Abstract: The article was prepared within the framework of the project "Development of a model of a unified educational space of organizations of preschool and general education in Ufa with in-depth study of the Bashkir language", implemented at the Bashkir State Pedagogical University named after M. Akmulla. The subject of the research is modeling the educational space of preschool and general education organizations for the development of professional competencies of a teacher. The structural and functional model of the unified educational space is developed on the basis of the principles of multidimensionality, horizontal learning, personification, eventfulness, subjectivity, continuous improvement of professional skills, continuity, guided development and post-training support. The model presents and describes: components of the educational space (subjects, technologies, events and phenomena, partner organizations, resource provision); functions (diagnosis of professional deficits of a teacher, formation of a map of professional deficits, determination of points of growth of a teacher and the construction of his individual educational route); mechanism of implementation of functions (automated assessment of subject and methodological competencies, determining the level of professional competencies, building an individual educational route). The article reveals the features of the functioning of the Center for scientific and methodological support of teaching staff. The description of the research and methodological blocks, as well as the mobile learning block and the block of high-tech learning tools is presented. The scientific and theoretical foundations of the management of the unified educational space of preschool and general education organizations have been developed to improve the level of professional skills of teachers. The main effect achieved in the implementation of the proposed model is the integration and coordination of teachers of preschool and general education organizations within a single educational space. Innovative educational environment of continuous professional development of teaching staff contributes to their professional development and career "lift"

Abstract: The object of this research is the process of advanced training of teachers; the subject is the system of distance education for teaching staff to acquire tutoring skills. Tutoring is analyzes as the teacher skills to plan the individual educational course for a particular student considering his intellectual and emotional inclinations, basic knowledge and optimal learning capabilities. The comparative analysis of functions and optimal character traits for the positions of a teacher, curator and tutor is provided. The author underlines that mastering tutoring techniques substantially complements the initial specialty of a teacher. The scientific novelty consists in implementation of distance education technologies for converting teacher’s position into tutoring on the basis of his pedagogical experience. It is concluded that distance education for training tutoring skills is based on the informational and communicative competence and caters to the distance consulting methods and system of complex educational-methodical tasks. It is noted that tutoring is a specific pedagogical position of a modern teacher that suggests the implementation of new pedagogical technologies, transformation in the structure of discipline and lesson, as well as organization of educational-upbringing process.

Abstract: The subject of this research is the application of the information-communication technologies in education. The object is the methodical approaches towards the construction of lectures-presentations in the college math course. Computer technologies allow integrating the productive aspects of the various educational methodic, as well as their effective realization in the new form of lectures. The article presents the experience of development and realization of the lectures-presentations for math course based on the principles of cognitive visualization. The lecture-presentation is aimed at intensification of the student educational activity and increase of the efficiency of education. The lectures-presentations are being developed using the Microsoft Power Point for static and dynamic representation of information. The educational presentation by animation and control of the screen can enrich the process of cognitive activity through illustrating what cannot be presented verbally. The proper developed and performed lecture-presentation also activates the processes of perception and digestion of information, and allows to significantly intensity the educational activity of the students, provide the methodological grounds for educational and scientific activity.