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.

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The  thesis  deals  with  actual  problem  of  the  shaping  intellectual  skills  of  senior  pupils  which emerge the factor of the readiness a personality to creative activity.  The condition of the problem in its history development is analysed in the process of study.  It is motivated  by the need of structuring such complex of larval formation as intellectual skill and the use of the designed structure on stages of diagnostic, the shaping and tracing dynamic changes to the process of learning intellectual skills. It is proved that the observance the didactic conditions of the efficient shaping the pupils intellectual skills has significant influence on increasing level of the shaping senior pupils intellectual skills. It is designed and improved the didactic model of shaping pupils intellectual skills, the structuring to scholastic information by means of modules, the intersubject task approach to the studies of natural subjects, the optional course "Cognition  bases  in  education",  pupils  diary  book-keeping  of  the  individual  observations  for  creative growing of the personality.

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Teachers and students of the Department of Mathematics and its Methods of Teaching at Kryvy Rih State Pedagogical University took part in the VIII International Scientific and Methodological Conference "Problems of Mathematical Education" (PMO-2019), which took place on 11-12 April, 2019, at the Bohdan Khmelnytsky National University in Cherkasy.

Problems of conference:

   Prospects for reforming mathematical education in general and vocational schools

• Setting up Mathematics teaching in the new Ukrainian primary school
• Challenges of upgrading mathematical education in higher educational institutions
• Enhancement of mathematical and methodical training of Mathematics, Physics, and Computer Science education students
• Development and application of ICT in teaching Natural Sciences and Mathematics
• Interdisciplinary connections and STEM-education
• Foreign experience of teaching Natural Sciences and Mathematics in secondary schools, vocational schools and higher education institutions
• Professional development of Mathematics teachers

Teachers and students of the Kryvyi Rih State Pedagogical University at the conference made the following reports.

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March 3, 2019 marks the 100th anniversary of the birth of the outstanding scientist-mathematician O. V. Pogorelov. In addition to fruitful scientific work, he paid special attention to mathematical education. Kharkiv National University named after V.N. Karazin together with the Kharkiv Academy of Continuing Education held National Ukrainian Conference "Problems of Teaching Geometry in Educational Institutions: Theory, Methodology, Practice" for teachers of schools, teachers and academics from the universities of Ukraine on April 8-10, 2019. Participants of the conference participated in the conference and delivered their reports to Senior Lecturer of the chair of Mathematics and methods of its teaching Dmytro (Yevhenovych) Bobyliev and Associate Professor Tetiana (Hryhorivna) Kramarenko. The conference was held at the Kharkiv National University named after V. N. Karazin.

Conference sections:

1. Mathematical education in Ukraine and the world: history, state, innovations.
2. Teaching geometry in school and higher: theory, methodology, practice.
3. Competency approach in mathematical education and educational measurements.
4. Use of computer mathematical systems in mathematics courses.
5. Distance learning forms of mathematics: state, problems, perspectives.
6. Problems of creating textbooks and geometry programs.
7. Interdisciplinary connections in mathematic classes.

1. D. Bobyliev made a presentation "Implementation of the connections of concepts of metric space with the school course of geometry while learning the functional analysis of future Mathematics teachers"
2. T. Kramarenko made a presentation "Competence potential of textbooks of geometry O. V. Pogorelov for secondary school"

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Stating the problem. The subject of the course "Functional Analysis" is the scope of functions and their reflection. Functional analysis as an independent section of Mathematics developed at the beginning of the last century as a result of the generalization of mathematical analysis structures, linear algebra and geometry. Since then, its ideas and methods have penetrated into all the fields of Mathematics, Physics and applied sciences on the rights of a powerful generalization theory and a convenient tool for the specific problems study. The study of functional analysis is typical for mathematical specialties of classical universities. But in the pedagogical higher educational institutions this course is found in the curricula of the specialty 014.04 Secondary education (Mathematics) with the additional specialty 014.09 Secondary education (Computer Science). The bachelor's program in these specialties involves studying the elements of functional analysis. It is usually the basic part of the fundamental cycle with the academic study time one semester, while the number of class hours is small. The framework of academic study duration, its applied orientation and the students’ level of basic training in modern pedagogical universities do not allow them to learn such a complex mathematical discipline from the standpoint of the classical approach, which provides for the fundamental and self-sufficient supply of purely theoretical material. In addition, pragmaticallyminded students are not interested in the idea of generalization and formalization of mathematical constructions. Obviously, the motivation increases if you bring the academic course to computing practice with compulsory engagement of computer technology. For future mathematics and computer science teachers it is necessary to emphasize the applied role of functional analysis, which is reduced to the analytical substantiation of the effectiveness of the numerical methods application. 

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Candidate of Pedagogical Sciences, assistant of the Department of Mathematics and Methods of its Teaching Kateryna Polhun presented the report “Organizing inclusive learning of physical and mathematical disciplines by students with disabilities in technical institutions of higher education”. The report contains the results of theoretical and experimental research of the organization process of inclusive learning of physical and mathematical disciplines by students with disabilities in technical institutions of higher education.

The scientific analysis of the issue of inclusive learning of persons with special needs has shown that the research was conducted in the following areas: the theoretical and methodological foundations of inclusive education; coming-into-being of inclusive education in Ukraine; the implementation of inclusive learning under the conditions of a higher education institution; the psychological support for students during classes in an inclusive group; the use of information and communication technologies when teaching physically handicapped individuals.

The basic directions of development of higher education of persons with special needs are analyzed; the conceptual-categorical apparatus of research is formulated. The basic concepts of the research are «inclusive education», «inclusive learning», «inclusive learning environment». Psychological factors of organizing inclusive learning of physical and mathematical disciplines by students with disabilities in technical institutions of higher education are identified.

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Candidate of Pedagogical Sciences, Docent of the Department of Mathematics and Methods of its Teaching Tetiana Кrаmаrеnkо presented the report “Forming of personality qualities of schoolchildren in the process of the computer-oriented studies of Mathematics”.

Report cleared out the integral computer-oriented approach. It in detail its use in the study of school course of Mathematics, directed on forming of personality qualities of student such as organizational, cognitive, creative; ones; criteria and levels of formed of personality qualities are specified. It was carried out the maintename of mathematics, proper theoretical and task material, in particular, for the deep study of mathematics, pedagogical programmatic facilities, computer-oriented methods and forms of studies, were considered principles of construction of the system of developing tasks. The methodical recommendations are developed in relation to the use GRAN1, GRAN-2D, GRAN-3D, DG, GeoGebra  in an educational process. The results of pedagogical experiments confirm the efficiency of the offered components of the computer-oriented system methodical of studies.

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