The problem of subject preparation of pre-service math teachers is considered from the perspective of modern psychological and pedagogical science. Independent learning and cognitive activity acts as a necessary condition for improving the quality of teaching elementary mathematics. The relevance of the problem study, stated in the article, is due to the increasing amount of independent work at the university, the need to move from teaching to learning and the insufficiently developed methodology of its organization. In this regard, this article is aimed at identifying psychological and pedagogical conditions for improving the effectiveness of independent learning and cognitive activity of future teachers of mathematics. The leading methods for studying this problem were theoretical analysis of the problem coverage, questionnaire, included observation, analysis of the products of creative activity. The study involved students of the pedagogical department of the Institute of Mathematics and Mechanics named after Nikolai Lobachevsky of Kazan Federal University and graduates, whose experience is less than three years. It was revealed that the majority of future mathematics teachers has not formed an understanding of the role and need for independent activities, and, as a result, readiness and ability to organize it. Accordingly, the study reflects the results of the organization of students’ independent work, based on the idea of a "flipped classroom". The program on the organization of independent activities of future mathematics teachers, presented in the article, is aimed at ensuring active and meaningful participation of everyone in educational process, at developing skills to diagnose their own cognitive need to expand and deepen knowledge, and to master time-management skills. It will help to independently find the best ways to solve educational problems and organize such work in a future professional activity.