Purpose of the study. This article analyzes the contribution of network human capital to economic dynamics and innovation through econometric modeling based on data for 70 countries for 2020–2021. The main goal of the study is to analyze the relationship between network human capital, economic development and innovation activity.

Materials and methods. The present study is based on feedback methodology. On the one hand, the development of human capital is a strategic factor in sustainable economic development. On the other hand, economic resources that increase under development conditions are invested in human capital. The authors have developed a two-stage method for assessing the contribution of network human capital to economic dynamics and the development of innovation. At the first stage, the influence of human capital on the factors of innovative development, assessed by the indexes of the Global Innovation Index (GII), was assessed. At the second stage, an assessment of the contribution of these factors to GDP per employee was modeled. The method was implemented through the development of econometric models that allow assessing the contributions of network human capital to economic dynamics based on the profile of the national economy and assessing the dependence of GDP per employee on the employment structure of the national economy.

Results. Based on the results of econometric modeling, the impact of human capital accumulation on the innovative development of the economy was assessed. Statistically significant relationships between: an increase in human capital and the acceleration of the pace of development of new technologies and the knowledge economy; development of creative activity; increasing innovative ties have been identified and substantiated. Based on the modeling results, we empirically assessed, firstly, the contribution of network human capital to GDP per employee; secondly, the increasing contribution of new industries to GDP per employee and the decreasing contribution of traditional industries (using the example of agriculture); thirdly, the more significant contribution of those employed in IT compared to the contribution of those employed in education and healthcare to GDP per employee.

Conclusion. The results of the modeling proved that network human capital influences economic growth and innovative development through two mechanisms. Firstly, network human capital is directly involved in the production processes of the platform economy as a factor of production. In this sense, the accumulation of network human capital directly increases aggregate output. Secondly, the accumulation of network human capital has a positive effect on classical factors of production and, in particular, contributes to technological progress.

The purpose of the study. The problem of using the capabilities of artificial intelligence and immersive technologies in educational programs is being updated. The article is devoted to the analysis of the role, functions and significance of artificial intelligence and immersive learning technologies in the development of an open educational environment and its personal segments formed by subjects of educational relations in the process of preparing graduates of pedagogical universities to change the conditions of modern society. The possibilities of Generative Pretrained Transformers (GPT) and virtual reality in its various manifestations (AR, VR, AVR) are discussed. Their influence on the formation of the personal educational environment of graduates of pedagogical universities is shown.

Materials and methods. The method of comparative analysis of scientific publications in the field of artificial intelligence development, immersive learning technologies, and the formation of a personal educational environment is used. The capabilities of a number of GPT services have been experimentally tested. The ideas about the role and functions of new resources in improving the educational process are summarized. The forecast of the integration of artificial intelligence and immersive technologies in pedagogical education is given.

The results of the study. It is shown that Generative Pretrained Transformers are able to implement reference and encyclopedic, constructive and creative, analytical, control and training functions in the educational process while observing the ethics of their application. The connection between the development of artificial intelligence and the appearance in the global information network of virtual characters imitating human appearance and behavior in various contexts, and anthropomorphic robots capable of communicating with humans for educational purposes is indicated. Attention is drawn to the inclusion of new means of communication with artificial intelligence in the personal educational environment of the lecturer, which provides him/her with a combination of the functions of a supplier and at the same time a consumer of knowledge. The prospects of the emergence of virtual and anthropomorphic pedagogical agents with artificial intelligence in the education system and in informal communications are assessed. The educational possibilities of augmented reality, virtual reality and augmented virtual reality as means of immersive learning technologies are defined. The pedagogical and technological conditions for the safe use of immersive learning technologies are given. It is noted that the creation of personal educational environments with components of artificial intelligence and immersive technologies makes it possible to organize the processes of teaching and self-education of a lecturer, ensuring the subjective nature of his/her personal and professional growth and mobility in a complicated world.

