The necessity of forming a project-technical competency of students in technical universities is due to the transition of the industrial areas to science-intensive technologies and the need for active involvement of professionals in their elaboration, implementation, and technical calculations. In this process, a key role should be given to a teacher of physical and mathematical disciplines, his readiness for the process of the students' project-technical competency formation in the study of these disciplines. In this regard, this article actualizes the problem of developing methodological support for professional development of physico-mathematical sciences teachers, contributing to their choice of optimal content and technologies for teaching mathematics and physics, aimed at forming the project-technical competency of technical university students. The article materials may be useful both for teachers of physico-mathematical disciplines, and for teacher education university students-future teachers of physico-mathematical disciplines.

The article aims to identify features of the implementation of the programs applied bachelor degree in secondary and higher vocational education. The article presents the initial results of the implementation of applied bachelor programs in institutions of higher and secondary vocational education, identifies the peculiarities of application programs and academic bachelor degree, justifies organizational and pedagogical conditions applied baccalaureate programs, highlights the advantages and disadvantages associated with realization of the programs applied bachelor degree in education institutions of higher and secondary vocational education. The article may be useful in the development of requirements for the content formation of the theoretical and practical training of applied bachelor degree in higher and secondary vocational education; program design methods for the study of applied bachelor degree in vocational education.Keywords: applied bachelor degree, features of the programs, secondary and higher vocational education

The relevance of the problem how to form the high school students' professional competences is due to the fact that professionals with "competencies", which have versatile abilities confirmed by practical experience of independent socio -professional problems are demanded. The results of the study indicate that didactic tasks become the most effective resources in this process, which transform the learning goals of the teacher into a productive construct for key professional competences developing in learning and professional activity. In this regard, this article is focused on the scientific and methodological justification of instructional tasks' basic components' structure and content aimed at the development of university students' key professional competencies. The leading method to study this problem is monitoring of students' key professional competencies' formation in the process of didactic tasks' realization. The article presents the theoretical and methodological bases of students' key professional competencies' formation in educational tasks systematic using as a set of knowledge, skills, qualities, experience, and operationally practical ways of activities necessary for professionally -oriented functions' creative performing. The article can be useful to high school teachers, young scientists, graduate students, university Methodists, the students of the teachers' advanced training and retraining system.