Modeling of Trajectories of Obtaining and Assimilation of Knowledge

Original article

DOI: 10.15293/1812-9463.2203.02

Antonina Valerianovna Ganicheva

Tver State Agricultural Academy, Tver, Russia

Alexey Valerianovich Ganichev

Tver State Technical University, Tver, Russia

AbstractThe article discusses new, visual, rather simple from a computational point of view, methods for calculating the individual trajectories of trainees. Indicators characterizing the effectiveness of the learning process are introduced: the volume and pace of knowledge acquisition, the student’s abilities. These indicators can be used to form individual educational trajectories. Econometric models have been constructed for these indicators. It is shown how to build models using dummy variables. Based on such models, it is possible to assess the presence of structural changes in the educational process. The aim of the study is to develop indicators that characterize the formation of individual educational trajectories of students and the construction of econometric models of regression dependences of these indicators on a factor sign (number of study hours). The models developed in the article can be used to monitor the educational process with the possibility of its adjustment, management, as well as to predict its effectiveness. These indicators can be used to form individual educational trajectories.

Keywordslearning process, amount of knowledge, learning trajectory, econometric model, dummy variables, subject learning performance, learnerʼs abilities.

For citation: Ganicheva A. V., Ganichev A. V. Modeling of Trajectories of Obtaining and Assimilation of Knowledge. Journal of Pedagogical Innovations, 2022, no. 3 (67), pp. 16–24. (In Russ.) DOI:



1. Barmatina I. V., Varakuta A. A. Assessment of the quality of educational activity of the university and training of students. Journal of Pedagogical Innovations, 2020, no. 4, pp. 15–22. (In Russian).

2. Bayuk O. V., Lozikova I. O. Ontological approach to the development of the knowledge base of the decision support system for choosing an individual educational trajectory. South-Siberian Scientific Bulletin, 2021, no. 5 (39), pp. 29–34. (In Russian).

3. Borisova E. Qualitative modeling of the education system. The Scientific Heritage, 2020, no. 51-3 (51), pp. 10–16. (In Russian).

4. Ganicheva A. V. The model of quality management of curricula. Quality. Innovation. Education, 2012, no. 4 (83), pp. 37–41. (In Russian).

5. Hasanova R. R. The problem of personal trajectories of additional education of teachers. Vocational education in the modern world, 2021, no. 11 (3), pp. 88–101.
(In Russian) DOI:

6. Herzen S. M. Individual educational trajectory and interactive technologies in distance learning [Electronic resource]. World of Science. Pedagogy and Psychology, 2020, no. 4. URL: (date of access: 15.04.2022).
(In Russian)

7. Zhuravleva N. N., Luferenko A. M., Tarasova I. V. Modeling of the internal education quality assessment system as an educational organization management tool. Journal of pedagogical innovations, 2020, no. 3, pp. 5–11. (In Russian)

8. Iblyaminova M. R. Definition of the content of the concept of “individual educational trajectoryˮ by the method of content analysis. News of Saratov University. New series. Series: Acmeology of education. Psychology of development, 2019, vol. 8, issue 4,
pp. 368–373. (In Russian)

9. Kravchenko A. M. Mathematical formulation of the task of searching for an individual learning trajectory. Big data in education: collection of articles on the results of the international conference (Moscow, August 29–31, 2020). Moscow: Ekon-Inform Publ., 2020, pp. 28–36. (In Russian)

10. Larionova G. A. Designing trajectories of professional development of university students in courses of mathematical and natural science disciplines. Bulletin of the Voronezh State University. Series: Problems of higher education, 2017, no. 1, pp. 71–75. (In Russian)

11. Shatalova A. O. An approach to designing an individual trajectory of a studentʼs education at a higher school. Science of man: humanitarian studies, 2020. vol. 15, issue 1, pp. 103–108. (In Russian) DOI:

12. Shemanaeva M. A. On the interpretations of the term “individual educational trajectoryˮ [Electronic resource]. Scientific and methodological electronic journal “Conceptˮ, 2017, no. S12, pp. 43–47. URL: (date of access: 15.04.2022). (In Russian)

13. de Melo G., Machado A. Educational trajectories. Evidence from Uruguay. International Journal of Educational Research, 2022, vol. 92 (1), pp. 110–134. DOI:

14. Frolova E., Rogach O., Ryabova T. Digitalization of Education in Modern Scientific Discourse: New Trends and Risks Analysis. European Journal of Contemporary Education, 2020, vol. 9 (2). pp. 313–336. DOI:

15. Gasanova R. R. The problem of studying individual educational trajectories in additional education of teachers. Professional education in the modern world, 2020,
vol. 10 (3), pp. 4053–4063. DOI:

16. Krasnopeeva T. O., Shevchenko A. I., Romanova I. V. How to create individual educational trajectories in the informational educational environment. SHS Web of Conferences, 2020, vol. 87. DOI:

17. Pallas A. M. Educational Transitions, Trajectories, and Pathways. Handbook of the Life Course, 2003, pp. 165–184. DOI:

18. Parnikova G., Antsupova S. Individual Educational Trajectories in Higher Education Institution- Global Challenges for Regions. International Journal of Educational Research, 2018, vol. 2, pp. 110–134. DOI:

19. Spahn A. Digital objects, digital subjects and digital societies: deontology in the age of digitalization. Information, 2020, vol. 11 (4), pp. 228. DOI:

Information about the Authors

Antonina V. Ganicheva – Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Physical and Mathematical Disciplines and Information Technologies,,

Alexey V. Ganichev – Associate Professor of the Department of Computer Science and Applied Mathematics,