Currently the pedagogy is in crisis, which is characterized by a change of the ideal of education, its transition from the educational paradigm to the cultural, from the 'educated person' to the 'person of culture'. The 'person of culture' matches irreducible to each other cultures in his mind, focuses his activities on the others, and this person is predisposed to a dialogue. Cultural models of education are included in the research program of the Russian Academy of Sciences. One such model is a student-oriented education. Personality-oriented model of education is aimed onto discovery and development of the individuality of each child and based on the formation of the basis of his personal culture. Formation of the subject relations in the pedagogical process can not be achieved through the traditional forms and methods of work. In addition to traditional organizational forms of education a teacher should use those which would help to solve the following problems as: the use of reflective analysis, dialogic interaction, conducting a research. The foundation of modern educational activity is self-education training in the process of pre-emptive execution of creative tasks. Organizational forms of learning that can be used in the process of teacher's work on the formation of a subject position of students are: a group discussion (the model assumes a certain sequence of goals and challenges for leading the discussion); training and simulation games; discussion with the division of roles; game forms of work; analysis of practical situations (where there is a change in the teacher's role; now the teacher is a catalyst of the discussion). Thus, a student representing a certain age period of development, as a subject of academic activities at each level of the education system is characterized by the specific nature of learning motivation, by system of relations and especially by the training activities.