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List of publications on a keyword: «Mathematica»

  • 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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  • Role of Mathematical Training of Schoolchildren in Mastering Skills of Future Profession

    Research Article
    Development of education Volume 8 No 3
    Author:
    Elena A. Barakova
    Work direction:
    Pedagogy and Modern Education
    Abstract:
    Specialized school education today aims to enhance learning motivation and acquire knowledge and skills necessary for future professions. The choice of specialized subjects by 9th-grade graduates for in-depth study in specialized 10th-11th grades also implies passing the Unified State Exam (USE) in these subjects at the specialized level. However, the results are often lower than expected by graduates, their parents, and teachers. This article, based on an analysis of the 2024 Unified State Exam (USE) results in mathematics (specialized level), examines the format of self-analysis of a mathematics teacher's own errors in teaching schoolchildren. It proposes a set of updated competencies for mathematics teachers to improve the quality of graduates' mathematical training. As a result of discussing the problems of modern specialized school mathematics education, particularly the update of the direction of specialized school education (introduction of agrotechnological classes), with participants of professional development programs (specialists from regional education development institutes overseeing specialized school education, and heads and deputy heads of general education organizations), constructive approaches to mathematical training of schoolchildren are outlined. These approaches aim to apply mathematical knowledge, applied mathematical skills, and abilities in mastering related academic subjects, using the example of mathematics education in specialized agrotechnological classes.
    Keywords:
    professional competencies of a mathematics teacher, school specialized education, approaches to mathematical training of high school students, agrotechnological classes
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  • Functional Literacy as a Tool for Improving the Quality of Mathematical Education

    Proceeding
    Pedagogy, Psychology, Society: from theory to practice
    Authors:
    Irina A. Ledovskikh, Kristina O. Dorzhu
    Work direction:
    Теория и методика общего и дополнительного образования
    Abstract:
    The article is devoted to the consideration of the possibilities of improving the quality of mathematical education by developing the functional literacy of schoolchildren. The problems of the modern system of teaching mathematics are analyzed, such as the separation of theory from practice, low motivation and the lack of conscious perception of the meaning of the subject. Ways to overcome these difficulties are proposed, including the integration of mathematical problems into real life, the organization of project activities, and skills for working with information
    Keywords:
    mathematical education, mathematical training, modern teaching technologies, functional approach, functional literacy, educational standards
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  • Formation of students' functional literacy in mathematics lessons through solving word problems

    Proceeding
    Pedagogy, Psychology, Society: from theory to practice
    Authors:
    Irina A. Ledovskikh, Kristina O. Dorzhu
    Work direction:
    Теория и методика общего и дополнительного образования
    Abstract:
    The article is devoted to the importance of the ability to solve word problems in mathematics lessons for the successful formation of students' functional literacy. In order to increase students' motivation and prepare them to use mathematical knowledge in everyday situations, the work emphasizes the importance of using educational and practical problems. Methodological recommendations and specific examples of the implementation of the methodology are presented, aimed at activating the cognitive activity of students and creating situations of success in the process of mastering mathematical knowledge.
    Keywords:
    educational process, digital literacy, creative thinking, financial literacy, functional literacy, mathematical literacy, natural science literacy, global competencies, word problem, mathematics teaching methods, knowledge application practice
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  • Metodical aspects of the organization of trigonometry classes for mid-level specialists in ship navigation management

    Proceeding
    Sormovo Readings- 2025: scientific and educational space, realities and prospects for improving the quality of education
    Authors:
    Valerii R. Sagiian, Tatiana K. Smykovskaia
    Work direction:
    Современные педагогические теории и методы: инновации в образовании и подготовка кадров
    Abstract:
    The article raises the problem of organizing trigonometry classes for mid-level specialists in ship navigation management without interrupting their professional activities. The article considers the substantive component of trigonometry classes, which provide systematization of knowledge necessary to solve the main problem of navigation.
    Keywords:
    systematization of knowledge, trigonometry, mathematical basis, navigation, navigation control, teaching methods in the postgraduate period, lesson system
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  • Mathematical principles of data processing in the sports industry

    Book Chapter
    Modern issues of pedagogy and psychology: theoretical and methodological approaches and practical research results
    Author:
    Elena G. Kostenko
    Work direction:
    Глава 20
    Abstract:
    Statistical research methods are used in all areas of the sports industry. Mathematical data processing is a basic tool for increasing the efficiency of the training process, analyzing athletes' technique, predicting competition results, modeling individual training programs and maintaining athletes' health.
    Keywords:
    analysis, modeling, physical education, evaluation, sports, forecasting, statistical analysis, mathematical data processing
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  • Formation of a sample of candidates for additional training, taking into account the requirements of the region

