In the present article one of “zones of modern achievements in science” of school mathematics by means of computer and mathematical modeling is investigated. Research concerns a problem of the modern section of mathematics development “fuzzy sets and fuzzy logic” by means, available to school, and by means of construction and adaptation to initial conditions of school knowledge of the major generalized constructs concerning the analysis and a being of fuzzy sets. The technology of school mathematics adaptation to the theory and practice of using of fuzzy sets and fuzzy logic on the basis of mathematical modeling and computer design of nonlinear dynamics of synergetic effects manifestation is developed. During development of difficult concept of fuzzy sets by means of visual modeling developed technological constructs of founding clusters of generalized construct components in the direction of availability and school mathematics maintenance. Equipment of a motivational field of school student’s research activity is revealed and the multiple goal–setting of processes of fuzzy sets and fuzzy logic development is realized. Means of communication on the basis of integration of mathematical, information, natural–science and humanitarian knowledge and procedures are developed. Research is conducted in the context of integration of mathematical and computer modeling at informative activity in small groups of school students and creations of conditions for manifestation of synergetic effects. Equipment and stages of the adaptation of modern achievements in science to initial condition of school students experience in longitude research are developed.