The article highlights issues related to the implementation of bilingual education in Ukrainian technical universities. The study of this problem contributes to the training of engineering specialists who are able to carry out professional activities in the conditions of a foreign-language multicultural environment. The model and levels of implementation of bilingual higher mathematics teaching/learning for students of engineering and technical specialties is considered. It is noted that the system of bilingual education should be integrated into the general model of the organization of training engineering personnel in a specific specialty. The formation of a certain level of students' foreign language communicative competence is considered as a criterion for the allocation of training stages. The following stages of bilingual mathematics teaching/learning in technical university are distinguished: preparatory, transitional, actual bilingual. Each stage of bilingual teaching/learning is analyzed in detail from the following points: 1) direction of content (socio-cultural, mathematical, scientific), main unit of content (bilingual didactic element, bilingual subject-thematic module, discipline in a foreign language); 2) organizational forms and methods of training (integrated lectures and practical classes; conversation; project activity; information technologies; traditional, developing learning methods; elective course, special course or optional classes; text information activity; solving language tasks; methods of active learning; soft immersion; problem-based learning, independent work with educational and scientific literature); 3) the ratio of native and foreign languages (duplicative model, additive model, parity model and displacing model). The designed model of bilingual mathematics teaching/learning ensures the formation of bilingual subject competence in mathematics and provides an interdisciplinary synthesis of subject, linguistic, general technical (engineering) and cultural components.
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