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Abstract: The urgency of this problem is due to the development of cooperation in the education system of Russia and foreign countries and the achievement of succession of natural-mathematical pre-university training. Organization of science and mathematical education at pre-university level in Russia is significantly different from the system of pre-university training in the countries of the Bologna process. This fact reduces the continuity of pre-university training in Russia as compared with other countries, which significantly impedes academic exchanges. In addition, poor knowledge of foreign languages reduces the effectiveness of the inclusion of Russian school leavers in the educational space of Europe. The math program itself has low variability in comparison with foreign analogues. The revealed problems of naturalmathematical education in Russia have allowed to develop a set of measures to improve the quality of education and its orientation to the possibility of attracting foreign students. Particular attention is paid to the need to develop courses in mathematics and science in English that would allow one to create cultural foundations of international space of cooperation of students as well as teachers practicing bilingual education. The article outlines certain forms of organization of educational process at schools by providing specially created training programs to bridge the gap of development programs in terms of full general secondary education in Russia and abroad. The proposed package of measures is designed to promote cooperation in the field of natural and mathematical education between different countries.