepted: 17 Feb. 2022 / Published: 8 Aug. 2022

Index Terms

Computer Science, E-Learning, Adaptation, Fuzzy Logic, Optimization, Mathematical Model.


The emergence of a large number of e-learning platforms and courses does not solve the problem of improving the quality of education. This is primarily due to insufficient implementation or lack of mechanisms for adaptation to the individual parameters of the student. The level of adaptation in modern e-learning systems to the individual characteristics of the student makes the organization of human-computer interaction relevant. As the solution of the problem, a mathematical model of the organization of human-computer interaction was proposed in this work. It is based on the principle of two-level adaptation that determines the choice of the most comfortable module for studying at the first level. The formation of an individual learning path is performed at the second level. The problem of choosing an e-module is solved using a fuzzy logic. The problem of forming a learning path is reduced to the problem of linear programming. The input data are the characteristics of the quality of student activity in the education system. Based on the proposed model the computer technology to support student activities in modular e-learning systems is developed. This technology allows increasing the level of student’s cognitive comfort and optimizing the learning time. The most important benefit of the proposed approach is to increase the average score and increase student satisfaction with learning.

Cite This Paper

Nataliia Barchenko, Volodymyr Tolbatov, Tetiana Lavryk, Viktor Obodiak, Igor Shelehov, Andrii Tolbatov, Sergiy Gnatyuk, Olena Tolbatova, "Mathematical Model for Adaptive Technology in E-learning Systems", International Journal of Modern Education and Computer Science(IJMECS), Vol.14, No.4, pp. 1-15, 2022. DOI:10.5815/ijmecs.2022.04.01


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