Synergy of complex systems and knowledge mastering as a factor of creative potential growth of each school student

Introduction. In modern conditions, the processes of school (specialized classes) mathematical education management based on synergy manifestation in the development of complex systems and knowledge during the search and research activities of each school student are a relevant area. Namely, on the basis of mathematical and computer modeling symbiosis, "problem areas" are updated and technologies are developed for generalized constructs adapting of complex systems and knowledge to school mathematics, including the modern achievements in science (synergy of Schwartz cylinder, elements of fractal geometry, theory of an information coding and encryption, fuzzy sets and fuzzy-logic, theory of L. Schwartz’s distributions, nonlinear and holomorphic dynamics, etc.) with the effect of creative potential increasing of each school student. Research problem: what is the content and technologies adapting synergy of complex mathematical knowledge to school mathematics with the effect of creative potential increasing during the search and research activities of each school student. The aim of the study was to develop the didactic foundations for synergy manifestation in complex knowledge teaching in mathematics at school with the effect of creative potential increasing during search and research activities of each school student. Materials and methods. The source base of research is the methodology of mathematical and computer modeling integration in the course of generalized constructs of complex systems and knowledge studying, method of parameterization and technology of mathematical objects visual modeling and founding of personal experience, computer design and computational methods of research results, methods of cultures dialogue and variability of perception modalities and growth of each student’s creative potential measurement. KEYWORDS Results. The factor – impetus for synergy manifestation in complex knowledge teaching in mathematics is the actualization of perception modalities typology and growth factors parameters of each school student’s creative potential, definition of technology stages of complex systems and knowledge studying, the analysis of standards and new results of “problem zone” studying at school mathematics (surface area and parameterization of Schwartz cylinder). Conclusion. The proposed innovations contribute to an effectiveness increasing of an innovative methodology for developing the creativity of each school student in search and research activities and an improving the quality of school students' mastering of mathematical constructs and procedures. The scientific novelty of the results of multi-stage mathematical and information problems studying for modern scientific knowledge adapting to school mathematics lies in synergy justification and technology in teaching mathematics to each school student and an updating the technology of mathematical and computer modeling symbiosis.