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Formulation of the problem. In modern economic conditions, the vast majority of master students of specialty "Secondary Education (Mathematics)" in NPU named after M.P. Dragomanov is in a situation of forced "duality" of their education. As a result, there are difficulties with the organization of the learning process of such students, as well as the quality of their assimilation of the material of the educational program. It seems natural to transfer such students to the dual form of education. This will solve a significant part of the mentioned organizational and methodological problems. Dual education requires fundamentally new forms of learning organization. An important element in its structure is the professional seminar "Basis of professionalism of teacher of general secondary education institution." This seminar is designed to quickly respond to current problems of young teachers that arise in the process of adapting to working conditions at school. Materials and methods. To achieve the aims of the article, we use empirical methods: our own survey using an electronic tool (Google forms), monitoring the learning process of students, as well as analysis of the results of their achievements. The article used a set of methods of scientific cognition: comparative analysis to clarify different views on the problem; systematization and generalization for the formulation of conclusions and methodological advices; generalization of pedagogical experience and observations Results. The content of the professional seminar we can divide into three main content modules - "Methods of organizing the educational process in modern school", "Modern methods of assessing the educational activities of students" and "Organization of extracurricular and educational work in modern school". Each of them is designed to form the professional competencies of the undergraduate in accordance with his (her) educational program. The content and procedure for studying of these modules is not strictly defined, this content should be tailored to the needs of a particular student. The head of the seminar also has the opportunity to involve external experts who are specialists in pedagogy, psychology, law, as well as practicing teachers and school administrators. Conclusions. According to the survey of masters and observation of their work during the professional seminar lessons, most students are positive about its introduction to the educational program and are satisfied with the quality of classes. All the material of the professional seminar curriculum is considered by master students as relevant and necessary for their further work that shows the correctness of the chosen direction of their training. Thus, the pedagogically balanced use of the dual form of education with the wide involvement of distance and mixed forms of classes based on modern technologies will ensure the proper quality of preparation of future teachers of mathematics.

Graduate student socialization has been studied in multiple disciplines, including communication. As their career trajectories change, faculty must consider how to socialize students into the field and their subsequent careers. Using a modified Delphi survey, we examined the differences in faculty and students’ perceptions regarding the content of a graduate professional seminar in communication. Results indicate that students would prefer a focus on implicit norms and the hidden curriculum, while faculty would prefer to focus on disciplinary content. We offer recommendations for developing a course that addresses both needs and, thus, simultaneously attends to the changing job market.