Social demand for educational services currently requires disclosure and capacity development of each individual, formation of desire for self-improvement, self-determination and creation of conditions for self-fulfillment in different types of teaching and learning activities, including teaching and research activities. Singling out teaching and research activity among other types of teaching and cognitive activities in the article and emphasizing its systemic and systematic organization is significant considering that the delineated area of activity is seen, on the one hand, as one of the most effective means of personal development, on the other, as a method aimed at the development of the students' teaching and research skills. The suggested theoretical rationale and guidelines allow a teacher to realize these approaches practically in the educational process of teaching mathematics.

activities, research activities, teaching and research activities, teaching and research skills, teaching and research tasks