Conclusion. The conclusion is made that the creativity of innovative lecturers, which is visible in their open educational environments, is a resource for overcoming the reproductive nature of the functioning of pre-trained neural networks. The authors believe that positive feedback in the joint evolution of artificial intelligence (AI) tools and personal segments of the open educational space will contribute to the transformation of the existing information society into a learning society. This makes it possible to form a system of open meta-education according to the needs of each individual.

Purpose. The purpose of the article is to substantiate the application of a collective method of teaching in computer science classes in the system of secondary vocational education, contributing to an increase in the level of cognitive activity of students.

Research methodology. The idea of the study is related to the implementation of collective learning methods in computer science classes to increase the level of cognitive activity of students. The use of collective learning methods in computer science classes is considered from three positions: organizational, methodological and diagnostic. The organizational aspect includes the conditions for the formation of student groups and scenarios of their interaction in the learning process. The methodological aspect is related to the selection and preparation of special educational and methodological support, including teaching methods. The diagnostic aspect provides an assessment of the effectiveness of learning the educational material, the level of cognitive activity and the state of the psychological atmosphere in the classroom. The measurement of the level of cognitive activity is carried out with the help of a simplified three-dimensional diagnostic method by O. Markelova. The observation of changes in the psychological atmosphere in the classroom is carried out by the method of pedagogical observation.

Results. Based on the adaptation of the principles and advantages of collective learning methods (according to V. Dyachenko) to the tasks of the secondary vocational education system, the conditions for the formation of student groups and scenarios of their interaction in the process of teaching computer science were outlined. A training cycle has been proposed for the implementation of a collective method of teaching in computer science classes and a collection of digital educational resources has been compiled. Diagnostic tools have been adapted to identify the level of cognitive activity in computer science classes. The diagnosis of the level of cognitive activity and the effectiveness of learning material in computer science classes was carried out, as well as the psychological atmosphere in computer science classes was analyzed.

Conclusions. The use of collective teaching methods in computer science classes in the secondary vocational education system helps to increase the level of cognitive activity of students and, as a result, provides a comfortable psychological atmosphere in the classroom and increases the effectiveness of learning material.

In this article, the author presents the methodology of organizing and conducting distance Olympiads in Korean as a second foreign language in the process of professional training of foreign language teachers.

The purpose of the study is to examine specifics of second foreign language distance Olympiads organization in the context of professional training, main objectives of the Korean language Olympiad (increasing motivation, interest in learning Korean, exposure to Korean culture, etc.), and to analyze the main requirements for distance Olympiad tasks of the first round (tests), and tasks of the second round, which are aimed to identify the level of communication abilities. Interview, testing and observation are used as the main methods of research.

Results. The methodology proposed by the author was tested in groups of 3–4 year students of Sarsen Amanzholov East Kazakhstan University (educational program 6B01703 foreign language: two foreign languages). The article presents analysis of the distance Olympiad’s results, examples of tasks for each round and the main criteria for evaluating the tasks. The requirements to the second foreign language Olympiad tasks implied: possibility of mass coverage of students with Olympiad tasks; compliance of the tasks with the curriculum; time limit; relying on the students’ experience, including their native language skills and abilities; increasing tasks complexity; variety of tasks forms and content, the tasks contents and novelty; problem nature tasks to stimulate students thinking, language guess; using authentic material for the Olympiad tasks; the use of local history and extralinguistic material. The general complexity of the tasks, and difficulties associated with the nature of the linguistic material were also taken into account.

Conclusion. According to the results of the experimental work, the author comes to the following conclusion: the leading principle of organizing distance Olympiads assumes that the university faculty will be focused on the timely identification of the future teachers’ interest to the Korean language, their involvement in preparation for the Olympiad, thus forming their interest in Korean culture and language. Olympiad assignments should be creative so that students learn to find their own ways of solving problems and develop self-education skills. Participation in the Olympiad increases students’ learning motivation, broadens their horizons, and develops their ability to express their opinions. The variety of requirements to the work of participants makes the assessment of each member of the jury quite subjective, but the collective nature of the evaluation procedure ensures correctness and objectivity of the final decision, allows participants to familiarize with the results of their work and consider appeals after each round of the Olympiad participants.

