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List of publications on a keyword: «learning»

  • DIGITAL CONTENT IN SECONDARY VOCATIONAL EDUCATION: DESIGN, INTEGRATION, AND QUALITY CRITERIA

    Book Chapter
    Digital content in the secondary vocational education system: design, integration, and quality criteria
    Author:
    Larisa N. Tsymbaliuk
    Work direction:
    Все направления
    Abstract:
    This monograph addresses the current problem of designing, integrating, and assessing the quality of digital content in the system of secondary vocational education. Based on a comprehensive analysis of the regulatory framework, domestic and foreign experience, as well as an empirical study conducted at the Polytechnic College of Yaroslav the Wise Novgorod State University, the key contradictions and systemic barriers hindering the effective use of digital educational technologies are identified. The work presents the author's developed network model of trajectory-based design for the digital educational environment. Its fundamental novelty lies in the transition from the paradigm of platform "filling" to the meaningful construction of educational trajectories based on a personalized database of tools and content. The model ensures a holistic approach to integration through four interconnected components: normative-target, content-didactic, technological-organizational, and assessment-
    Keywords:
    e-learning, digital educational environment, digital tools, digital content, secondary vocational education, instructional design, distance learning courses, integration of digital content, network design model, quality of a digital course, digital didactics of vocational education

  • Network-based organization of training for future journalists in the context of connectivism theory: a theoretical analysis

    Proceeding
    Sormovo Readings - 2026: vectors of education development: practices, quality, prospects
    Author:
    Elena S. Doroschuk
    Work direction:
    Цифровая трансформация и обновление содержания образования
    Abstract:
    The article discusses the features of organizing the training of future journalists at a higher school in a network format. Based on the principles of connectivism, the author describes and models the features of the network format in the structure of professional education for media workers. The integration characteristics of the network format allow it to be included in the system of practice-oriented disciplines and courses, bringing the process of creating media products closer to real practice through interaction in a network format between educational entities.
    Keywords:
    journalist, media system, network learning, connectivism, network community
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  • «Особенности применения цифровых образовательных ресурсов в начальных классах»

    Proceeding
    Relevant problems of modern science and education
    Authors:
    Valeriia A. Baraniukova, Natalia O. Gordeeva
    Work direction:
    Влияние цифровизации, искусственного интеллекта, социальных сетей на все сферы жизни человека
    Abstract:
    The advantages of using DER, such as the activation of perception, the increase of motivation and the individualization of learning, are considered. At the same time, the potential risks associated with the dependence on external stimuli, the deterioration of concentration and the negative impact on the physical health of children are outlined. A list of key recommendations for the effective implementation of DER in the educational process is given, aimed at maintaining a balance between traditional teaching methods and modern digital tools.
    Keywords:
    motivation, information technologies, pedagogy, interactive methods, elementary school, psychophysiology, individual differences, Digital educational resources (DER), visual-figurative thinking, concentration of attention, optimal use, protection of vision, improvement of learning, effective learning strategies
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  • Development of creative abilities among senior schoolchildren using intellectual games in the classroom

    Proceeding
    The development of modern education in the context of educational competence
    Authors:
    Alina A. Diachenko, Oksana N. Tikhonova
    Work direction:
    Современные подходы в обучении и воспитании
    Abstract:
    Today, a generation with developed creative potential, flexible thinking, and capable of non-standard solutions is in demand in society. In this regard, high demands are placed on school graduates. The relevance of the topic is due to the contradiction between social demand and the lack of development of methodological material that promotes the development of creative thinking in the classroom. In our study, we reveal the potential of intellectual games using the example of mathematics lessons in high school, taking into account the age characteristics of students, the content features of the educational material, diagnostic indicators and the integration of reflexive and evaluative mechanisms, which provided a positive dynamic.
    Keywords:
    creativity, development, learning process, intellectual games

  • The pedagogical potential of project-based learning in the modern educational space

