Vol 27, No 3 (2025)

The presented article describes visualization as a method of activating cognitive activity of students in the process of studying mathematics. The article examines the essence of the concept of "visibility", defines the effectiveness of visibility as a means of teaching mathematics. The relevance of the research lies in the fact that currently the problem of using clarity remains important in the process of teaching mathematics at the university. The formation of spatial-figurative thinking among students has become a priority area of mathematical training. This method allows you to use the reserves of visual thinking of students, promotes the development of mental operations, helps to develop the ability to model processes and phenomena of the surrounding reality. Pedagogical experiments have confirmed an increase in academic performance and an improvement in exam performance when using demonstration techniques. The study showed that the clarity in the presentation of mathematical theories significantly affects the quality of learning the discipline. In addition, the use of visual technologies in solving professionally oriented tasks contributes to the acquisition of experience in applying mathematical methods and models in economic research. The approbation and implementation of the research results was carried out by conducting practical classes in mathematics at the Volga State University of Railways (PrivGUPS) for students of economic fields and specialties.

This study examines the problems of developing the competence of teachers of primary, general secondary and higher education in the diagnosis of hidden forms of extremism in the educational environment. The use of the author's methodology allowed to state the insufficient level of teachers' preparedness to solve problems related to the identification of hidden forms of extremism among students. The experiment showed that 37.5% of teachers had a low, 59.5% had an average, and only 3.0% had a high level of competence at the entrance test. After the educational conversation, the results of solving quasi–professional tasks (22% – low, 72% – medium, 6% - high) showed a positive trend in teachers' ability to recognize markers of hidden forms of extremist ideology in the educational environment. The proposed author's methodology for diagnosing teachers' competence in recognizing the hidden ideology of extremism among students can also be used to train students – future teachers in order to develop competencies related to monitoring the ideological stability of Russia's state interests and psychological and pedagogical strategies for fostering patriotism among students. The conclusion is made about the need for further research on the prevention of extremism in the educational environment for all age groups of students.

One of the effective forms of organization of research activities of students of transport universities in the field of transportation optimization is the establishment of a student scientific circle (SNK), organically integrated into the structure of the university's student scientific society. This work considers a specific mechanism for the formation of research competencies of students on the example of choosing the optimal method of cargo transportation, which is a complex, critical task. As material for the study, the results of solving the assignment problem for the model of distribution of cargo transportation of one transport problem are taken in several ways. This approach allowed students to conclude that various methods were rational, which gave the study practical focus and specificity. The theoretical importance of the work lies in the fact that in the course of finding solutions to the problem, not only the research skills of students are developed, but also the competencies necessary for further professional activity. The participation of students in scientific circles provides them with the opportunity to gain practical experience in working on relevant scientific and professional projects, which greatly facilitates their integration into the future professional environment. Thus, the activities of the SNK are aimed at the formation of competitive specialists in this field.

Environmental education plays an integrative role in the entire education system at different stages. It performs a variety of pedagogical functions, including promoting the formation and development of a unified picture of the world in the minds of learners (students and schoolchildren); is an essential component of the humanization of education at all levels; forms general skills to predict one's own activities and the activities of others; expands the possibilities of moral education in the learning process; promotes the development of patriotism. The foundation of the environmental consciousness of each person, especially at the time of personality formation, is natural science knowledge, which forms a balanced, competent, scientifically based understanding of the surrounding world and a reasonable attitude to the phenomena and processes occurring in nature. Additional education in the natural sciences, aimed at developing the relevant competencies in children and young people, has a significantly greater variability in the activity of forming the environmental culture and consciousness of students and schoolchildren. Participation of schoolchildren and students in the implementation of various social and environmental projects, campaigns, competitions forms the acquisition of knowledge, value systems in the activity, allows them to become patriots of their homeland. The Regional Ecostation (Samara Regional Children's Ecological and Biological Center, Samara) has been implementing various bioecological events and campaigns for children and young people for many years. The teachers of the ecostation have developed and are holding the ECO-Monitor competition, which has now reached the all-Russian level. The competition has been held for four years, showing the interest of the participants and good coverage of participants. An increase in the number of applications was noted in all competition nominations. In 2021 and 2022, applications from primary school children prevailed, who are most often more active as participants. However, in 2023, the results of the competition showed a noticeable increase in the number of participants in the middle and older age groups, including students. Feedback from the participants of the competition shows interest in it from different age groups, both schoolchildren and 1st and 2nd year students. The competition allows you to realize your potential in the course of performing project and scientific work in accordance with the nominations of the competition - ECO-view, ECO-perspective, ECO-team, ECO-mentor. Most of the students presented various projects that are relevant, novel, scientifically and practically oriented.