The purpose of the study. Modern teaching tools and methods, as a rule, implicitly rely on the “black box” model. In contrast, the “white box” model has clear didactic advantages. Unfortunately, they are difficult to implement in the educational process due to the lack of available ways to construct this model. The purpose of the study is to develop a technology for constructing a “white box” model in the form of a structural and mental scheme of calculation tasks in the field of elementary physics. This technology involves the use of calculation primitives to design task schemes by superposition.

Materials and methods. Development of technology for constructing the “white box” model in the form of a structural and mental scheme of calculation tasks in the field of elementary physics. The use of calculation primitives to construct task schemes by superposition. Determining the complexity of a specific task through the number of primitives involved in the “route” of the solution. Organization of students’ training according to the “white box” model with visualization of the process of forming skills to solve calculation tasks.

Results. Schemes have the ability to ensure the strength and completeness of the formation of the ability to solve problems of the student. At the same time, the variety of routes and the set of weights of the paths make up the information model of learning. As an example, structural and mental schemes on the topic “thermal phenomena” are presented. They show the need to use several types of primitives, in particular, function primitives, sum primitives. Structural and mental schemes allow students to organize training according to the “white box” model, visualize the process of formation and development of students’ skills to solve calculation tasks, thereby ensuring control and self-control of educational activities.

Conclusion. Based on the provisions of the mental approach, a technology for constructing structural and mental schemes representing a cognitive way of thinking in solving computational problems is proposed. The basic technology is computational primitives, with the help of which problem schemes are constructed by superposition. The complexity of a particular task is determined by the number of primitives involved in the “route” of the solution. The proposed technology is applicable to the construction of structural and mental schemes of computational problems in various subject areas.

Purpose. Modeling systems and programming platforms provide ample opportunities for the use of statistical tools in research activities. Since the normal distribution is one of the most common distribution laws, the criterion for checking the sample for normality is in high demand among statistical assessment tools, among which the Epps-Pulley test has the status as one of the most powerful tests to check the deviation of the distribution from the normal one. There are a number of implementations of this test in the R and Python languages. However, this test is not implemented in one of the most popular Matlab modeling software. Thus, the purpose of this study is to develop a software implementation of the Epps-Pulley criterion in the Matlab environment and verify the correctness of the performed calculations.

Materials and Methods. We implemented the calculation of Epps-Pulley statistics by two methods – classical, using cycles, and matrix-vector, using linear algebra operations. The classical method requires calculating the intermediate values necessary to obtain the criterion statistics using two independent cycles, the second cycle being a double one, in which one cycle is nested into the other. The matrix-vector method requires fewer code by performing calculations using linear algebra operations on matrices and vectors. We obtained critical statistical values for the sample size from 8 to 1000 observations with two-dimensional linear interpolation of tabular values. We used an approximation by a beta function of the third kind for a sample of over 1000 elements.

Results. An assessment of the computational efficiency of the methods showed that the cyclic approach is about three times higher than the matrix-vector approach in terms of consumed time, which is presumably due to the processing of insignificant elements in triangular matrices when performing component-by-component operations. The correctness of the software implementation of the Epps-Pulley criterion was tested on several examples, which confirmed the compliance of the calculated values of the criterion statistics, as well as the critical values of statistics, with known data. We carried out a criterion statistical evaluation based on the empirical values of the error of the first kind. We obtained the error values correspondence to the specified significance levels. We performed comparative estimates of the Epps-Pulley test with the Anders-Darling and Shapiro-Wilk tests in terms of the criterion empirical power and tabulated the evaluation results. We published the software implementation of the Epps-Pulley test on the MATLAB Central Internet resource and for free use.

Conclusion. We developed software implementation of the Epps-Pulley criterion as a new research tool that was previously unavailable in the Matlab modeling environment. We used the time spent on calculations to make a reasonable choice of the calculation algorithm for the criterion statistics. We confirmed correctness of the calculation algorithms by a set of selective checks and statistical estimates that showed the compliance with well-known theoretical provisions.