The paper is devoted to the implementation of competence-based approach to professional education. The paper describes the author's experience in the development of normative and methodological and didactic materials of competence-based approach implementation to the formation and the diagnostics of specific subject competences in teaching students of mathematical specialties. A general approach is proposed to the allocation of knowledge and skills as a component of competencies. The authors constructed an algorithm for the determination of levels of formed competencies, criteria, scale and means of evaluation. The developed methods are implemented on the example of the special subject of the mathematical competence. This approach is universal and can be used to develop similar materials for other competencies.