    Book Chapter
    Pedagogy and psychology as sciences of building the potential of modern society
    Author:
    Olga V. Khotuliova
    Work direction:
    Глава 1
    Abstract:
    The chapter examines the pedagogical potential of project-based learning as an effective tool in the modern educational space. The key aspects of project-based learning are analyzed, including its impact on the development of critical thinking, creativity and independence of students. Special attention is paid to the integration of the project approach into educational programs at various levels, as well as its role in shaping 21st-century skills necessary for successful socialization and professional activity. The chapter examines examples of successful implementation of project-based learning in schools and universities, as well as methodological recommendations for teachers on the implementation of project technologies in the educational process. The article highlights the importance of project-based learning in the context of the current challenges of education and its ability to adapt to the demands of modern society. In the paper, the author present the results of an experiment on mastering the method of project-based learning in school.
    Keywords:
    mathematical data processing, project-based learning method
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  • The pedagogical potential of Taoism in the formation of a harmonious personality

    Book Chapter
    Pedagogy and psychology as sciences of building the potential of modern society
    Author:
    Aleksandr I. Kugai
    Work direction:
    Глава 4
    Abstract:
    This chapter examines the pedagogical potential of Lao Tzu's philosophical concept of Tao through the prism of developing a harmonious personality in modern society. The author conceptualizes Tao, interpreting ancient postulates as a methodological basis for modern humanistic pedagogy. The study is based on the following provisions: 1) the limits of verbalization in education (it is proven that the essence of personality development (Tao) is broader than any formal descriptions and boundaries, which requires the teacher to move to non-linear methods of transmitting experience); 2) sensory comprehension of the world (Tao is viewed not as an abstract substance, but as a living process, comprehended through involvement with the surrounding world, which substantiates the importance of empirical and existential learning); 3) the dialectic of pedagogical discourse: Lao Tzu's use of rational and metaphorical speech is analyzed as a prototype of modern problem-based learning methods.
    Keywords:
    personal potential, personality development, conceptualization, humanistic pedagogy, Lao Tzu, Tao, Taoism in education, pedagogical potential, linguacognitive approach, nonlinear learning
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  • Features of the use of interactive teaching methods in solving situational (economic) problems

    Book Chapter
    Pedagogy and psychology as sciences of building the potential of modern society
    Author:
    Oksana M. Komarova
    Work direction:
    Глава 8
    Abstract:
    The chapter considers the features and effectiveness of the practical application of interactive teaching methods in the process of ensuring the solution of situational economic problems and the formation of quality education. The subject of the study is the process of using interactive forms and methods of teaching (interactive technology) when conducting classes in a cycle of economic disciplines. The methodological basis of the research consists of general scientific techniques and approaches supplemented by the principle of epistemological pessimism and the method of system-structured analysis. The author pays special attention to the description of the advantages of using various methods and forms of organizing classes implemented using interactive learning technology to solve situational economic problems and study economic disciplines of the professional cycle. The chapter may be useful to teachers, methodologists and other specialists of educational organizations engaged in the adjustment of educational programs and the development of the structure and content of professional competencies that take into account the requirements of employers to modern personnel.
    Keywords:
    competence approach, system-activity approach, innovative pedagogical model, interactive learning technology
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  • Mathematical training in the system of higher sports education as a pedagogical resource for the formation of professional potential

    Book Chapter
    Pedagogy and psychology as sciences of building the potential of modern society
    Author:
    Elena G. Kostenko
    Work direction:
    Глава 10
    Abstract:
    This chapter examines the mathematical training of students at higher education institutions specializing in sports as a significant pedagogical factor in the development of an individual's professional and intellectual potential in the context of modern society. The role of mathematical disciplines in the development of analytical thinking, research skills and the ability to make informed decisions in the professional activities of physical education and sports specialists is substantiated. It is shown that a practice-oriented model of mathematical training facilitates the integration of pedagogical, scientific, and applied components of education. The chapter's materials can be used in the design of educational programs and the development of professional education theory.
    Keywords:
    personality development, mathematical training, pedagogy, practice-oriented learning, higher sports education, professional potential, analytical competencies
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  • Martial arts games as an additional teacher's tool in extracurricular activities

    Book Chapter
    Pedagogy and psychology as sciences of building the potential of modern society
    Author:
    Sergei M. Gerasimchuk
    Work direction:
    Глава 14
    Abstract:
    This chapter presents a selection of martial arts games aimed at solving a wide range of pedagogical tasks. The proposed games allow teachers, instructors and parents to diversify physical activity, developing in school-age children not only strength and dexterity, but also skills of self-regulation, respect for the opponent and the ability to act according to the rules. The materials of the chapter are adapted to work both in general education groups and with children with disabilities. Depending on the purpose of the lesson, games can be used as a warm-up element, the main part of the lesson, or included in the sports section program.
    Keywords:
    variability, Game-based learning method, martial arts games, specialized game systems, ease of learning, pedagogical objectives
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  • The Challenges of Lifelong Learning in Modern Schools

