No 1 (2025)

The article considers the problem of using the algorithm of educational mathematical modeling in teaching primary and high school students to solve text problems as a tool of the scientific method. It is shown that despite the requirements for the results of mastering educational cognitive, logical and research activities, primary and high school students have difficulty solving text problems, demonstrate a low level of skills to analyze the condition of the problem, create a mathematical model, and find a reasonable answer using the studied mathematical methods. The results of comparing the algorithm of the scientific method of solving research problems and the algorithm of educational mathematical modeling in solving text problems are presented. In the course, it is proved that these algorithms correlate, i.e. educational mathematical modeling is a tool of the scientific method in solving text problems by students. It also provides a detailed description of the student's universal learning actions at each stage of the learning mathematical modeling algorithm when solving a text problem. An example of solving a typical text problem for movement using this method is given. At the end of the article, the results of a study conducted by the authors within the framework of events for teachers and students of primary and high schools, during which an algorithm of educational mathematical modeling was used when students solved text problems.

The development of information technology is one of the important factors in the development of a social society. The main task of education and science is the formation of a student's personality for further professional activity in modern society. The use of media in teaching mathematics performs several functions, realizing informational, educational, educational and entertaining aspects. However, there is not enough research in the scientific literature on the problem of media literacy formation in mathematics lessons. This article analyzes the historical aspects of the development of media education in Russian and international contexts; highlights the main stages of the development of media education in general; examines various ways of using media educational components in mathematics lessons. The study showed that the success of introducing new technologies into the educational process directly depends on government policy and the informatization of society.

The article presents the results of diagnostics of future mathematics teachers, analyzes the problems of subject and methodological training of students: poor preparation of applicants, especially in geometry; difficulties in applying theoretical knowledge to solving problems of increased complexity, which are mastered in senior years; do not know the methods of criterial assessment of students' written work, etc. The main directions for eliminating professional deficiencies of the future mathematics teacher in the context of a digital society are proposed: implementation of individual educational routes for students with increased attention to the consideration of types of problems, techniques and methods for solving them; creation of a methodological piggy bank of complex mathematical problems; use of didactic capabilities of generative artificial intelligence; high-quality formation of mental images, schemes and models of the academic discipline. Some didactic capabilities of generative artificial intelligence are considered, which can be used in the preparation of a future mathematics teacher in order to eliminate professional deficiencies. Artificial intelligence can be used in the preparation of future mathematics teachers as a working tool in the formats of adaptive and personalized learning. The format of personalized learning serves as an effective tool for improving the performance of future mathematics teachers based on timely support for feedback and communication of all participants in educational processes, automation of the main types of educational activities. Examples of methodological tasks for future mathematics teachers, completed as part of the study of methodological disciplines, are given.

The digital transformation of higher education is an important process that affects all aspects of the educational environment. The introduction of digital technologies, including Python programming, is becoming a key factor in the teaching of mathematical disciplines. Today, there is a need to find new teaching practices in integration with digital technologies in order to develop the necessary competences in students, especially in the field of mathematical disciplines. In this regard, the use of Python as a tool for modelling and data analysis opens new horizons for the development of new training courses, deepening subject knowledge in practice, improving research activities, innovativeness of the educational process in general. The application of Python for modelling probabilistic problems contributes to the development of new approaches to solving complex problems in various fields of science and technology. Research Methods. The basis for solving probabilistic problems on the example of studying random variables is the use of Python programming language libraries: NumPy and SciPy. Results. The program of the course within the framework of an optional discipline for students of training direction 44.03.05 Pedagogical Education (with two profiles of training), orientation (profile) Mathematics and Computer Science, Physics, demonstrating ways of modelling probabilistic problems in the study of random variables using Python is proposed. The relevance of integrating programming into the curriculum of mathematical disciplines is determined by the need of modern information society. The digital transformation of higher education, leading to the application of Python in mathematical disciplines, is a significant direction for both science and practice. This approach improves the quality of education, prepares students for the challenges of the modern world, providing them with useful skills for successful professional activity.

In the context of reforming the higher education system in the Russian Federation, the issues of meeting certain requirements and provisions of regulatory and legal acts related to digitalization and informatization of the learning process and accounting for its results are of particular relevance. In order to improve the quality of students education, various automation systems and educational management systems are currently being intensively implemented in educational institutions of the Russian Federation. The analysis of open sources of information conducted by the authors team has shown that cases of falsification of educational documents in order to mislead employers about the actual formation of certain competencies of an employee of the company are still possible. The reason for this problem is that universities often keep records of learning outcomes «on paper» without using computerization tools, which does not exclude the possibility of re-registration of students credit lists and credit books retroactively. The article describes the developed demonstration prototype of an automated system for recording the results of intermediate certification of students in a higher education institution. In order to avoid making changes to accounting documents, the development of the prototype used the capabilities of blockchain technology, which has proven to be effective in preserving the integrity of user data. In addition, based on the experience of implementing other automation systems, requirements were formed for the system of accounting for the results of intermediate certification of students in higher education institutions. The use of the developed system will increase the complexity of entering data into the system retroactively to an unacceptable level, or this possibility will be excluded altogether.

April 3, 2025 is the 100th anniversary of the birth of the Russian mathematician, a prominent specialist in the field of multidimensional differential geometry, a talented organizer of educational and scientific processes in the work of the mathematical department of a technical university, a participant of the Great Patriotic War, Doctor of Physical and Mathematical Sciences, Professor Georgy Ionovich Kruchkovich (1925-1985). For 20 years the scientist headed the Department of Higher Mathematics: the All-Union Correspondence Energy Institute (VZEI) for two years (June 1965 - June 1967), which was later renamed the Moscow Institute of Radio Engineering, Electronics and Automation (MIREA), for 18 years (June 1967 - July 1985). He is the author and co-author of textbooks, which were used and recognized as the best by students of correspondence, evening and full-time departments of technical universities of the Soviet period. But these books have not lost their relevance to this day. The name of the scientist is very rarely mentioned in studies of historical and mathematical character. The purpose of this article is to eliminate this injustice. The article provides little-known information from the biography of G.I. Kruchkovich, reconstructs his scientific and methodical achievements, describes his public, educational and organizational work as head of the Department of Higher Mathematics, as well as his scientific and pedagogical heritage.