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Abstract: The article reveals the urgent problems of teaching mathematical disciplines to foreign students in Russian universities and search for the best ways of their solution in additional education. The reasons reflecting the desire of foreign students to get Russian education are disclosed. The research urgency is caused by the appearance of a new complex of organizational-methodological tasks in the universities of the Russian Federation related to their transition to the international market of educational services, development and introduction of competitive and relevant educational products. A leading approach to the study of this problem is the system approach, allowing to consider the peculiarities of educational process in the single-stage model of training foreign students on the example of the Mordovian State Pedagogical Institute. The article presents the experience and capabilities of the institute in the field of education of foreigners. It reveals the priorities of the Institute in the implementation of educational services for international students, aimed at creating favourable conditions to obtain high-quality mathematics and science education. The peculiarities of the system of additional mathematical education of the Mordovian State Pedagogical Institute are described by its structural components. The article presents some peculiarities of methods of teaching mathematical subjects to foreign students. The research was conducted on the basis of application of theoretical (study and analysis of psychological and pedagogical, scientific and methodological and educational literature, in particular research of programs of school of mathematical education of other states, in particular Turkmenistan) and empirical methods (observation and conversation with students and teachers of higher education institutions). The materials of the paper have practical significance for teachers of mathematics in the context of teaching foreign students in universities of the Russian Federation.