    Proceeding
    Socio-Pedagogical Issues of Education and Upbringing
    Author:
    Aleksandra A. Baldina
    Work direction:
    Образовательный процесс в организациях общего и дополнительного образования
    Abstract:
    The article is devoted to the analysis of key systemic contradictions that hinder the implementation of the principles of lifelong learning in the modern Russian school. The author considers school as a launchpad for developing the "learning to learn" competence, which forms the basis for personal self-development in a rapidly changing world. The focus is on the gap between the declared need to teach how to learn and the real educational practice, which is oriented towards a knowledge-based paradigm and successful completion of final assessments. The article sequentially explores problems such as: the predominance of standardization over personalization, the disconnect between school knowledge and the real world, a punitive assessment system that generates a fear of failure, as well as digital inequality and teacher overload.
    Keywords:
    lifelong learning
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  • Mentoring in the team: how to involve teachers in effective education of parents

    Proceeding
    Socio-Pedagogical Issues of Education and Upbringing
    Authors:
    Elvira V. Afanaseva, Nataliia A. Avramova
    Work direction:
    Теория и методика обучения и воспитания
    Abstract:
    The article examines the mentoring model within the kindergarten teaching staff as a key mechanism for improving the quality of interaction with the families of pupils. An integrated system of work is presented, combining proven and new, non-standard forms. It is aimed at unlocking the professional potential of each teacher, ensuring continuity of approaches and creating a single, trusting space "Kindergarten – Family".
    Keywords:
    mentoring, teaching staff, parent education, professional growth, effective methods, mutual learning, trusting relationships
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  • Developing Critical Thinking in Future Foreign Language Teachers Through Generative Language Models: A Systematic Review of Empirical Studies

    Review Article
    Development of education Volume 9 No 1
    Authors:
    Svetlana V. Chusovlianova, Elena G. Zharikova
    Work direction:
    Pedagogy and Modern Education
    Abstract:
    In the context of digital transformation in education, the development of critical thinking among future teachers has become increasingly urgent due to widespread integration of generative artificial intelligence (AI) into teaching and learning processes. This paper presents a systematic review of empirical studies (2019–2025) that examine the pedagogical potential of generative language models for fostering critical thinking among students in teacher education programs. This work constitutes a secondary analysis; it synthesizes findings from ten peer-reviewed empirical and theory-informed empirical studies conducted in Russia, China, Saudi Arabia, and other countries. The literature analysis reveals that effective use of neural network-based AI tools can support the development of core critical thinking operations provided that specific pedagogical strategies are employed. At the same time, the review systematically identifies key risks associated with AI integration: cognitive laziness, academic dishonesty, and the unreliability of generated information. The paper emphasizes the necessity of cultivating students’ digital and critical literacy as a prerequisite for mindful engagement with AI-generated content, as well as the transformation of the teacher’s role from a knowledge transmitter to a facilitator of a reflective-discursive learning environment. This systematic review contributes to the theory of digital pedagogy by proposing an approach to integrating generative AI models into the professional training of language teachers.
    Keywords:
    critical thinking, teacher training, active learning, artificial intelligence in education, future foreign language teachers, reflective learning
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  • The Process of Integrating the Interactive Video Service Playphrase.Me into the Development of Phonetic Competence in 6th Grade Students at the English Language Lessons

    Research Article
    Development of education Volume 9 No 1
    Authors:
    Emiliia I. Sabirova, Guzel R. Nasibullova
    Work direction:
    Pedagogy and Modern Education
    Abstract:
    The article discusses the problem of developing phonetic skills in secondary school students through the integration of digital interactive technologies, in particular the online platform PlayPhrase.me. In the context of globalisation and increasing demands for practical foreign language skills, the issues of forming stable pronunciation and listening skills are becoming particularly important. Analysing the limitations of traditional methods based on textbooks and reproductive exercises, the authors conclude that the modern educational reality requires new teaching methods that are appropriate for the digital age. The article proposes a specific methodology for organising the English language learning process through the systematic use of interactive resources. It justifies the use of authentic video materials selected with the help of PlayPhrase.me in lessons, which help students immerse themselves in a natural language context, increase their motivation to study the subject, and contribute to more effective acquisition of phonetic norms and the development of communication skills. The experiment with 6th grade students at Arskaya Secondary School No. 6 showed a significant increase in phonetic competence using this platform, highlighting its flexibility for adaptation to different learning stages and language aspects.
    Keywords:
    authentic materials, interactive learning, digitalisation of education, pedagogical technology, PlayPhrase, game-based methods, phonetic skills, listening comprehension
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  • Ispol'zovanie neirosetei v sisteme obrazovaniia: preimushchestva i riski

