Purpose of research. The purpose of the article is to substantiate the development of an integrated model of pedagogy and engineering in the educational space of the school. The relevance of the research at the socio-pedagogical level is related to the solution of key tasks of the state and the need of society for the training of engineering personnel, tools’ design for the development of scientific and technical creativity and research potential of schoolchildren, stimulating their motivation for engineering professions and the field of high technology. At the scientific and methodological level, the relevance of the research is determined by the need to develop and implement innovative teaching methods related to the synthesis of various academic subjects of the humanitarian cycle in conjunction with technical disciplines.

Materials and methods of research. To achieve this goal, an integrated approach to the analysis of integration processes in education is used. This approach is provided by a system of research methods: descriptive and analytical (analysis of sources on the research topic; generalization of psychological and pedagogical literature; interpretation of data), contextual analysis (identification of the meaning and function of a concept in a situational environment, surrounded by and interrelation with other elements) and empirical method (observation, study of products of activity, analysis of documentation).

The model of integration of pedagogy and engineering through modification of the content, forms, and technologies of educational activity helps to overcome the fragmentation of knowledge, establish deep connections between subjects, and allows participants of the educational process to accumulate technological and humanitarian knowledge, develop value orientations and cultural field of personality. 

Results. The essence of the integration of pedagogy and engineering in the educational space of a secondary school is revealed. Using the example of the activities of the educational institution “Integration” of the city of Tomsk, the organizational and pedagogical conditions for the development and design of a new educational reality, actualizing the design of an effective model for the integration of pedagogy and engineering in the educational space of the school, are described. New forms of training using modern educational technologies are presented: from organizing spectacular, technically challenging competitions in robotics, teaching skills in designing, developing and operating unmanned aircraft systems (UAS) to methodological cases for training cultural leaders from among teachers and schoolchildren. The stages and phases of substantiating the concept of an integrative model based on a system analysis that ensures the feasibility of the model and the correlation of results are described in detail. Criteria and performance indexes of the model have been developed to ensure control and reliability of the results.

Conclusion. The application of the model of integration of pedagogy and engineering contributes to the formation of a motivating educational environment for professional and personal growth, development and self-realization of students and teachers. The implementation of interdisciplinary connections in the process of developing integrative training programs that include the latest technical achievements in dialogue with socio-humanitarian knowledge is relevant not only for schools, but also for universities, vocational secondary education, enterprises as a factor of continuity. It is advisable to extend the model of integration of pedagogy and engineering to educational organizations across Russia.

The purpose of research. This study aims to identify new approaches to the formation of digital competencies of university graduates in the digital era. The relevance of this study is based on the requirements of the modern labor market for qualified specialists with skills in the digital environment, in multitasking conditions, able to constantly improve their level of qualification and digital literacy, which in turn serves as a guarantee of the development and competitiveness of the socio-economic complex of all regions of the country. This study shows that in the modern period, the educational process in higher education institutions (universities) should be based on the constant interaction of graduating departments with representatives of the practical sphere, considering all innovative developments of the socio-economic complex of individual regions and the country as a whole. In addition, this study confirms the relevance of the fact that in the modern period, digital competencies instilled in university graduates contribute to the implementation of modern tasks of ensuring the technological leadership of the country.
Materials and methods. In the course of conducting the research and presenting its results in the form of this article, a whole range of methods was used, such as studying and analyzing scientific sources, comparison, generalization, classification. Special methods of working with electronic libraries and platforms, web services and Internet sources were also used.
Results. This article proves that digital competencies in the modern period are one of the main components in the training of highly qualified specialists. Digital competencies allow graduates of various fields of education to implement individual development trajectories and immediately after graduation to take high-paying positions at competitive enterprises in various regions of the country. This paper identified a number of factors that determine the need for intensive training in digital competencies. These include high speeds of information transfer, the need to analyze data using statistical, mathematical and systems analysis, multitasking and the ability to work with modern software products and digital devices. In addition, digital competencies of university graduates in the digital era consider the entire range of employers’ requests, which in turn contributes to an increase in the level of competitiveness of industries and sectors of the economy and the successful implementation of strategies for the country’s socio-economic development.
Conclusion. This paper analyzes scientific approaches to the study of digital competencies, considers modern models and frameworks of digital competencies (digital skills), and classifies them. In addition, economic, social, administrative, technological and educational effects of increasing the level of regional development based on the development of digital competencies of university graduates are identified. The author has proven that digital competencies contribute to the fulfillment of strategic tasks for the training of highly qualified personnel and ensuring technological independence and technological leadership of the Russian Federation. 

