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Abstract: The problem of domestic education is not only in the bureaucratic vertical of education management, the problem is also in motivation. The authors confirm that it is necessary to radically change the pedagogical and psychological component of teacher’s training, and the content of General professional (primarily psychological, pedagogical and methodic) training. It is explained why the change of the content and organization of the educational process should be carried out on the basis of the ideas about the cognitive portrait of a student. The paper proposes a cognitive-information pedagogical paradigm based on the combination of cognitive, information and pedagogical technologies. A brief review of the works devoted to the cognitive approach to learning is given. The goal of this research is formation of the student's stable cognitive schemes with the help of a special learning environment — a communication network of group learning. To implement the method of cognitive training, it is proposed to create a group communication network, the key role is given to students, while the teacher is a facilitator, and a cloud storage of all necessary materials. Factors are indicated that contribute to the increase of the level of motivation of study of educational material by students. As one of the motivators to the study of the subject Methods of Teaching Mathematics is the cross-platform on-line processor of knowledge WolframAlpha, which allows the student to do various tasks (including research problems) not only in mathematics but also in science and technology, everyday life of man and society. Thus, systematic work by methods of cognitive training in accordance with the goals and objectives of the educational process contributes to the formation of a wide range of operating concepts as well as educational activities.