The article considers some contextual, interdisciplinary and linguistic aspects of developing non-linguistic students' speaking skills necessary for cross-cultural academic communication, with special attention being paid to the their abilities to master the culture of debating, acquiring specific features of their future profession through learning specialized vocabulary and using a foreign language as an effective tool to reach the professional goals. The proposed strategy of FL communication

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... teaching is rooted in the basics of D. Dorner's situation integrity' theory, on the one hand, taking into account discovery patterns of science undergraduates' educational activity, on the other, and cognitive aspects of academic discourse as well with an emphasis on acquiring professional interlanguage dialogic skills. The proposed course of study is meant to master the professional speaking skills of science undergraduates. The algorithm of teaching has been tested in FL classes with Maths and Physics students of MGOU (Moscow Region State University) during 2019/2020 academic year and obtained the positive approval of FL teaching staff.