Abstract: A system of criteria for evaluating the solution of problems from the subject area while training future teachers of mathematics is described. The criteria are formulated in terms of activities and are aimed at strengthening the professional component of the process of mastering mathematical disciplines. Using this system of forming criteria in the study of basic structures of calculus is proposed.

Abstract: The article describes the main difficulties that students face in the initial period of study at a higher educational institution as part of the study of mathematical disciplines. Possible ways of overcoming these difficulties for students in the field of training Pedagogical education – future teachers of mathematics – on the example of the discipline «Mathematical Analysis» are given.