Purpose of research. The study is aimed at developing and justifying a four-level classification of digital competencies for education workers for instructional design of online courses based on a smart approach that ensures flexibility, adaptability, variability and technological effectiveness of professional training in the context of implementing state policy of digital sovereignty and technological independence of the Russian Federation. The relevance of the study is determined by the need to develop competencies for educational personnel to work with domestic digital platforms and software solutions in the context of import substitution strategy for educational technologies.
Materials and methods. The methodological basis of the study is the integration of taxonomic, competency-based and contextual approaches with smart education principles. The research is based on analysis of professional standards requirements and qualification characteristics of pedagogical workers in information and communication technologies. Theoretical analysis included studying modern approaches to digital competency classification considering the specifics of the Russian educational system and principles of technological vertical of educational processes. Systematization of subject-activity areas of digital competencies was carried out based on principles of hierarchy, contextuality, operationality, proactivity and spirality. Research methods included structural-functional analysis of competencies, typology by distribution pattern between levels, operationalization through specific measurable actions. Classification development was conducted using systematic approach to educational technology design and considering requirements of state policy of digital sovereignty in education.
Results. Theoretical results include: development of hierarchical classification of digital competencies including general user, general professional, subject-professional and supra-professional levels; introduction of original typology of competencies by distribution pattern between levels into cross-cutting, semi-cross-cutting and complementary; definition of classification construction principles ensuring systematic integration of different levels of professional training. Practical results include: structuring subject-activity areas for each level with detailing of specific professional actions; systematization of general user level in seven areas from file operations to information security; defining content of general professional level in six areas from instructional design to educational analytics; structuring subject-professional level by nine disciplinary areas; development of supra-professional level content in three areas of strategic planning, research activities and technological entrepreneurship with indication of key competencies for each area.
Conclusion. The created model provides a scientific and methodological basis for designing personalized educational trajectories in the system of continuous professional development of educational personnel. Typology of competencies according to the principle of inter-level distribution creates conditions for flexible formation of individual programs for mastering digital technologies, considering professional needs and initial level of training. Operationalization of competencies through measurable actions allows for objective diagnostics of professional deficits and planning of targeted corrective work in conditions of using domestic software and digital platforms. 

The research purpose. Professionally important personal qualities of an IT specialist are valued in the labor market on a par with professional competencies, therefore, in the process of studying at a university, it is important to keep their development in focus. The purpose of the performed research is to substantiate, implement in a digital learning environment, and test in the educational process a technological way of monitoring the development of professionally important qualities of IT students in close connection with the development of their professional competencies. The article presents a detailed analysis of the results of experimental training, which allowed the authors to identify correlation dependencies within the selected set of professionally important qualities and assess the impact of their development level on the results of mastering professional competencies, as well as to track the dynamics of the development of students' personal qualities during the learning process. 

Methods and materials. Based on the analysis of various sources, including the requirements of the labor market, the authors identified and systematized a set of professionally important qualities of an IT graduate that can be developed during the learning process. The architecture of the educational environment and the logical model of the data warehouse are presented, which allow accumulating the results of students' learning and development in a form convenient for analysis. The implementation of monitoring of interrelated processes of competence acquisition and development of professionally important qualities in the presented educational environment  are described. A correlation analysis of learning and development results were performed, which made it possible to identify and evaluate the dependencies between the individual components of the unified IT training process at the university with the use Pearson coefficients.

Results. The article presents an example of the implementation of the proposed method for monitoring the development of professionally important qualities in the bachelor's degree program 09.03.04 “Software Engineering”. As a result of the correlation analysis of the outcome of experimental training, the basic set of professionally important qualities of an IT graduate was clarified, its non-redundancy and the close connection of each of the identified qualities with professional competencies were proved (using the example of one of the general professional competencies, for which three specialized disciplines are responsible). The experiment also revealed a positive trend in the development of professionally important qualities in the learning process, however, it should be noted that this process is slow and uneven.

Conclusion. The results of the study confirm the relevance of the statement about the importance of professionally important qualities in the competence model of an IT graduate. The proposed basic set of personal qualities and a way to monitor their development can be extended to various areas of training for IT specialists. The continuation of this research has good prospects for organizing the process of purposeful development of professionally important qualities in the learning process, as well as for building individual educational trajectories that take into account personal qualities of a particular student. In general, this will lead to an increase in the effectiveness of the educational process and have a positive impact on the quality of training of IT specialists at the university.

The aim of this paper is to develop a methodology for teaching mathematics at universities that makes extensive use of modern digital and information technologies. The relevance of developing a new methodology for teaching higher mathematics at universities is driven by several factors. Firstly, it is necessary to increase students’ motivation for studying at university by explicitly demonstrating the connection between abstract mathematical knowledge and real-world physical and technical processes. Secondly, it is necessary to develop students’ skill in consciously using artificial intelligence to gain new knowledge, rather than mindlessly obtaining ready-made solutions. Thirdly, it is necessary to make applied mathematical software packages a working tool for solving mathematical, physical, and technical problems.

Methods. To improve student academic performance and motivate them to study complex disciplines such as mathematics and computer science, it is proposed to consider the possibilities of the educational approach: mathematics, computer science, and engineering. This approach involves the extensive use of modern software tools for studying higher mathematics, physics, and other general professional disciplines. Mathematics, computer science, and engineering enable the transition from solving complex abstract mathematical problems “on paper” to the use of modern mathematical software packages not only for analytical but also for numerical solutions of differential equations, as well as numerical integration. Essentially, computer science becomes a tool for studying mathematics.

Results. This article presents a methodology for implementing the educational approach: mathematics, computer science, and engineering in higher mathematics classes at universities. Three case studies are presented demonstrating solutions to standard problems in mathematical analysis and mathematical statistics using mathematical software packages and programming skills. An example of an analytical and numerical solution to a Cauchy problem using the Smath Studio mathematical package is considered. The same mathematical package was used to solve an integration problem analytically and numerically (Monte Carlo method). The possibility of using the Python programming language to write applications for statistical data processing is demonstrated. The formulation of the problems allows students to independently choose the solution method for the given problem.

Conclusion. This educational approach, discussed in this article, enables the widespread use of modern information and digital technologies for the study of higher mathematics at universities. This approach increases students’ interest in the subjects they study and develops skills in using the Python programming language and the Smath Studio software package for the analytical and numerical solution of complex mathematical problems.