Main problem: the article raises the question of the need to create innovative methods and models of functional-system thinking and pedagogical cultivation of students' intellectual abilities to improve the quality of education. Emphasis is placed on the development of reflexive, schematic, organizational and communication abilities. Purpose: to provide an overview of the basic theoretical concepts of functional tools for self-determination and interaction of subjects (teacher and student). Methods: observation and analysis of teaching activities of teachers, systematization of methods and models of functional-system thinking of a teacher. Results and their significance: the article highlights the basic theoretical concepts of functional tools for harmonious personal, social, professional self-determination and interaction of subjects in the context of the innovative and technological development of the country in abstract-concrete and task-qualification coordinates, to create conditions in the professional activities of methodologists, teachers, managers of all educational organizations and students in colleges and universities.