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The constantly changing labor market requires the formation of specialists with a desire for self-improvement, capable of moving from one type of activity to another, perhaps not related to the previous one. This task can be called a priority in the field of professional education, which dictates its relevance for mathematics education. When setting the formulated problem and solving it, special attention should be paid to recognizing the importance of the formation and development of the educational potential of the creative activity of students. The article presents an analysis of the possibilities of a continuous education system, put forward theoretical provisions and pedagogical conditions for the effective formation of research skills of students within this system. The characteristic of the structural-content model of the formation of the research competence of future teachers (or specialists of other professions requiring the formation of research competencies) in the system of three-level education is given on the example of studying one of the directions of discrete mathematics.

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