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| 1 | Ukhta State Technical University annually trains students from near and far abroad in bachelor’s and master’s degree programs in basic educational programs in Russian. Despite passing the propaedeutic mathematics course at the preparatory department, students experience significant difficulties in studying higher mathematics in the first year. The initial testing conducted for the purpose of the first diagnostics of knowledge in the field of mathematics and the Russian language showed that the majority of students make not mathematical errors related to solving equations, inequalities, etc., but linguistic errors related to misunderstanding of the verbal text of the subject content. The obtained test results, and the studied experience of teaching mathematics to foreign students in universities of the Komi Republic and other regions, served as a reason for the development of a special own teaching system. The methodological basis of the teaching system is the principle of gradual expansion of knowledge, skills and abilities in the language, subject-language and subject-thematic area in a non-native Russian language, ensuring the normalization of the linguistic load and the achievement of the planned teaching outcomes. The main components of the system are: the goals and content of teaching adapted to the teaching of foreign students; interactive teaching methods (interchange of topics, interchange of tasks, interdictants, etc.); collective organizational forms; specialized educational resources (didactic materials with methodically sound lexical and grammatical constructions, bilingual mathematical dictionaries, visualization of educational information, etc.). The search and development of effective organizational forms and methods of teaching foreign students are actual tasks that require a great personal contribution and professionalism of teachers, and productive cooperation with the educational structures of the university aimed at social and linguistic adaptation of students and support of the educational process. The ideas of teaching mathematics to foreign students put forward and implemented in pedagogical practice allow us to talk about the development of a system of teaching students who do not speak Russian well at th e university. Keywords: technical university, teaching mathematics in a non-native language, subject-language and subject aspects of teaching, the principle of gradual expansion of knowledge, special didactic materials, interactive teaching methods | 777 | ||||