This study reflects an analysis of the use of information and communication technologies (ICT) in the higher education system based on the experience of Bryansk State University named after Academician I.G. Petrovsky (BSU). The relevance of the research lies in the fact that the role of information technology in all spheres of life is increasing, and therefore there is a need to transform the HE system, which will be aimed at the effective use of ICT to improve the quality of education, develop students' professional competencies and ensure their competitiveness. The purpose of the study is to identify problems and prospects related to the use of ICT at BSU, and to develop practical recommendations for improving the effectiveness of digitalization of education at this university. The article analyzes the current state of the use of ICT in BSU, identifies strengths and weaknesses, as well as factors affecting the effectiveness of the introduction of digital technologies. Based on this, ways to solve the identified problems are proposed and prospects for further development of ICT in the BSU HE system are determined. The necessity of using high-quality electronic educational resources and creating a favorable environment for the introduction of innovative educational technologies is emphasized. In conclusion, it is concluded that the effective use of ICT can significantly improve the quality of higher education at BSU and contribute to the training of competitive specialists.

A.P. Chekhov's childhood and adolescence were associated with carrying out "church-parish obedience" in the choir of the writer's father. What he saw and heard during this time was long remembered by A.P. Chekhov. This was reflected in his work. Numerous quotes from the Holy Scriptures and biblical reminiscences are abundantly present in the prose of the Russian classic. In his stories there are many images of clergy - from bishops to deacons. The young deacon Pobedov, a character in Chekhov's "Duel", appears as a man with common sense. Funny and sometimes naive, he turns out to be able to convey Christ's teaching about love for one's neighbor to his older acquaintances - Laevsky and von Koren - and plays a decisive role during their duel. With a cry of "He will kill him!" The deacon makes von Koren miss, saving the duelists' lives and giving hope for a change in their souls. Against the background of a duel, a confrontation between the two main characters, deacon Pobedov acts as the "third", who gives the right direction to life and helps to avoid mistakes. The image of the deacon, who descended from the church pulpit onto the Caucasian landscape, complements the author's narrative and invites the reader to draw independent conclusions.

In the cultural process, a stable and functionally balanced structural order can only be formed under conditions of coordinated diversity, that is, a proper relationship between traditions and innovations. If traditions displace innovations, this state can be likened to a structural emptiness with the inherent homogeneity and total community of the collective unconscious. If innovations displace traditions, everything becomes excessively changeable and blurred, and the cultural order is shaken. Symbols and rituals reconcile the traditional and the innovative, prepare society to accept new trends to expand the boundaries of culture. But if the confrontation between traditions and innovations in culture drags on and is not resolved, the disintegration of values ​​and the breakdown of familiar foundations begins, and unstructured relations run rampant. The opposite relationship also takes place. Innovation prepares the ground for ritual. But if the ritualization of social drama does not begin, then culture becomes a victim of external expansion or the internal collapsing development of society. Unlike traditions, which are characterized by increased staticity and immobility, innovations that have not yet had time to take root in culture are highly adaptable and maneuverable. They show a large number of connections, conjugations and mediations. However, all of them are predominantly unstable, amorphous, transient in nature, since at the stage of innovations, elements of culture are not yet firmly attached to its root system. In this regard, the objective world of ancient cultures can clarify a lot, especially in the situation of changing life cycles of culture, which is most fully and expressively represented in the symbolic practices of complex (potestary) societies, and in particular, in various accessories of the funeral rite. This article shows the forms and mechanisms of interaction between traditions and innovations in the cultural process of a changing society using the example of artifacts of the proto-Bactrian pre-urban civilization.

The work of the young director Kira Kovalenko attracts with the author's careful attitude to the languages ​​of the peoples inhabiting Russia. In the film, the actors speak Ossetian. It is worth noting the originality of the film director's view of the drama of a girl who survived the seizure of a school in Beslan by terrorists. The film "Unclenching Fists" was awarded the "Un Certain Regard" award at the Cannes Film Festival. The fate of a girl in the modern world is part of the idiostyle of Kira Kovalenko. The value of family relationships, where elders take care of children, children are obedient and respond to the care of their parents, understand and accept their will, rarely arouses the interest of filmmakers. At the center of the narrative are the broken destinies of film heroes, where in an incomplete family, the obedience of children is based on fear of their father, who is crushed by an event that brought grief to his family. He cannot unclench his fists with which he tries to protect his children, and does not let them out of his care. The children grow up, try to prove to their father that they are capable of living independently, but the fear of the head of the family that he can lose the most precious thing - children - does not give him peace. He transmits his love through prohibitions, strict control and unwillingness to see that children suffer. His task is not to unclench his fists, not to let the children go away from him, to keep them constantly in sight in order to come to the rescue at any moment. The daughter has the hardest time in the family, who needs special attention, after the explosion at school she became disabled, she needs an operation. The cinematic cultural value of this film is that it is connected with the leading theme of Russian cinema - fathers and children - and transmits the view of contemporaries on the events associated with the consequences of terrorism in Russia.