    Book Chapter
    Principles of building a new ecosystem: Economic, legal and social aspects
    Authors:
    Olga A. Astafurova, Irina I. Kulagina
    Work direction:
    Глава 5
    Abstract:
    Formation of human resources potential is an important task at the current stage of economic development of Russia. Digitalization of the economy gives rise to problems, including the risk of reduced employment stability (due to the fact that artificial intelligence replaces human resources and reduces the number of jobs) and the need to retrain specialists both within the region and their migration to areas with a shortage of labor resources. The difference between supply and demand in the labor market is explained by many factors. This may be a national problem – an excess of graduates in humanities and social sciences, which leads to a situation where candidates are forced to look for work unrelated to their education. Or these may be regional reasons. This problem can be reduced by the sphere of additional education, which allows retraining and developing the necessary competencies for applicants. Identification of the complex effect of the influence of various factors on the successful employment of citizens; is a time-consuming, complexly structured scientific task, for which it is proposed to use cognitive modeling. Based on the constructed model, scenarios for the development of labor resources are determined, taking into account regional peculiarities; assessment of the needs of the region in training and retraining of personnel. Their analysis and selection of the most promising scenarios from the standpoint of minimizing the costs of retraining citizens, as well as the constructed functional models of the procedure for selecting candidates among unemployed citizens for additional training (a model reflecting the current state of the research object and models reflecting possible scenarios for the development of the research object) can become the basis for developing a methodology for selecting candidates for additional training for a program that meets the needs of the citizen and the existing offers in the region.
    Keywords:
    human capital, labor market, additional professional education, labor resources, functional modeling, personnel reserve, employee competitiveness, unemployed citizens, economic and mathematical models, cognitive modeling
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  • Primenenie sredstv STEAM-obucheniia v shkole

    Book Chapter
    Modern Challenges of Education and Psychology of Personality Formation
    Authors:
    Svetlana M. Koniushenko, Mariia O. Komissarova, Zarina N. Khisametdinova
    Work direction:
    Глава 14
    Abstract:
    The chapter examines the results of a study on the content of the concepts of STEAM learning tools: «gamification», «game mechanics». The authors justified the relevance of their application in the educational process of STEAM teaching mathematics as a new learning tool is substantiated. The key to gamification lies in its ability to make mathematics relevant and exciting by fostering a positive relationship between learners and this important subject.
    Keywords:
    game, gamification, STEAM-learning, game mechanics, mathematical education of students
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  • Some aspects of the development of functional literacy of students in computer science lessons

    Research Article
    Development of education Volume 7 No 3
    Author:
    Irina A. Dudkovskaya
    Work direction:
    Pedagogy and Modern Education
    Abstract:
    The article discusses some aspects of the development of functional literacy of students in computer science lessons. The author reveals the essence and content of functional literacy, the main components of functional literacy, and the signs of a functionally literate person. A solution to the problem of developing students' functional literacy within the framework of the implementation of the updated Federal State Educational Standard is proposed through the use of teaching methods and techniques, forms, tools, techniques and tasks aimed at developing students' functional literacy. This approach is possible when teaching computer science, since computer science is one of the subjects in which functional literacy can be most effectively developed. In computer science lessons, it is possible to use elements of a large number of educational technologies that make it possible to successfully develop the functional literacy of a future graduate who is able to adapt to the changing conditions of modern life. The purpose of the study is to identify opportunities for developing functional literacy of students in computer science lessons. The methodological basis of the article is a complex of general scientific, paradigmatic and instrumental approaches. The results obtained can be used as a resource for expanding the factual base in the application of various teaching methods for the development of functional literacy of students.
    Keywords:
    reading literacy, financial literacy, computer science, functional literacy, mathematical literacy
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  • Economic Aspects of Automation of Production Management of a Modern Enterprise (by the Example of Kaluga Pjsc Cadvi)

