To the question of ways to enhance students' educational and cognitive activities

The need to train specialists with a high level of professional training requires the development of teaching methods and tools that ensure the formation of professional competence of future engineers, including the activation of the stu-dent's educational and cognitive activity, shows the relevance of developing forms and methods of such activation. In this paper, the authors consider one of the possible methods for activating the educational and cognitive activity of uni-versity students, for which it is divided into levels: reflection, comprehension, algorithmization and control; describe the psychological processes implemented at each of them. At all levels of cognitive activity, there is a consistent move-ment through the stages: recognition, reproduction, application and creativity. Thus, the process of learning the educa-tional material can be represented by a matrix of dimension. The work shows the organization of the student's educa-tional and cognitive activity at the first, elementary level, where at the stage of recognition there is a movement from reflection to control. An example of a mathematical problem from the "Analytical Geometry" section of the first level of complexity is given, and the solution consists of four educational components. The proposed approach makes it possible to combine the educational material into a common system by dividing it into four levels, corresponding to the degree of difficulty of the tasks.