Vector-stochastic description of a joint portrait of a teacher and a student

Abstract: One of the most important problems in the organization of an effective educational process is the problem of matching the qualities of teachers and students. The relevance of solving this problem is determined by the growth of the volume and complexity of educational material, as well as the introduction of digital technologies into the educational process. Digital technologies allow us to formally describe the characteristics of the personalities of teachers and students who have the greatest influence on the educational process. These properties of personalities form their portraits. The purpose of the article is a vector-stochastic description of a joint portrait of a teacher and a student. To achieve this goal, the apparatus of formal grammars is used. It is proposed to associate a vector of a point assessment with each student and each teacher. The vector evaluation is presented in the form of deducible chains of a formal language in a probabilistic grammar. The corresponding output tree is built. The output tree is considered as a network of a special type – an information graph. Matrices describing the graph are constructed (the adjacency matrix and the matrix of the sum of adjacency matrices in different degrees). The resulting graph describes the information system. It is shown how to calculate the probabilities of finding the system in each level. To explain the developed method, a specific numerical example of calculating the system parameters is considered. The criterion of the dynamic unity of the portraits of the teacher and the student is formulated. The result of the research is the developed new method of mathematical description of the joint portrait of a teacher and a student. The developed method can be used in models of digitalization of education and similar areas.

1. Antsiferova A. G. Interaction of a teacher and a student as a factor of influence on the personal and professional growth of a student. Electronic scientific and methodological journal of the Omsk State Agrarian University. 2016;3(6):23.

2. Zagorodnyuk A. N. Psychological and pedagogical portrait of a modern university teacher. Kant. 2018;4(29):26-30.

3. Tatarina T. M. Portrait of a competent (ideal) teacher: the point of view of students and teachers (based on the material of the language department of a non-linguistic university). Samara Scientific Bulletin. 2020;9(2 (31)):290-293. DOI: 10.17816/snv202314.

4. Bulatova D. S., Kazbekova A. A., Liberman Ya. L. A modern student of a technical university: elements of a psychological portrait. Pedagogical education in Russia. 2016;4:87-92.

5. Kovalsky R. M. Impression management: a literature review and two-component model. Psychological bulletin. 2013;107(1):46-58.

6. Göncz L. Teacher personality: a review of psychological researchand guidelines for a more comprehensive theory in educational psychology, Open Review ofEducational Research. 2017;4(1):75-95. DOI: 10.1080/23265507.2017.1339572.

7. Romanov D. K, Dauksha L. M. Psychological aspects of perception and inderstanding of teachers by university students. Integratsiya obrazovaniya. Integration of Education. 2016;2(20):228-237. DOI: 10.15507/1991-9468.083.020.201602.228-237.

8. Murphy N. A., Hall J. A., Colvin C. R. Accurate intelligence assessments in social interaction: Mediators and gender effects. Journal of Personality. 2013;71(3):465-493. DOI: 10.1111/1467-6494.7103008

9. Ganicheva A.V. Evaluation of psychological and pedagogical portraits of teachers and trainees. Economic and humanitarian studies of the regions. 2018;5:30-33.

10. Ganicheva A.V., Ganichev A.V. Model of matching portraits of teachers and trainees. Modeling, optimization and information technologies. 2020;8(3(30)):16-17. DOI: 10.26102/2310-6018/2020.30.3.009.

11. Ganicheva A.V., Ganichev A.V. Coordination of portraits of teachers and trainees (Materials of the IV International Scientific Conference "Informatization of education and methods of e-learning: digital technologies in education". In two parts, Krasnoyarsk, October 06-09, 2020. Collection of scientific papers). Krasnoyarsk: Siberian Federal University, 2020:78-82.

12. Makarova L. N., Startsev M. V. Problem areas of interaction between teachers and students. Socio-economic phenomena and processes. 2017;12(5):210-216.