    Book Chapter
    Development of the Russian socio-economic system: challenges and prospects
    Authors:
    Vladimir N. Kruglov, Dmitrii V. Tiutin
    Work direction:
    Глава 8
    Abstract:
    The chapter examines algorithms for improving automated production management systems. The epistemological roots of various stages of the process are analyzed: automated control systems (ACS), automated production development systems (APS), computer-aided design (CAD) systems and Robotic Process Automation (RPA), as a developing technology involving bots that imitate human actions. The relevance of the problems raised lies in the lack of alternatives to innovative development for the domestic economy. This concept inherently includes a component of artificial intelligence associated with the implementation of automated control systems in production cycles. Using the example of Kaluga PJSC CADVI, the authors prove the effectiveness of introducing self-developing technologies for management activities. Systemic, complex, process and situational types of analysis are used. Layers of monographic and statistical developments are taken as the initial base. Specific proposals are given for choosing the most effective and reasonable platforms, taking into account current production realities.
    Keywords:
    Management, competitiveness, outsourcing, automation, production, informatization, economic effect, life cycle, functional connections, mathematical analysis
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  • On the issue of multi-level educational tasks in mathematics for an engineering and mathematics class

    Book Chapter
    Theoretical and practical aspects of pedagogy and psychology
    Author:
    Vladimir A. Sapegin
    Work direction:
    Глава 11
    Abstract:
    The chapter discusses multi-level math assignments for an engineering and mathematics class. The requirements for mathematical questions, mathematical dictation, mathematical exercises and educational tasks for students of three level groups (proposed by the author) are highlighted and justified. The training tasks on the topic «Irrational equations with parameters» are given in accordance with the presented requirements.
    Keywords:
    multi-level learning tasks, multi-level learning exercises, multi-level questions, multi-level mathematical dictation, tasks with parameters, level groups, engineering and mathematics class
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  • L. F. Magnitsky and his "Arithmetic": based on publications of the XIX – early XX centuries

    Proceeding
    Pedagogy, Psychology, Society
    Author:
    Alexander N. Pozdnyakov
    Work direction:
    Общая педагогика, история педагогики и образования
    Abstract:
    The presented work, based on materials published in the XIX – early XX centuries, traces the main stages of the life and organizational and pedagogical activity of Leonty Filippovich Magnitsky, a mathematician, author of the first printed work in this field in Russia, shows the features of the textbook and its place in the educational literature
    Keywords:
    the origins of Russian education, the formation of Russian pedagogical thought, the school of mathematical and navigation sciences
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  • Factor analysis of economic activity of a branch of the economy

    Proceeding
    Socio-Economic Processes of Modern Society
    Authors:
    Mariia A. Kalinina, Valentina V. Poladova, Aleksandr V. Shmatov
    Work direction:
    Вопросы социально-экономической эффективности предприятий
    Abstract:
    In this work, a three-factor multiplicative mathematical model of deterministic factor analysis by the integral method is studied on the example of solving a specific problem of analyzing the economic activity of the manufacturing sector of the economy. As intermediate indicators, the average number of employees in the industry, the number of days worked by an employee per year and the average annual production of products by an employee of the industry were taken. The resulting indicator was the output of the industry.
    Keywords:
    factor analysis, economic analysis, integral method, multiplicative mathematical model
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  • DEVELOPMENT OF THE REFLECTIVE COMPONENT OF ENGINEERING COMPETENCE OF UNIVERSITY STUDENTS WHEN STUDYING MATHEMATICS

    Proceeding
    Engineering education in the conditions of digitalization of society and economy
    Author:
    Natal'ia A. Lozovaia
    Work direction:
    Инженерная подготовка в условиях модернизации высшего профессионального образования
    Abstract:
    The work updates the role of reflection in the engineering training of students. The methods and means of developing the reflective component in the professional training of future engineers when studying mathematics in the conditions of digitalization of education and the strengthening of the role of independent work of students are considered.
    Keywords:
    project, engineering competence, reflection, independent work, student, mathematical preparation
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  • Formation of self-control in mathematics lessons for students of grades 5-6 as a condition for preparing for training in engineering classes

    Proceeding
    Engineering education in the conditions of digitalization of society and economy
    Authors:
    Iuliia A. Bondareva, Tatiana K. Smykovskaia
    Work direction:
    Инженерные классы: опыт и перспективы развития
    Abstract:
    The article presents various aspects of teaching in engineering classes, substantiates the role of self-control for the successful development of engineering thinking and improving the quality of teaching mathematics in engineering classes. The necessity and possibilities of forming self-control in students of grades 5-6 in the study of mathematics, which is the basis for the construction of educational mathematical activities, the organization of which is necessary for training in engineering classes, are shown.
    Keywords:
    self-control, preparation for specialized teaching of mathematics, engineering classes, educational mathematical activities
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  • Matematicheskoe modelirovanie rezhimov elektricheskikh tsepei

