In present article the possibilities of synergy revealing of mathematical education in secondary school on the basis of modern achievements in science adaptation are investigated. The technology is based on the study of "problem zones" of the development of school mathematics with synergetic effects manifestation on the basis of visual modelling of founding environment using computer and mathematical resources. The technology of modern achievements in science adaptation to school mathematics (chaos "area" of lateral surface of Schwarz cylinder, fuzzy sets and fuzzy logic, fractal geometry, coding theory, etc.) on the basis of phased mathematical modelling and computer-aided design with the manifestation of nonlinear synergetic effects is developed. The founding cluster of generalized construct of modern knowledge, consisting of 4 implementation stages: "initial level" of the essence development of generalized construct for intuitive visual level, "functional stage" of awareness and correction of the features, options, and terms of limit process, "operational stage" of awareness and generality of temporal and functional sequence of learning activity of generalized essence of the construct, assessment stage of empirical verification of results, quantitative and qualitative analysis of teaching actions by means of mathematical modelling and computer-aided design, "integrative stage" aimed at the ability to translate the situation of entity's development into the processes of modelling, generalization and transfer. Each stage is integrated with two spirals of founding by means of processes equipment of essence deployment for generalized construct: motivation and applied maintenance of essence development, mathematical and computer modelling of synergetic effects manifestation and attributes. [For "NORDSCI International Conference Proceedings: Education and Language Edition (Helsinki, Finland, July 17, 2018). Book 1. Volume 1," see ED603189. Funding for this research was provided by the Russian Science Foundation.]