    Proceeding
    Current problems of communication: theory and practice
    Authors:
    Iurii A. Denisenko, Daniil F. Klimenko
    Work direction:
    Конвергентные коммуникации будущего: интеграция цифровой среды, нейронаук, искусственного интеллекта и новых медиа
    Abstract:
    Over the past three years, neural networks and other artificial intelligence (AI) technologies have become one of the most discussed topics in education, from school to university. This article examines the main uses of neural networks in the educational process, analyzing their key benefits (personalization, automation of everyday tasks, expanding access to knowledge) and risks (ethical issues, substitution of independent work, digital divide, unreliable information). Based on an analysis of modern scientific and educational literature, it shows how neural networks are changing education and what conditions are necessary for their safe and effective implementation. The research methods include analysis and synthesis of scientific literature, comparison of approaches by different authors, and practical examples.
    Keywords:
    education, information security, artificial intelligence, Digitalization, neural networks, personalized learning, academic integrity
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  • Creating an interdisciplinary project using digital technologies

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Anzhelika V. Kudashkina, Elena L. Makarova
    Work direction:
    Современные технологии в образовании
    Abstract:
    The article discusses what interdisciplinary projects are and how they can be implemented in the educational process. It provides an example of such a project and shows how modern technologies can be used. The article concludes that generative AI can successfully handle tasks of simple and medium complexity, but it faces challenges when the complexity increases, especially when there are subtle dependencies and unusual conditions.
    Keywords:
    innovative methods, machine learning, digital technologies, creative thinking, scientific research, Interdisciplinary project, generative AI, integration of disciplines, project implementation, geometric proof, solving geometric problems, planimetry, and automated problem solving
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  • MODERN TECHNOLOGIES IN EDUCATION

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Polina A. Riazantseva, Daria A. Riazantseva, Sofia A. Kravchenko, Dar'ia D. Shipil', Sofia R. Letuchaia, Alina N. Kostenko, Iurii O. Vrublevskii
    Work direction:
    Современные технологии в образовании
    Abstract:
    The article is devoted to the study of modern digital technologies that have a significant impact on the transformation of educational processes. The key areas of technology integration are considered: adaptive learning systems based on artificial intelligence, virtual and augmented reality (VR/AR) technologies, the use of big data and learning analytics, as well as the development of massive open online courses (MOOCs) and blended learning formats. Special attention is paid to the practical aspects of implementing these technologies in the higher education process and their impact on the development of students' digital competencies. An analysis of potential benefits is carried out, including increasing the level of personalization, interactivity and accessibility of education. In parallel, the main challenges are explored, such as the problem of the digital divide, cybersecurity and personal data protection, and the risk of digital fatigue. The methodological basis of the work was the analysis of current scientific publications, a review of existing technological solutions and platforms. The conclusion is made about the need for a balanced approach in which technological tools serve to expand the capabilities of traditional pedagogy, and not its complete replacement.
    Keywords:
    higher education, artificial intelligence, virtual reality, digital transformation, digital technologies, MOOC, blended learning, learning analytics
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  • Digital transformation of the educational process: a systematic approach to technology integration

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Andrei A. Aleksandrov, Aleksandr S. Astaichenkov, Mikhail S. Afanasev, Iurii O. Vrublevskii
    Work direction:
    Современные технологии в образовании
    Abstract:
    The article is devoted to the analysis of digital transformation processes in the modern educational environment. The research aims to develop a model for the effective integration of key digital technologies (adaptive platforms, immersive environments, communication tools) into the pedagogical process and to assess their impact on educational outcomes. The methodological basis includes systematic analysis, comparative method, and synthesis of data from empirical studies (2020–2024). The work identifies the main stages of integration, formulates criteria for evaluating the effectiveness of technology use, and analyzes typical barriers (technological, methodological, psychological). The results of the study are presented in the form of a generalized integration model and a comparative table of technological tools. The conclusion substantiates the thesis about the need for a comprehensive and phased strategy for digital transformation, in which technological innovation is subordinated to pedagogical goals. Prospects for further research are related to the development of universal diagnostic tools for assessing the digital maturity of the educational environment.
    Keywords:
    adaptive learning, pedagogical design, digital educational environment, immersive technologies, integration of technologies, effectiveness of education, digital transformation model
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  • Psychological characteristics of preschool children as a factor in increasing the effectiveness of preparation for school

