Problem and aim. The search for relevant solutions to the restructuring of the architecture of modern education, elements of a new system through the organization of an intellectual learning environment adapted to the research activities of schoolchildren on the development of complex mathematical knowledge is a research problem. Materials and methods. 52 teachers and 234 students of schools in Moscow (Russian Federation) took part in the survey. Diagnostic methods were aimed at obtaining data on the use of various digital resources and tools in everyday learning activities and the level of their intellectualization. The methods of descriptive statistics were used (variation series, histograms, measures of central tendency and scatter), as well as Pearson's χ2-test. The results of the study. About 90% of the surveyed teachers and 80% of schoolchildren spoke in favor of the idea of introducing intelligent systems into the learning process, but more than 75% of respondents cannot give examples of such systems and environments. The opinion of trainees on the introduction of digital tools into the educational process differs significantly from the opinion of their mentors (χ2 emp=33,4> χ2 cr (0,01)=2,65). The main stages of designing an intelligent learning system are presented: the development of methodological provisions for the intelligent management of the educational process; determination of personalized parameters of scientific potential that determine the structure of educational and research content; development of a database and knowledge of the subject of project activities; choice of architecture and functionality of the hybrid neural network. Conclusion. The author's methodological and technological solutions will provide scientists with a reference point for further research in the field of improving high-tech forms of e-learning, and teachers will have the opportunity to explore practical ways to implement personalized and adaptive distance learning through automated intelligent systems. Keywords: intelligent systems, research activities, teaching mathematics, complex knowledge

Introduction. The problem of developing and implementing intelligent digital technologies in the system of teaching subject areas of knowledge for the purpose of self-organization of the individual, understanding and comprehending complex mathematical knowledge as a principle of personal development based on individualization of learning, establishing personalized and computerized feedback of cognitive and evaluative processes is relevant and far from solved. In this problem field, the issues of organizing the research activities of students in the process of adapting modern achievements in science to school mathematics through intellectual management are updated. Materials and methods. To identify new trends in the development of the concept of "research activity", methods of theoretical and methodological analysis (comparative, retrospective, modeling), analysis of mathematical, psychological, pedagogical, technical literature, methods of systematization of existing experience on the research problem were used. The possibilities of methods of intelligent management, design of a hybrid intellectual learning environment for creating a model of research activity are studied. The results of the study. A didactic model of research activity is developed based on the use of hybrid intelligent systems in the course of adapting modern scientific achievements with the manifestation of the effects of self-organization of the individual. The author's concept of intelligent management of the educational process in a hybrid intellectual learning environment was the structure-forming module of the model construction. The system of principles considered in the context of the unity and mutual influence of the three components of the structure of the information and educational space is formulated and justified: a set of digital educational platforms and technologies; digital interaction infrastructure in the context of the interactive triad "teacher-computer-student" of the educational process; digital information and educational content. In the course of mastering complex knowledge through historiogenesis and the range of its applications, technological constructs of clusters of foundation components of the generalized structure are built in the direction of building individual educational trajectories of schoolchildren using hybrid neural networks that make up the content component of the research activity development model. Conclusion. The results of the study are of practical value, as they serve as a methodological basis for creating a software package that implements the functionality of a hybrid intelligent system for developing students' research activities based on the developed principles and structural components using expert systems and fuzzy modeling.

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At the present stage of society's development, there is an increasing need for highly qualified specialists who are ready for continuous updating of knowledge and skills, solving research problems in their professional activities. In this regard, one of the important tasks of the implementation of educational programs is the achievement of a high level of research competence by graduates. Teaching mathematics opens up unlimited opportunities for the development of the intellectual sphere and research skills of schoolchildren. However, the insufficient development of pedagogical technologies focused on the implementation of psychodidactic patterns of research activity development is a negative factor that prevents the realization of the developing potential of mathematical disciplines. The article presents the author's approach to the organization of research activities of high school students, based on the idea of integrating the process of educational cognition and modern digital technologies. As a key aspect of personal development in teaching mathematics, we consider the activity of mastering complex knowledge in the course of performing ordered, forming a single motivational and applied integrity of the complex tasks of a research nature, in the process of which there is an active mastery of knowledge, deeper penetration into the essence of mathematical concepts,methods, ideas. At the same time, intelligent management of research activities of high school students is carried out within the framework of using the functionality of a hybrid learning environment that integrates the functions of artificial neural networks, genetic algorithms, fuzzy logic, expert systems, providing individualization of learning, synthesis of mathematical and computer modeling of the content of knowledge and procedures. The paper describes the content and functionality of the basic modules of the intellectual learning system, describes the theoretical, methodological, and technological aspects of the organization of research activities of high school students to master complex mathematical knowledge.

The study is aimed to develop the open innovation model of student’s research activities based on the adaptation of modern scientific achievements in the context of transition to sustainable development of the education system. It advances a general approach to the design of the structure and implementation of main components of hybrid intelligent system to integrating a production-frame model of knowledge and neural network algorithm for the formation of an individual learning scenario. The software implemented as a hybrid intellectual environment for organizing student’s research activities is conventionally represented as a combination of blocks: a graphical user interface; technological core of hybrid learning environment, including a neural network classifier and a training data bank; a system for interaction and activation of third-party software and software and hardware. The technological basis for the individualization of the learning trajectory is the automated construction, forecasting of development and interactive correction of competence-oriented and associated models of a subject area. As a technological core, it uses a hybrid system of interaction between an artificial neural network and an expert system functioning based on a database of research projects. The presented innovation algorithm makes it possible to implement the technology of student’s research activities organizing as a process of setting up the generalized constructions of complex knowledge. Further research prospects consist of the program implementation of hybrid intellectual learning environment for the development of student’s research activities and its preparation for trial operation.