The current changes in high education in the context of globalization have affected the educational institutions of all countries extensively. In the context of globalization, representation of national systems of high education in the world’s educational space determines their competitiveness. Today, the education, along with its traditional functions by transferring knowledge, has been also considered as a market. In the context of growing competition between universities in search of students, it is necessary to overcome language, mental, national, cultural, historical and pedagogical barriers. However, within these barriers, there has been still an overwhelming majority of the universities both in all countries including the Republic of Kazakhstan. In order to interact constructively in spite of these barriers, it is needed to take a step to make a planetary noosphere by the educators. In the process of the teacher-student relationship the growth of "self" in both of them, and its development take place. Considering the forms of internationalization and integration, actively participating in international student exchange programs, project activities, sandwich programs and other forms, the current generation of future Kazakhstan teachers has shown a certain willingness to go beyond the stereotypes and restrictions accepted in the society. The purpose of this study was to examine the process of formation of the transcultural competence in future educators as a tool of developing the students’ "self" personality, and propose practical ways of its formation in the context of university education. The transcultural competence of the personality has been a mix of puzzles that have been formed of the heterogeneous and, at first sight, chaotically combined elements of the self in the consciousness of an individual at the moment of their demand. It would allow an individual, in a supracultural space, to overcome the subjectivity of evaluating "one's own" and "others’", seeing their differences, retaining each of them and taking an individual position in the communication of cultures. The article highlighted the results of the approbation of teaching methods aimed at the formation of the transcultural competence of the individual.
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