Foreign Affairs of the Russian Federation, RussiaIn this article, the urgent problem of control systems modeling of professional competences and knowledge assessment of students is discussed. Pedagogical expediency in management of students' cognitive activity by using of new informational technologies instruments in monitoring and assessment of knowledge is proved. The possibility of fractal methods application in perfecting of the system of computer monitoring of students' knowledge of as a part of the adaptive training systems is considered and realized. The design of the technology of computer monitoring of students' knowledge on the basis of fractal methods includes the following stages: development of cross-disciplinary fractal and organized base of key concepts; the creation of the expansible bank of educational and cognitive research tasks, which is coordinated with fractal structure of the conceptual framework; the development of the program module, which is focused on individual estimation of quality of students' educational cognitive activity in two characteristics-depth of knowledge based on the Hurst exponent and the size of synergetic effect of educational cognitive activity. The software realization of technology of the computerized control of training in disciplines quality as a part of the adaptive training system is enabled in the programming language C#. The experience of implementation and operation of the controlling systems realized in the adaptive training systems based on the fractal model operation showed reliability of their work and allowed to increase the quality of educational process management and its effectiveness in general. Using of fractal techniques in computer assessment of students' knowledge makes it possible to increase the accuracy and speed of evaluation of the students' knowledge to diagnose a wide range of cross-disciplinary knowledge within one discipline.

Abstract

The relevance of this study is due to the practical significance of the issues of using game mechanisms in the process of teaching mathematics, the lack of research into the issues of symbiosis of game and didactic technologies in mastering complex mathematical knowledge, the need to search for effective technologies to establish how they affect the development of students and the formation of a modern style of thinking. The analysis of global trends and practices of introducing elements of gamification into the education system has shown that the mastering of complex knowledge and patterns of mathematical activity, the solution of problem areas of mathematics at different levels of learning and complexity is carried out by a complex of mathematical and information methods without the integration of game elements. It has been substantiated that gaming technologies in combination with the informatization of mathematical activity give a powerful motivational charge to the study of mathematics, actualize the processes of self-organization of cognitive activity, and contribute to the development of a probabilistic style of thinking. The purpose of the study is to provide a theoretical substantiation and effective methodological support for the process of professional development of mathematics teachers in the context of gamification in mathematics study with the effect of developing a probabilistic style of thinking. The authors have developed an arrangement mechanism and determined the content of scientific and methodological support for teachers working in the constituent entities of the Russian Federation to provide additional educational services in the context of gamification in education. The developed materials, in particular, include evaluative case tests for identifying competence deficiencies in teachers, which ensure the formation of a probabilistic style of thinking based on gamification processes by managing the information saturation of the motivational field of learning. In addition, the authors proposed an additional professional education program for teachers, Mathematics in Gaming Activities (Business, Didactic and Intellectual Games) , and developed new forms of certification and assessment materials (gamification-based didactic solutions and effective practices). Using the concept of gamification, it was possible to demonstrate the activation of cognitive and motivational structures, in particular, the effective development of a probabilistic style of thinking in the process of mastering complex mathematical knowledge through its adaptation to school mathematics. The results of the study allow making it possible to bring the process of teaching students and developing their personalities to a modern qualitative level using current achievements in the field of digitalized education.

No abstract

The study actualized the complex and large-scale problem of adapting the theory of risk man-agement for the education system. A comprehensive analysis of domestic and international stud-ies revealed the lack of a theoretical framework, a general methodological vision of the problem of riskiness and risk-taking in the educational sphere. While effective management of education-al activities, ensuring the development of the competitiveness of the individual in the labor mar-ket and its potential for active participation in the life of society is possible on the basis of the modern paradigm of risk management, integrating achievements in pedagogical, economic, mathematical and computer sciences. A new methodology in the study is the fractal approach, which defines the idea of quantitative and qualitative analysis and assessment of the risk of non-formation of professional competencies, complex educational and cognitive constructs of subject activity. The fractal model of assessing the formation of knowledge and competencies, its risk landscape, taking into account the subject and cognitive divergence, will ensure the effective-ness of the structure of knowledge storage in the educational process, minimizing the time for building space and engineering knowledge bases, and the depth of solving the problem of pre-dicting educational risks. New methods of risk modeling based on machine learning algorithms and factor analysis, methods for constructing neural integrators, quantitative methods with and without taking into account the probability distribution will ensure the accuracy and speed of risk assessment and prediction, will allow one to identify new patterns of risk activity and further ways to develop the theory of risk. The presented effective strategies and innovative tools will solve the problem of minimizing unplanned chaos, the cascade of negative consequences of risky situations, including the COVID-19 epidemic.