    Book Chapter
    Psychological and Pedagogical in High School
    Author:
    Andrei S. Isaev
    Work direction:
    Глава 6
    Abstract:
    In the chapter modelling of transient process in electric RLC-chain is considered. The software-mathematical model of the mode is constructed and implemented. Matlab is used as a toolkit. At the same time the traditional engineering methods of calculation, directed on linearisation of the considered processes, are rejected. The choice is made in favour of direct application of mathematical methods (application of the apparatus of differential calculus). Correctness of the results is confirmed by earlier calculations and correspondence of the general topology of the considered circuits.
    Keywords:
    Matlab, Simulink, differential equation, electric circuit, transient states, transient process, mathematical modelling
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  • Otritsatel'naia zona sovokupnogo riska predpriiatii i puti vykhoda iz nee

    Book Chapter
    Strategic Directions of the Development of Russian Regions: Issues of Economy, Accountance, Taxification, Economic Security, Theoretical and Applied Finance
    Author:
    Margarita V. Pinegina
    Work direction:
    Глава 6
    Abstract:
    Currently the business risk assessment monitoring becomes increasingly relevant for enterprises. The aim of the article is to determine to quantitative risk value of aggregate risk of enterprises located in two zones: one part in positive while the other in quite significant negative. The article resulted in development of the approaches enabling the firms to reduce aggregate risk in order to remove it from negative zone. This result is achieved with the help of application theoretical help of theoretical method.
    Keywords:
    financial risk, aggregate risk, business risk, probability, mathematical expectation, variance, standard deviation, degree of financial leverage, effect of financial leverage, degree of total leverage
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  • PROGNOSTIC FUNCTION OF RESEARCH IN INTERNATIONAL LEGAL PROBLEMS OF MODERNITY

    Proceeding
    Law, Economics and Management
    Author:
    Liliia S. Karimova
    Work direction:
    Международное право
    Abstract:
    This article discusses the key issues of forecasting in the theory of international law and international relations. It is concluded that the prognostic method includes socio-legal methods of collecting and studying individual facts and phenomena, statistical-mathematical and empirical methods.
    Keywords:
    mathematical method, international law, international relations, legal monitoring, predictive method, prognostic method, statistical method, theoretical method, legal forecasting
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  • Succession in Mathematical Preparation of Preschoolers and Junior Schoolchildren

    Book Chapter
    Issues of pedagogy and psychology
    Author:
    Tamara S. Khazykova
    Work direction:
    Chapter 10
    Abstract:
    The chapter examines the issues of continuity in the theory and practice of mathematical training of preschoolers and primary school students, investigates the psychological and pedagogical foundations of this process. The author substantiated the choice of an effective means in ensuring the continuity of mathematical training at the stages of preschool education – primary school.
    Keywords:
    mathematical training, continuity, primary school child, preschooler
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  • Formation of cognitive universal educational actions when teaching combinatorics

    Proceeding
    Pedagogy, Psychology, Society
    Authors:
    Tatiana I. Goncharova, Antonina A. Zheludkova
    Work direction:
    Теория и методика общего и дополнительного образования
    Abstract:
    The article analyzes the need for an approach to the organization of teaching elements of combinatorics at school, aimed at the formation of cognitive ECD. Based on the study of scientific, psychological, pedagogical, methodological literature, the process of formation of cognitive universal educational actions in mathematics lessons has been studied. The content-methodological aspects of teaching combinatorics to junior schoolchildren are revealed, three interrelated directions of the teacher's work are considered, the stages of teaching the solution of combinatorial problems are highlighted depending on the methods of calculating the number of combinations. Each of the stages serves as a foundation for the formation of the UUD of the next stages.
    Keywords:
    FGOS LEO, universal educational actions, combinatorics, probability theory, mathematical statistics, combinatorial problems, combinatorial thinking
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  • Sovremennye problemy teorii ustoichivosti i soderzhanie kursa matematiki v tekhnicheskom vuze

    Book Chapter
    Psychological and Pedagogical Issues of Modern Education
    Authors:
    Olga G. Antonovskaia, Antonina V. Besklubnaia
    Work direction:
    Chapter 1
    Abstract:
    This paper addresses the problem of the "Stability reserve" issue in the "Stability theory" section in the system dynamics, differential equations and other courses for students of technical specialties. The problems of stability reserve determination are examined first of all from the point of view of accessibility of material account and possibility of its practical use when solving applied problems on the base of knowledge obtained by the students of technical high educational institutions in mathematical courses.
    Keywords:
    professional activity of the trainee, fundamentals of education, ability to construct models of real phenomena, mathematical methods of research, stability theory, robust stability, stability reserve
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  • Using V. Voskobovich's Game Technology in Kindergar-Ten as a Basis for Creating a Psychologically Comfortable Developing Environment

