Annotation: Based on the psychological aspect of the concept of "qualification", the article analyzes the main directions of the formation of methodological qualifications of future teachers of mathematics and advanced training in pedagogical universities. It is possible to achieve high-quality teaching of geometric subjects in higher educational institutions by using methodological and meaningful methods in organizing the educational process. The creation of a certain structure of the educational process, the definition of teaching methods and means, the careful selection of subject content were determined by the specific principles of pedagogy. Basically, these principles are the real achievements of modern pedagogy and are constantly changing. The existing system of didactic principles can be gradually changed and expanded The purpose is to choose the main didactic principles and to offer a scientific-methodological basis for improving the methodological preparation of future mathematics teachers in the Pedagogical University for solving and teaching geometrical problems. In this regard, interviews, questionnaires, analysis of the curriculum and its content, as well as discussions with experienced teachers and methodologists in teaching geometry were conducted; pedagogical control and diagnostics of the educational process were carried out. In order to test the effectiveness of the methods proposed by us, pedagogical experiments were carried out. The entire system of training future teachers of mathematics faces new challenges related to the implementation of effective didactic principles for teaching geometry in pedagogical universities. First of all, it is the principle of mastering innovative teaching methods of the future teacher of mathematics and the principle of mastering new pedagogical and information technologies of education. The results of the study can be used as a methodological basis for further research on the professional orientation of teaching mathematics in universities.

Annotation: Das Hauptproblem: die allgegenwärtige Einführung von Informationstechnologien führt zu erheblichen Veränderungen in verschiedenen Bereichen der menschlichen Tätigkeit. Auch der Bildungsbereich ist keine Ausnahme. In diesem Zusammenhang hat der Autor in diesem Artikel ein aktuelles Problem behandelt, das in der Entwicklung elektronischer Lehrmittel liegt und eine der aktuellen und vielversprechenden Richtungen der Informatisierung des Bildungsprozesses ist. Es wurden die Arbeiten von Wissenschaftlern S.S. Sysoeva, V.M. Kuharenko, A.I. Bashmakova, T.I. Koval, E.S. Polat, A.Y. Uvarova, P.I. Serdjukow, A.A. Andreev analysiert. Diese Arbeiten enthalten Anforderungen an die Entwicklung elektronischer Lehrmittel. Nach der Analyse beschrieb der Autor die Entwicklungsschritte von elektronischen Lernprogrammen, die Prinzipien, denen sie entsprechen sollten, und führte eine Liste der Module an, aus denen das elektronische Lernprogramm bestehen sollte. Aus der vorhandenen Vielfalt an Softwarekomplexen hebt der Autor CourseLab, Smart Builder, MOS Solo, Google Sites, iSpring Suite, TurboSite, Adobe Animate, HTML5 hervor. Die Entwicklung von elektronischen Lehrmitteln für die vom Autor des Artikels vorgestellte Technologie und deren anschließende Anwendung im Bildungsprozess wird dazu beitragen, die Lehr- und kognitive Aktivität der Lernenden auf einem effizienteren Niveau zu organisieren. Zweck: beschreibung der Technologie zur Entwicklung von elektronischen Lernprogrammen unter Berücksichtigung bestehender Anforderungen. Methoden: der Artikel verwendete Methoden zur Analyse, Synthese und Abzug. Die Analyse der Anforderungen und Prinzipien für die Entwicklung elektronischer Lernprogramme basiert auf einer deskriptiven und analytischen Methode. Ergebnisse und ihre Bedeutung: das praktische Ergebnis der vorgeschlagenen Technologie war das entwickelte elektronische Lernprogramm «Entwicklung mobiler Anwendungen». Die Ergebnisse der Studie haben neben der theoretischen Bedeutung auch eine praktische Bedeutung, die in einer positiven Dynamik liegt, um den Widerspruch zwischen dem ständig wachsenden Informationsfluss und der begrenzten Fähigkeit der Lernenden, ihn zu erlernen, zu lösen. Die bewusste Verwendung elektronischer Lehrmittel im Lernprozess ist eine grundlegende Möglichkeit, die Bildungsqualität zu verbessern, indem die verwendeten Unterrichtsmethoden und -techniken in Richtung Individualisierung und Fokussierung auf den Lernenden geändert werden.

