The paper is devoted to developing the research competence in the process of student multilevel training. Upgrading the student’s ability for research activity is an important task of higher education that should be continually emphasized at all levels. The author suggests the model developing the research competence in the context of mathematical disciplines studies at bachelor level of different educational profiles: mathematical, natural sciences, vocational. The model in question represents the hierarchical tree of goals based on the principals of expansion, subordination and  correlative importance – all of them reflecting the links between the goals and the educational levels ( bachelor or master level) - which facilitates the plan systematization for achieving the main goal of students’ research competence development.

The essential content, criteria, indices and development levels of the competence in question are defined. The given approach provides the continuity in mastering the competencies at different levels in a sequential advancing from the theoretical to practical knowledge and makes it possible to avoid the formal approach to teaching the undergraduates.

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