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Marina V. Piriazeva, Daria D. Mordovkina
    Work direction:
    Современные технологии в образовании
    Abstract:
    This article provides a theoretical analysis of the psychological characteristics of preschoolers that influence their successful adaptation and preparation for school. It examines the key areas of a child's psychological readiness for learning and identifies factors that contribute to successful socialization and the development of academic competence.
    Keywords:
    preschoolers, preschool age, cognitive development, motivation for learning, preparation for the learning process
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  • Risks and Limitations of VR Technologies in Education: The Case of a Russian History Course in Secondary Vocational Education

    Proceeding
    Education, innovation, research as a resource for community development
    Author:
    Egor A. Kuznetsov
    Work direction:
    Современные технологии в образовании
    Abstract:
    The paper examines the pedagogical risks and limitations of using virtual reality technologies in teaching Russian history at the level of secondary vocational education. The methodological framework combines comparative and theoretical–methodological analysis of Russian and international studies on VR technologies with a classification of the risks identified by researchers. On this basis, we distinguish cognitive, value–semantic, and emotional–psychophysiological groups of risks and demonstrate how they manifest themselves in the context of teaching Russian history within the system of secondary vocational education. The study substantiates the need to design VR episodes as integral components of holistic instructional situations that explicitly take these risks and limitations into account. The paper also outlines directions for further research related to a more detailed elaboration of organizational–methodological and technical constraints.
    Keywords:
    secondary vocational education, VR technologies, Russian history, risks in education, immersive learning
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  • Multi-level assignments as a means of teaching mathematics in a modern school

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Ekaterina V. Dubovaia, Tatiana K. Smykovskaia
    Work direction:
    Инновационные технологии как ресурс повышения качества образования
    Abstract:
    The article is devoted to the issues of individualization and differentiation of learning in the educational process. Various approaches of researchers to the concepts of "individualization" and "differentiation", their interrelation and role in the development of the student's personality are considered. Special attention is paid to differentiated learning and its types, in particular, level differentiation, developed by V.V. Firsov. The article focuses on the description of the levels of differentiation of tasks (reproductive, productive and advanced), as well as the requirements for cards with multi-level tasks. The author emphasizes the value of systematic use of multi-level tasks to adapt the learning process to the cognitive abilities of each student, diagnose his intellectual development and form a stable motivation for learning.
    Keywords:
    teaching mathematics, individualization of learning, multi-level tasks, differentiation of learning, differentiated learning, level differentiation
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  • AI Assistants as Tutors: Ethical Boundaries for Using Neural Networks to Personalize Programming Education

    Proceeding
    Education, innovation, research as a resource for community development
    Authors:
    Inna G. Iglinskaia, Anastasiia V. Petrakova
    Work direction:
    Использование нестандартных решений для повышения качества, доступности и эффективности образования
    Abstract:
    The article discusses the current problem of integrating artificial intelligence (AI), in particular, large language models (LLM), into the educational process of training specialists in the specialty 02/09/07 "Information Systems and Programming". The purpose of the study is to analyze the potential of AI assistants as personalized tutors to develop programming skills and identify the associated ethical risks and pedagogical limitations. Based on the analysis of modern literature and the author's practical experience, key dilemmas have been identified: the reliability of the generated code and explanations, the risk of intellectual dependence, issues of academic integrity and digital inequality. The article offers a model for the balanced use of AI assistants based on the principles of pedagogical support, the development of critical thinking and the formation of digital hygiene among students. It is concluded that AI is a powerful tool for improving the accessibility and effectivenes
    Keywords:
    pedagogical design, tutoring, ChatGPT, programming, AI ethics, academic integrity, artificial intelligence in education, learning personalization, large language models (LLM), and professional education
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  • Blended Learning as a Modern Educational Strategy: Advantages and Challenges

