Abstract
The article presents the development of innovative technological constructs of professional training of future specialists in higher education on the basis of the deployment of spirals and clusters of founding of mathematical knowledge in the course of synergetic effects actualization in teaching mathematics. The founding procedures are based on the study of complex knowledge, fractal interactions and integrative relationships in modern mathematics and their transfer into the technological field of training. The components and content of teaching mathematics technologies and innovative activity of students to master the complex content of mathematics as a pedagogical task in various conditions of information technologies support are presented. Effective development of professional competences, communicative and personal qualities of students, increase of motivation of future specialists are predicted.