Abstract: The subject of the research is the practice of applying educational materials created with the help of artificial intelligence in teaching the imperative mood of the Russian language as a foreign language (RFL), specifically the forms of the third person, considering the previously studied forms of the first and second persons. The focus is on the didactic functions of AI resources: mind maps, interactive games, digital avatars, and the "Syuésitun" educational platform, as well as their integration into the lesson according to the BOPPPS model. The methodological line "visualized introduction – game practice – quasi-real communication – platform expansion" is considered. The perception of cognitive support, gamification, contextual communication, and digital homework by students is analyzed. A particular emphasis is placed on the contradiction between the effectiveness of the digital format and attention concentration, as well as the limitations of AI materials. Thus, the subject covers methodological, cognitive, and organizational aspects of integrating artificial intelligence into grammar education in RFL. The research was conducted based on the "Basic Russian language II" course with the participation of 15 Chinese students. The lesson was designed according to the BOPPPS model using an AI mind map, interactive games, a digital avatar, and the "Syuésitun" educational platform. Empirical data were obtained through an open questionnaire survey and processed using qualitative content analysis. The scientific novelty of the research lies in the fact that at the micro level of an individual classroom session, a reproducible model of systemic integration of AI resources into teaching the imperative mood of RFL has been proposed and tested. Differentiated didactic functions of AI materials have been delineated: the mind map serves as a cognitive bridge, interactive games ensure gamification of practice, the digital avatar creates quasi-real communication, and the "Syuésitun" educational platform expands extracurricular learning. The BOPPPS model is supplemented by a circular composition of the lesson. The empirical research revealed a contradiction of "effectiveness – concentration": digital assignments are convenient and provide immediate feedback, but about 40% of students prefer traditional written tasks due to better attention concentration and motor memory. It is concluded that AI resources increase interest, lower the threshold of understanding, and expand the boundaries of learning, but do not replace the teacher. Limitations include insufficient elaboration of grammatical nuances, managing attention in the digital environment, and high time expenditures for the teaching staff. It is recommended to combine digital and written formats.

Keywords: educational resources, imperative mood, teaching grammar, BOPPPS model, digital educational environment, feedback, AI in education, digital avatar, interactive games, attention management

Abstract: The subject of this study is the conditions and means by which a methodological system for teaching mathematics generates a personalized content framework for engineering students, achieved through the integration of invariant and variable components at each vertex of the system's graph. The object of the research is the mathematics education of future engineers in the context of mass training. The author examines various aspects of the topic in detail, including the invariant framework of the methodological system defined by a five-vertex graph schema, the distinction between personalization and its related concepts of differentiation and individualization, as well as the necessity for a coordinated restructuring of the content of all components of the methodological system for each individual student. Special attention is given to the properties that the graph of the methodological system must acquire and to the differentiation of the functions of machine learning and neural network technologies in aligning the graphs of the subject area, the student, and the teacher. The research methodology is based on the concept of a mathematical teaching methodological system, employing systematic, activity-based, and competency-based approaches, along with graph theory, machine learning theories, and neural network technologies. Techniques utilized include system analysis, comparative analysis and generalization of educational system models and curricular content, graph modeling, and pedagogical design of the system architecture. This study is primarily theoretical in nature. The novelty of the research lies in the justification for the necessity of graph representation in the methodological system: by emphasizing the principle of personalized mathematics education, the system graph enhances the manageability of content across its components, reveals each vertex as a subgraph, and aligns the system with the graphs of the subject area, the student, and the teacher. A significant contribution of the author to the research topic is the differentiation of the functions of intelligent tools. Machine learning serves as a means for forming the student's graph vertices based on learning analytics and variable goal content, while large language models provide consultative support to learners and generate personalized methodological materials within scenarios defined by the teacher's graph. The main conclusions of the conducted research indicate that the methodological system for personalized mathematics education develops, rather than replaces, the classical five-component system. The personalized content is formulated through the alignment of three graph models, with artificial intelligence technologies operating within the boundaries established by the teacher. Future research will focus on the development of the student and teacher graphs and the experimental verification of the system.

Keywords: methodical system, teaching mathematics, personified learning, graph modelling, machine learning, neural networks, artificial intelligence, learning analytics, language models, future engineers

Abstract: Based on an analysis of policy documents, scholarly literature, and representative practical cases, this article examines the evolutionary trajectory of digital education in China since the beginning of the 21st century. The study demonstrates that the policy focus has undergone a structural shift following the scheme “infrastructure — platform hub — systemic transformation,” while the research focus has moved from the question of “how to ensure connectivity” to questions of “how to govern” and “how to reconfigure the ecosystem.” The practices of the Beijing Institute of Technology, Chongqing Jiaotong University, Zhejiang University, and Changzhou Institute of Industry Technology indicate that the unit of analysis in digital education has risen from the level of paired relations “technology — user” to the level of the ecosystem “technology — institutions — practice.” The main problem is that early studies tended to fall into the linear hypothesis of “technological determinism”; at present, challenges remain, such as the transparency of platform algorithms and data boundaries, the institutional alignment of teacher transformation, and the correspondence between industry-education integration data and the logic of the industry. On this basis, the article advances the proposition that research logic is undergoing three successive turns: from the “application of technologies” to the “reconfiguration of the ecosystem,” from monodisciplinarity to multilevel mixed methods, and from “catch-up interpretation” to “independent construction.” In the future, it is necessary to strengthen empirical research, interdisciplinary methodology, and the construction of autonomous theoretical identifiers. The findings are relevant for educational policy and for research methodology in the field of digital education, and they suggest that further work should combine large-scale empirical evidence with conceptual frameworks capable of capturing the institutional and practical dimensions of digital transformation.

Keywords: digital education, higher education, teaching model, innovative learning models, innovative practices, the role of the teacher, teachers’ digital literacy, industry and education, artificial intelligence, digital transformation