The relevance of the study is due to the contradiction between the mass transition of the Russian system of higher education to the distance learning format and the insufficient willingness of participants in the educational process to work under the new requirements caused by the COVID 19 pandemic. Teachers, students and administrators of higher educational institutions in Russia have encountered a number of difficulties. Their analysis will highlight the objective and subjective factors of their occurrence and develop recommendations for the further organization of distance learning in its combination with the traditional format. The purpose of the study was to analyze the modern work experience in the remote format of one of the leading Russian universities – Kazan Federal University. On this basis, the article analyzes successes and problems of this process, shows the contradictions between traditional and distance learning, considers the main models of educational organization that involve traditional and remote learning formats using distance educational technologies. It is concluded that in the system of basic formal education at all levels and areas of training, distance learning can be considered as a form that complements and strengthens the social, pedagogical, organizational, psychological, and didactic potential of the traditional (face-to-face) educational format.The work comprehensively used the methods of theoretical (analysis, synthesis, systematization, comparison, etc.) and empirical (study of literature, conversation, questioning, observation) research.

The lack of sufficiently developed methodological basis before graduation adversely affects the mathematical competency of future experts that are required by the modern economy. The study aims to investigate the features of the development of a personalized model of teaching mathematics by means of interactive novels to improve the quality of educational results. The main methods of research were the generalization of pedagogical experience and science literature, modelling, observation, analysis of results in AXMA Story Research methods. The chosen methods made it possible to justify the necessity of using interactive novels to personalize teaching mathematics and to confirm the qualitative improvements in the pedagogical system. Fisher's criterion was used to evaluate the results. 121 schoolchildren from Russian and Uzbek schools participated in the experiment. Individual educational routes supporting the studying of mathematical theory, problem solving in the interactive space AXMA Story Maker were developed. The peculiarities to be considered when designing a personalized model of mathematics learning by means of interactive novelties were formulated. These are the correlation between the didactic goal and the result of educational and research work in a nonlinear environment, the selection of the plot for a visual novel, the elaboration of the text component and the personalized learning track, etc. According to ANCOVA test results, the post-score of the experimental group is statistically higher than the control group. The results of the article can be used to develop ideas for personalising of learning in the digital school, as well as justification for the need for inclusion of digital interactive tools in mathematics education at all levels of education and training.

In accordance with the requirements of the Federal State Educational Standard of Higher Education ++, the graduates of the master’s programme on “Teacher education” must be ready to solve research problems in their professional field. This implies that the students develop an appropriate methodological culture through their involvement in independent project and research activities. However, the analysis of the current state of practice in training master students in the field of education demonstrates that it is still dominated by teaching technologies that focus on performing and reproduction activities of students, contributing to developing the habit of receiving ready-to-use knowledge. As a result, the contradiction between the objective need for the formation of a methodological culture among students on the one hand, and inadequate development in many students in the field of “Teacher education”, on the other, is aggravated. The research aim was to show and substantiate the didactic conditions for project- and researchbased learning as a technology aimed at the efficient development of master students’ methodological culture. Research methods were theoretical (analysis, synthesis, comparison, generalization and etc.), empirical (educational experiment, testing in order to assess the level of research competence formation), and mathematical methods of data processing. Results: The process of master students' methodological culture development is based on a search for information and implementation of didactic activities and conditions that serve as a motivation tool for students to be a part of research activities. The course on “Methodology and methods of educational research” becomes a platform for methodological culture development among master students on the “Teacher education” programme. The efficiency of students’ methodological culture development is increased if: (a) the structure and content of their methodological culture are designed on the basis of convergence of conventional and research-based approaches and (b) the project-and research-based teaching technology is implemented through a short-term (limited by the course duration) projects and a number of variable components (a combination of individual and team forms of independent activities),“inverted” or “blended” learning techniques; interdisciplinary, problematic and interactive training; reflection at the end of each class; exams in the form of a project defense, etc.). Impact: The results will be useful for development of educational and methodological support for research-oriented teaching in the process of theoretical and practical training of future bachelors, masters, graduate students, as well as in the system of additional and vocational education.

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Science motivation scale is a valid and reliable tool used to determine students' motivation in learning science courses. In the study, science learning motivations of students studying at Kazakhstan and Russian Universities were compared. In addition, it was also examined whether the science motivation scores of the students changed according to the demographic variables. The science motivation scale was used as a measurement tool. For statistical analysis, t-test and ANOVA from Bayesian statistics were used. As a results, the data supported the students' motivation levels a) at a high level, where they differed from the countries they studied at b) at a moderate level, where they did not differ by gender c) at a moderate level, where there was a difference in the total score according to the age group, d) at a moderate level, where there was no differentiation by departments.

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There is a contradiction in the system of pedagogical education between on the one hand, the objective demand for research-oriented training as a mean of forming research competence among graduates of pedagogical magistracy, and on the other, their lack of readiness for the design and implementation of research-oriented training due to the lack of development in didactics goals, principles, forms, methods and means of designing such training. This study aims to develop and justify the methodology of research-oriented training in the pedagogical education system. We hypothesized that the effectiveness of research-based learning will increase if the process of its design and implementation is based on a system of knowledge about the methodology of training and the essential features of research-based learning. The study had three objectives: 1) to identify the essence and content of the concept of "methodology of training"; 2) to show the main characteristics of research-oriented training in the pedagogical education system; 3) experimental testing of the methodology of research-oriented training of undergraduates in the pedagogical education. The research methods included the theoretical analysis of scientific and pedagogical literature on the problem, generalization, transfer, abstraction, modeling, empirical testing through pedagogical experiment, and methods of mathematical processing of empirical data. The research shows that research-oriented learning in the modern pedagogical education system is formed as an independent didactic system, which has grown on the basis of the theory of problem learning and is aimed at the formation of students' research competence. The methodology of research-oriented training in the pedagogical education system is the doctrine of the organization of research activities of students, including a system of knowledge about its logical (features, forms, methods, tools) and time structure (phases, stages, stages). implementation of research-oriented training in accordance with the methodology proposed in the study contributes to the effective development of undergraduates' research competence of "pedagogical education. The study can inform researchers in the field of pedagogy and teachers of higher education, and to improve the development of students' research competence, as well as teachers in secondary schools.