    Proceeding
    Modern educational process: psychological and pedagogical support, educational strategies
    Author:
    Айкерим Ж. Жайырбекова
    Work direction:
    Инновационные технологии в образовании
    Abstract:
    This article provides an in-depth examination of blended learning as a multifaceted educational strategy that integrates online technologies with traditional face-to-face instruction. Positioned within the broader context of the digital transformation of education, the study analyses the conceptual foundations of blended learning and its relevance for contemporary teaching practices in both secondary and higher education. Particular attention is given to the pedagogical mechanisms through which blended learning enhances learner autonomy, supports the development of digital competence, and enables the design of differentiated and personalized learning pathways. The review further explores the motivational, cognitive, and social aspects of blended learning environments, highlighting their potential to promote active participation, reflective engagement, and improved learning outcomes. At the same time, the article addresses the persistent challenges that institutions and educators face during the implementation process, including insufficient teacher preparedness, unequal access to technological infrastructure, variability in students’ digital readiness, and the absence of coherent institutional strategies for integrating digital tools into curricula. The analysis demonstrates that, while blended learning offers substantial educational benefits, its success is contingent upon deliberate instructional design, sustained professional development for teachers, and the systematic evaluation of both online and face-to-face components. The paper concludes by proposing recommendations for optimizing blended learning models to ensure pedagogical effectiveness, technological sustainability, and long-term institutional impact.
    Keywords:
    digital education, educational technologies, blended learning, online teaching, student motivation, hybrid instruction, instructional design, learning engagement
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  • Virtual laboratories and simulations in the study of information technology and computer science

    Proceeding
    Modern educational process: psychological and pedagogical support, educational strategies
    Author:
    Sergei V. Ozerskii
    Work direction:
    Инновационные технологии в образовании
    Abstract:
    The article discusses the issue of introducing virtual laboratories and simulations into the educational process of higher education institutions, in particular, in teaching information technology and computer science. The author does not agree with the approach in which virtual environments are positioned as a direct replacement for traditional physical practices. Instead, the need for a transition to a complementary or hybrid model is justified, where virtual and physical laboratories are used together, reinforcing each other's advantages. The paper analyzes the unique advantages of each format: tactile experience and working with physical limitations in real laboratories, as well as the safety, scalability, and cost-effectiveness of virtual simulators. It describes a two-stage hybrid learning model that combines theoretical modeling in a virtual environment with subsequent practice on real equipment. Finally, the paper highlights the organizational, methodological, and infrastructur
    Keywords:
    higher education, information technology, pedagogical model, digitalization of education, virtual laboratories, hybrid learning, educational simulations, complementarity, physical workshops, and equipment skills
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  • Speech development of primary school students in conditions of motivation of educational activity

    Proceeding
    Modern educational process: psychological and pedagogical support, educational strategies
    Author:
    Irina V. Shatokhina
    Work direction:
    Инновационные технологии в образовании
    Abstract:
    The article is devoted to the complex problem of primary language teaching related to the use of educational technologies that promote both the stimulation of learning activities and the speech development of students. In this regard, the author considers the possibilities of such educational technologies as problem-based learning, game learning, creating a situation of success and organizing educational cooperation. The author describes the methodical aspects of organizing speech work in Russian language lessons in elementary schools using these technologies, such as relevant types of tasks, methods and techniques.
    Keywords:
    educational technology, Speech development, Russian language lessons, elementary school, motivation for learning
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  • Application of set theory and logic in the design of intelligent educational environments

    Proceeding
    Modern educational process: psychological and pedagogical support, educational strategies
    Authors:
    Ivan A. Rozhkov, Aleksandr E. Sergeev
    Work direction:
    Инновационные технологии в образовании
    Abstract:
    The article examines the fundamental role of the apparatus of discrete mathematics, in particular set theory and mathematical logic, in the design and development of intelligent educational environments (IEDs). The key tasks of IEDs are analyzed, such as knowledge formalization, adaptive planning of learning trajectories, gap diagnosis and generation of personalized tasks, the solution of which is based on operations on sets, Boolean algebra, logical rules and predicate calculus. It is proved that the use of these formal methods makes it possible to move from intuitive design of educational content to a precise, algorithmically controlled process, which is a critical factor in improving the quality and accessibility of education. The work highlights promising areas of integration of these disciplines into modern EdTech solutions.
    Keywords:
    adaptive learning, personalization, set theory, intellectual educational environments, mathematical logic, knowledge formalization, ontologies, logical inference
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