Annotation: The concept of resilience, the ability to withstand crises and adversities and recover from them, has valuable potential for research, intervention and preventive approaches aimed at strengthening the family. There are many paths to relationship resilience, varying depending on different forms of family, psychosocial problems, resources and constraints. Shared beliefs that promote alignment and cooperation are vital to overcoming adversity. Measures to increase the resilience of families are of timely importance to overcome the rapid social changes and uncertainties that families face today. According to research by sociologists and family consultants, each family goes through several stages of development, and the transition from one to another is usually accompanied by a crisis. It is generally believed that domestic difficulties lead to complications in family life, first of all. The purpose is to identify the types of problems and causes leading to crisis situations in marriage. In this regard, the methods such as analysis of literary sources on this topic, generalization, synthesis, psychological experiment, diagnosis of the psychology of family crisis by H.I. Olioirovia, T.A. Zinkevii-Kuzemkin, T.F. Velenta were used. The authors of the article come to the conclusion that stress is a part of life, and the slings and arrows of misfortune hit all families throughout their lives. The concept of family resilience confirms the reparative potential of all families and offers a valuable basis for research and clinical practice. Just as families face a variety of challenges, there are many ways to increase family resilience. By understanding key processes, clinicians can mobilize untapped resources, allowing families in distress to cope with difficulties more effectively and recover through their mutual support and cooperation. Therefore, it is necessary to understand the patterns of crisis situations and the socio-psychological causes of their occurrence.

Annotation: The article highlights the problem of coping behavior of students in stressful situations of the educational process. Purpose of the article - determination of the dominant productive and non-productive strategies of coping behavior among undergraduate students. While doing research the following methods were used: Coping with Stress Questionnaire (COPE) by K. Carver, M. Scheier and J. Weintraub, adapted by E.I. Rasskazova, T.O. Gordeeva and E.N. Aspen. Fourth-year students show significant variability in the choice of methods of coping behavior. This means they have a wider range of coping strategies. At the same time, first-year students do not have a diverse enough range of coping strategies. This may be due to their less experience and unfamiliarity with various coping techniques. Significant differences were found in the activity of using the effective strategy “Finding a solution to a problem” among students at different stages of training. This suggests that fourth-year students are more prone to problem-oriented coping, while first-year students prefer emotionally oriented coping with exam stress. As a result of the study, it was determined that the most common methods of coping behavior among students are the strategies “Accepting responsibility” and “Planning a solution to the problem.” This means that most students prefer active and mindful approaches to coping with difficulties. It has been proven that the relationship between methods of coping behavior and anxiety of students is different in all courses of study. This may be due to varying levels of experience, degree of curriculum difficulty, and other factors that influence perception and coping with stressful situations. These results highlight the importance of developing a variety of coping strategies in first-year students, as well as the need to support and train fourth-year students in using effective coping strategies.

Annotation: Discovering the intellectual and professional abilities of special children, first of all, depends on the language environment created by teachers. In this regard, the task is to create an effective pedagogical paradigm of thinking and activity (concepts, categories, concepts), ensuring its constant updating. Purpose of the research is revealing the intellectual and professional abilities of special children. The main research methods are ascending from the abstract to the concrete, descending from the concrete to the abstract, from the concrete to the abstract and again to the concrete, from the abstract to the concrete and again to the abstract and method of working with text. Between 80 and 85 % of incoming information is perceived by the human visual organs, and our brain performs several functions. The main function is speculation, i.e. in understanding the essence, knowledge embedded in information. For example, a person can observe a rainbow, without understanding or knowing its nature. Only speculatively can he cognize the essence, i.e. a certain law, a scheme for the origin of this unusual phenomenon. Thus, knowledge is a product of a person’s own thinking, extracted from information.

