In the process of learning mathematics, students practice various forms of thinking activities aimed to substantially contribute to the development of their different cognitive structures. In this paper, the subject matter is a "cognitive obstacle", a phenomenon that occurs in the procedures of solving mathematical tasks. Each task in mathematics teaching should potentially be designed so that it contains requests that should be performed. Based on that, a cognitive obstacle that students face at the thought plan is created, as well as a cognitive challenge. In the process of "overcoming a cognitive obstacle" in solving the assigned task in mathematics teaching, it is necessary for a student to make an adequate cognitive effort and to optimally engage reference part of the actual cognitive capacity. The process takes place through exercising different thinking activities (thinking operations), using the previous knowledge and experience in solving certain groups of tasks. A system of cognitive obstacles should be grounded in the teaching mathematics, in order to enable an adequate level of thought activization of students and the development of various mathematical cognitive micro-structures (abilities, skills, knowledge, etc.). It also enables students to develop and improve their capacity of mathematical thinking.