    Proceeding
    Psychologically Safe Educational Environment: Design Problems and Development Prospects
    Authors:
    Evgeniia N. Grigorenko, Marina G. Pogretskaia, Iana A. Shnareva, Irina E. Serbina
    Work direction:
    Creating a psychologically comfortable and safe educational environment: technologies, diagnostics, practice, expertise
    Abstract:
    This article introduces a unique gaming technology in its capabilities “Fairy mazes of the game”, as well as a system of developing of logical and mathematical representations and skills based on the use of games by V. Voskobovich.
    Keywords:
    game technology, child's mental abilities, child's creative abilities, logical-mathematical games, discoveries
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  • Priamoi metod Liapunova i ego izlozhenie v sovremennom uchebnom protsesse

    Book Chapter
    Education and science: current trends
    Authors:
    Olga G. Antonovskaia, Antonina V. Besklubnaia
    Work direction:
    Глава 1. Теоретические аспекты образования
    Abstract:
    The article is devoted to the problem of the full treatment of the subject “Construction of Lyapunov functions” in the “Lyapunov's direct method” section in the courses on system dynamics, differential equations, etc., for students of mathematical and technical specialties. The authors of the article point out that first of all Lyapunov function method is considered the method useful for studying dynamics of concrete technical systems by mathematical methods. Since for practical use of this method it makes sense to construct Lyapunov functions in simplest form, the methodology for constructing Lyapunov functions in positive definite quadratic forms with given properties, certain features of original problems is proposed by the authors.
    Keywords:
    professional activity of the trainee, fundamentals of education, professionally significant and practical goals of education, ability to construct models of real phenomena, mathematical methods of research, stability theory, Lyapunov's direct method, positive definite quadratic form, Lyapunov matrix equation
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  • Ob ispol'zovanii sistem komp'iuternoi algebry v universitetskikh kursakh matematiki

    Proceeding
    Pedagogical and sociological aspects of education
    Author:
    Aleksei V. Genk
    Work direction:
    Тенденции развития цифрового образования
    Abstract:
    В статье обсуждается возможность применения систем компьютерной математики «Maple» и «Mathematica» в преподавании общих курсов математики (математического анализа, линейной алгебры, теории вероятностей и др.) в университетах не только технических направлений. На ряде примеров показывается эффективность их использования для углубления понимания материала и расширения возможностей обучающихся для решения сложных задач.
    Keywords:
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  • Analysis of Applied Problems in Modern Textbooks of Algebra and Geometry from Positions of the FSES BGE Requirements

    Research Article
    Development of education No 4 (6)
    Author:
    Aleksandr V. Bychkov
    Work direction:
    Education system in Russia
    Abstract:
    The article discusses the concept of «mathematical literacy», which is important from positions of the PISA international studies requirements. There are three types of activity (formulation of the situation mathematically, application of mathematics, interpretation of the result), the possession of which is checked in the PISA study. The article presents the subject results formulated in the FSES of BGE, on the study of which the subject area «Mathematics» is aimed, reflecting the need for the formation of selected components of mathematical literacy in students. The article presents the results of the analysis of tasks presented in the most common textbooks on algebra and geometry of the main school. The purpose of the analysis was to identify the presence of practice-oriented tasks in textbooks that meet the requirements of the FSES of BGE and the requirements of diagnostic tools used in international PISA studies. During the study the following methods were used: comparison, analysis, theoretical. The study was based on the most frequently used in school practice textbooks of the following authors: L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev, E.G. Poznyak, I.I. Yudina, L.S. Atanasyan, V.F. Butuzov, etc. Result: the article presents the results of the analysis of the problem material presented in the most common textbooks on algebra and geometry of the general school. On the basis of the analysis of three author's lines on the study of geometry in the general school, common problems are identified. An example of a practical problem, confirming the conclusions, formulated during the analysis is given. The authorcomes to the conclusion that there is still lack of practice-oriented tasks in modern textbooks on algebra, helping to motivate students to conscious assimilation of mathematical facts and statements, providing the formation of the ability to model on the basis of a real, life situation.
    Keywords:
    international PISA studies, FSES of BGE, disadvantages of national tasks, formulating situation mathematically, application of mathematics, interpretation, algebra, geometry
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