Annotation: Main problem: the issue of self-actualisation of schoolchildren is one of the most urgent problems of pedagogical science, aimed at investigating and comprehending the contradictory processes of development, training and education of schoolchildren’s personality in modern socio-cultural conditions. Thus, one of the tasks of the secondary school and the teacher is to create optimal conditions for the development of adolescents’ personality abilities for self-realisation. Purpose: is to reveal the optimal pedagogical conditions that promote the process of development of teenagers’ personality abilities to self-realization. Methods: the task of the research cintains the study and experimental verification of a certain set of conditions which contribute to the self-realisation of students in the process of fine arts lessons at a comprehensive school. Results and their significance: organizational forms of conducting classes for the formation of abilities to creative self-actualisation are defined. It is shown that the most important pedagogical conditions for the self-realization of the teenagers’ personality are the combination of individual and collective organization of learning at the fine arts lessons and the wide use of the problem-based method of teaching.

Annotation: The main problem: the current directions of its development are determined in the article by conducting a theoretical analysis of philosophical, pedagogical, psychological, scientific and methodical works on the training of specialists for the development of the cognitive activity of teenagers. Currently, it is shown that the training of specialists in the development of cognitive activity of teenagers is a pedagogical and psychological problem. Purpose: to clarify the theory and propose a technology for the training of pedagogical and psychological specialists for the development of the cognitive activity of adolescents. Methods: When conducting the research, it was important to take into account statistical data that were sufficiently understandable and reliable. Therefore, in the framework of our research, we used the methodology of B. E. Milman, survey, method of expert evaluation, conversation, questionnaire, interview, series of tests, which include observation and open questions. The results and their significance: according to the results, the methodological predominance of the average level of social intelligence allowed students to see the following signs: the social significance of professional behavior, actions, relationships, full mastery of theoretical knowledge. During the course, we believe that the existence of a reflexive culture, which is evidenced by the improvement of communication in everyday life, in turn, is very valuable. Development of thinking, training and education of future teachers-psychologists, preparation for creative activity depend on methodological competence, qualifications and training of the teacher in the organization of research activities. Self-learning needs and skills do not arise by themselves. Such qualities begin to be formed in the process of organizing educational activities during the joint work of teachers and students in and out of class, even during school. In accordance with the tasks of the professional training of the future pedagogue-psychologist, active methods of training - problem-based lectures, seminars, debates and discussions, professional-oriented special courses, course and diploma works, scientific studies of school pedagogy and didactics, educational events such as scientifically organized forms of continuous pedagogical practice. As a result of mastering pedagogical activity, professional motivation of future pedagogical-psychological specialists is formed, understanding of goals and tasks, subject, psychological-pedagogical and didactic-methodical knowledge is developed, as well as relevant skills and abilities necessary for the development of cognitive activity of teenagers.

Annotation: Main problem: the article raises the question of the need to create innovative methods and models of functional-system thinking and pedagogical cultivation of students' intellectual abilities to improve the quality of education. Emphasis is placed on the development of reflexive, schematic, organizational and communication abilities. Purpose: to provide an overview of the basic theoretical concepts

Annotation: Main problem: The article highlights the problem of tests as methods of psychology, the influence of validity and reliability on the results of psychological research. Purpose: Uncovering the significance of validity and reliability on psychological research results. Results and their significance: Testing is an important method in psychology, allowing measuring various aspects of the psyche and behavior of a person. The history of the development of tests in psychology goes back more than a century and began with the work of Francis Galton and Alfred Binet. Over time, the tests have become widely used in various fields such as education, personnel selection, clinical diagnosis and research. Basic requirements for tests include reliability (repeatability of results), validity (measurement accuracy), standardization (same test conditions) and objectivity (lack of subjectivity in assessment). Tests must be designed using psychometric principles to ensure accuracy and validity of results. Modern tests include a variety of measurement techniques, such as tests of personality, intelligence, aptitude, and professional skills. The use of tests in psychology requires professional training to correctly interpret the results and make valid conclusions. Testing as a method of psychology continues to evolve, and its role remains key in the study of the human psyche and behavior. Testing in psychology has a wide range of applications, including assessing personality traits, identifying psychological disorders, and predicting behavior and success in various areas of life. The development of computer-based tests and online platforms makes testing more efficient and convenient for researchers and participants. Modern tests increasingly take into account cultural differences and the diversity of individual characteristics, which contributes to more accurate and tailored assessments. It is important to remember that the use of tests requires ethics, confidentiality and compliance to ensure the reliability and validity of the data obtained.