Founding complexes of multi-stage mathematical and informational tasks in the hybrid intellectual environment of school mathematics
Authors:   Yaroslavl State Pedagogical University named after K. D. Ushinsky, Smirnov Eugeny I. , Tikhomirov Sergey A. ,   Yaroslavl State Pedagogical University named after K. D. Ushinsky, Zubova Elena A. ,   Tyumen State University
Published: September 2023

Introduction. The development of educational motivation and creativity of each student is possible in the conditions of complex knowledge level adaptation with the support of hybrid intelligent systems. The multiplicity of goal-setting and choice, the symbiosis of mathematical and computer modeling become the real result of founding complexes mastering multi-stage mathematical and informational tasks in student’s research activity in secondary school. These processes lead to each student’s self-organization and cultures dialogue, support for the development of scientific knowledge methods and modern achievements in science adaptation to school mathematics. The main objective of the study is the development of methodological, substantive and technological foundations of the design and actualization of digital transformation processes and hybrid intellectual environment support of student’s scientific potential growth. Support of hybrid intellectual environment in the development of hierarchical bases and founding complexes of multi-stage mathematical and informational tasks in student’s research activities are revealed. Materials and methods. Using the methods of visual modeling and founding of personal experience, the architecture, parameters and functional organization of the intellectual management of each student’s design and research activities in a rich information and educational environment of complex mathematical knowledge mastering are determined. Founding complexes research of multy-stage mathematical and informational tasks are presented as mechanism of each student’s scientific potential growth. Mathematical and computer modeling is the main instrument of modern achievements in science adaptation to school mathematics. Results. We propose the following typology and stages of design levels of student’s research activity in hybrid intellectual environment: search-reproductive, empirical, theoretical and creative. The architecture, content and structure support of hybrid neural environment determine the factors of effective growth of each student’s scientific potential. The technological stages of founding procedures into the adaptation processes of complex knowledge introduction (modern achievements of science) to school mathematics reveal the orientation and essence of pedagogical innovations. The model of founding generalized cluster for the adapting process of complex knowledge mastering (using the example of fuzzy sets and fuzzy logic) integrates the motivational, meaningful and applied complexes to support the creative activity of each student. Conclusions. The implementation of these stages led to synergetic effects manifestation and phenomenological type of modeling reflection of generalized construct essence and each student’s research activity with hybrid neural environment to support the growth of student’s scientific potential.