The dissertation is devoted to the problem of scientific substantiation of the theoretical-methodological bases of formation of professional orientation of the individual students in the senior profile school during their mathematical training, creating and implementing real learning process of methodical system of professionally oriented teaching mathematics. The dissertation is offered the concept of mathematical training of pupils of profile school which basic provisions are based on: the role of mathematical training in education; on the group of the principles, among which the classical didactic principles; the principles of profile training; the principles of mathematical training of seniors; the principles of design of process of training in mathematics at the profile school. Methodological tools of research of problems of profile differentiation of training are chosen: in historical aspect – the comparative approach (for comparison in the sphere of a diachrony and comparison of the phenomena removed spatially); general scientific approaches (system-structural, operational, axiological, semiotic, competence) to provide training, which ensures the formation and development of the individual pupil; task approach to teaching mathematics, which provides the organization of mastering the content of professionally directed training of mathematics profile school pupils through the introduction of a learning content professionally designed tasks; the state documents on updating and improvement of the content of mathematical education; the historical and modern tendencies of development of school mathematical education in the context of its profiling. The study analyzes the concept of «professional identity», «professional training», clarified that the latter is the category of pedagogical science, and is based on the principle of professional orientation courses, which, in turn, determine professionally directed learning. The author's interpretation of the term «the learning mathematical activity» is offered. Its levels and means of teaching pupils for transition to higher levels of mathematical activity are defined.

The study of the psychological foundations of teaching of senior pupils to mathematics in the profile school has made possible the construction of a structurally meaningful mathematical subject competence model of a graduate. The structural components (target, preparatory, procedural and effective) are interconnected in a model. The content of each component is determined by the educational profile and aimed at forming a competent graduate of the profile school with an appropriate level of mathematical training. The achievement of the objectives and problems of modern education in personal development of pupils, to formation of a professional orientation of the identity of seniors in profile training of mathematics is promoted by introduction of methodical system of training of seniors to mathematics. This system dialectically combines the purposes, the contents, the methods, the forms and the tutorials directed on formation of professionally significant qualities of the identity of graduates of profile school; considers physiological features of pupils of the senior school age; provides introduction of psychology and pedagogical approaches to studying and development of the identity of the senior, adapted in the conditions of information society. The methodical bases of realization of the task approach are worked out to the studies of mathematics at the profile school. The task approach provides organization of mastering of maintenance of the professionally directed studies of mathematics senior pupils through introduction to maintenance studies of the professionally directed tasks, that is oriented to the level of mathematical preparation of senior pupils and sent to forming of interest in the professional sphere «the mathematics» and also forming professionally of important qualities of personality of pupils. In research system requirements are set forth the professionally directed tasks in maintenance of studies of senior pupils to mathematics. The frame model of individual educational trajectory of pupil is worked out in the process of his mathematical preparation. The efficiency of the theoretical and methodical bases and the developed methodical system is experimentally proved. The efficiency of its introduction in the educational process of senior school in the conditions of its profiling is checked.

Dissertation for the degree of doctor of pedagogical sciences, specialty 13.00.02 – theory and methodology (mathematics). – Bohdan Khmelnytsky National University at Cherkasy. – Cherkasy, 2015.