The urgency of the problem is due to the insufficient development of theoretical, content-technological and methodological aspects of the integration of mathematical knowledge and chess skills. The manifestations of synergistic effects arising in the course of the integration of mathematical and game chess activity, while resolving uncertainties on the chessboard due to the activation of key components of creativity, have not been sufficiently studied. The synergistic effect of the integration of mathematical knowledge and chess skills is considered from the perspective of the components of theoretical thinking and is evaluated by the student’s creative choice in the search for alternative solutions. The purpose of the study is to describe and evaluate the manifestations of the structural components of the creative effect in the context of the introduction of funded complexes of mathematical problems on a chessboard. The hypothesis of the research: theoretical analysis of educational material, reflection and an internal plan of action as comparable processes for solving mathematical problems in terms of implementation substantiate complexes will lead to manifestations of arguments-heuristic, intellectual and logical and motivational components of creative activity. The research assumed the measurement of the manifestations of the structural components of creativity in the context of the introduction of funding complexes of mathematical problems on a chessboard. In the process of identifying the structural components of creativity, psychodiagnostic diagnostics tools were developed for intellectual-heuristic, intellectual-logical, motivational and reflexive aspects, comparative diagnostics were carried out for all structural components, the average level and integral indicators in the control and experimental groups were calculated. The formation of creativity was carried out by developing the ability to argue in the process of solving multi-stage mathematical problems on the chessboard. The choice of cause-and-effect relationships stimulated creative independence and reflexivity, enhancing the manifestations of the synergistic effect. On the basis of internal cognitive consonance, non-standard original ideas were identified; by overcoming emotional instability, the logical component of argumentation was strengthened. The results of the research revealed a positive trend in the key components of creativity in the context of the introduction of a chess game in the process of learning mathematics. In the future, it is possible to upgrade the methodological educational material for the system of inclusive mathematical education.

Управление школьным математическим образованием с синергетическим эффектомИсследуются процессы управления школьным математическим образованием (профильные классы) с синергетическим эффектом на основе выявления и исследования «проблемных зон» школьной математики средствами компьютерного и математического моделирования. Исследование касается задач освоения школьниками сложных понятий и процедур в контексте уровневой организации и наглядного моделирования в процессе выявления сущности учебных элементов (площадь поверхности, функциональные зависимости, итерационные процессы, геометрические фигуры и т.п.). Актуализируются современные достижения в науке (фрактальная геометрия, теория кодирования, нечеткие множества и fuzzy-logic, нелинейная динамика и т.п.) и адаптация важнейших обобщенных конструкций к наличному состоянию школьных знаний, касающихся анализа и существа возникающей «проблемной зоны» школьной математики. Разработаны на основе концепции фундирования опыта личности технологические конструкты и процедуры, компьютерный дизайн нелинейной динамики проявления синергетических эффектов и выявлены динамические инварианты в ходе освоения сложных понятий. Актуализированы процессы интеграции математических, информационных, естественнонаучных и гуманитарных знаний в ходе обучения математике. Показана эффективность процессов управления математическим образованием с синергетическим эффектом для развития интеллектуальных операций мышления и повышения качества освоения математики.Ключевые слова: управление математическим образованием, наглядное моделирование, компьютерный дизайн Перспективы Науки и Образования Международный электронный научный журнал

Introduction. The problem of improving the process of organizing and supporting the project and research activities of schoolchildren through intelligent management for the purpose of self-organization of the individual, understanding and comprehending complex mathematical knowledge as a principle of personal development is relevant and far from solved. Intelligent systems provide the process of individualization of learning, the establishment of personalized and computerized feedback of cognitive and creative processes. The purpose of the article is to assess the student's readiness for research activities in the context of designing a hybrid intelligent learning environment. Materials and methods. The assessment of the student's psychological readiness for research activities in the conditions of using a hybrid intellectual environment was carried out on an experimental representative sample of students of 1-2 courses of secondary vocational education (n1=42) and students of the senior classes of secondary schools (n2=30). The diagnosis was carried out using the intelligence structure test of R. Amthauer, the creativity questionnaire of D. Johnson, the test "Individual styles of thinking" by A. Alekseev, L. Gromova, the methods of value orientations by M. Rokich, etc. The significance of the differences was established by means of Student's t-test, Fisher's angular transformation, χ2-test. The results of the study. The assessment of psychological readiness for research activities in mathematics was carried out on the basis of the developed nine parameters of scientific potential. The presented results allow us to pre-set the framework of boundary conditions in order to minimize the imprinting time of a hybrid intelligent system (including the selection of the neural network topology). For all three groups of criteria, differences by gender were established, for example, by the parameter "value orientations" (temp  = 2.26 > tcr = 2.02); by the parameter "creativity" (χemp2 = 6,02 ≥ χcr2 (0,05;2) = 5,99). And also by the type of educational institution, for example, by the parameter “motivation to achieve the result” (φemp = 0,186 > φcr = 1,64). Conclusion. The results of the research are of practical value, as they serve as a technological basis for establishing the boundaries and boundary conditions of the most significant parameters for the effective realization of scientific potential, expressed in the work of a specialized web interface created with the student's personal account.

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