Gamova N.A., Girina A.N., Spiridonova E.V.
THE PERIODIZATION OF A.N. KOLMOGOROV AS THE BASIS OF IDEAS ABOUT THE HISTORY OF THE DEVELOPMENT OF MATHEMATICAL SCIENCE ^{[№ 4 ' 2023]}
The periodization of the development of mathematical science was proposed by A.N. Kolmogorov. He identifies four periods in the development of mathematics. The basis of periodization includes assessment of the content, level of achievements and features of mathematical research: its most important methods, results, ideas. Particular attention is paid to the development of probability theory structured according to Kolmogorov periods. The prerequisites for the formation of probability theory began to appear during the second millennium BC — the first period. During the period of accumulation of knowledge (before 600 BC), the concept of “chance” — the main concept in the science in question – began to develop. Until the third period, the concept was invariably associated with the philosophical category “fate,” that is, a certain predetermined process, which contradicts modern ideas about chance. Probability Theory received its unofficial name precisely from the period of elementary mathematics (before the 15–16th centuries) — the second period. The next period was called by Kolmogorov “Mathematics of Variables” (XVII–XVIII centuries). Since the beginning of the period of modern mathematics (since the 19th century), random variables and the patterns associated with them have come to the fore in probability theory. This is due to the general scientific growth in the 19th century. The main problems that arose by the end of the third period are being solved: all the basic concepts, rules for their application, and theorems are clearly defined. By the beginning of the 20th century — the fourth period–there was a need to formalize the acquired knowledge. Andrei Nikolaevich built a system based on modern and already developed by that time set theory and measure theory. The periodization of the development of mathematical science, proposed by A.N. Kolmogorov, with the rapid progress of mathematical knowledge and the emergence of information technologies in the future may require adjustments to the last stage of development of the history of mathematics or will lead to the emergence of a new stage of periodization.

Zubova L.V., Gamova N.A., Girina A.N.
FORMATION OF MOTIVATION OF PROFESSIONAL ACTIVITY OF STUDENTS OF ECONOMIC DIRECTIONS OF THE UNIVERSITY ^{[№ 4 ' 2020]}
The emergence of new production technologies put forward new requirements for a university graduate. In training, the formation of motivation for the professional activity of student training is actualized. The relevance of the phenomenon under consideration is due to the fact that motivation, acting as a conscious motivation, is a necessary factor in the volitional behavior of an individual, the basis for the professional development of an individual. To solve this problem, the authors studied the materials of theoretical and experimental research, reflected in the psychological and pedagogical literature on this topic. The content, forms and methods of motivation formation of professional activity of students of economic directions of the university have been developed. The analysis of curricula of special, economic, humanitarian and social disciplines at the university is carried out. An experimental check of the successful formation of motivation for the professional activity of students of economic directions of the university is carried out. As a result of the research, the value orientations and personal characteristics of students of economic directions, influencing the nature of motivation for professional activity, have been identified and characterized. The students’ emotional-cognitive attitude to the profession has increased, the motivation associated with further professional activity has increased. The motivation for achieving success from the work performed has increased; the attractiveness of the future profession has increased. The practical significance of the study is that the results obtained will allow teachers to take into account the nature of the motives of students of economic directions to professional activity when organizing the educational process.

Sikorskaya G.A., Gamova N.A., Kulish N.V.
ABOUT THE PREPARING OF HIGH SCHOOL STUDENTS FOR THE UNIFIED STATE EXAM IN MATHEMATICS ON THE BASIS OF THE PRINCIPLES OF STUDENT-ORIENTED EDUCATION ^{[№ 3 ' 2018]}
Universities are interested in strong applicants, able to harmoniously integrate into the educational environment of the university. USE, as an independent examination of students’ knowledge, requires systematic, competent training, which can be achieved only in the process of systematic, thoughtful work. The inadequacy of the methodology for preparing for the USE is one of the problems facing the school teacher today.
The main role of the teacher in the preparation for the USE is to orient the student to different levels of complexity of the program material. A close relationship between the supply of educational material through personally oriented tasks with value orientations and personal relations to educational and cognitive activity was revealed. Personally oriented tasks are based on the characteristics: the nature of the requirement, the composition of the source data, the way of implementation. The developed basis for the transformation of traditional tasks into personalized ones allows us to find the most optimal methods for solving problems. The trajectories of modeling the personally developing situation through personally oriented tasks on the basis of the structural-component composition of problems with parameters form the ability to analyze, to search for creativity, and to evaluate the result.
At the end of the work done, on the preparation of high school students of the lyceum for the Unified State Exam on mathematics on the basis of personally oriented assignments, the mathematical literacy of the trainees increased sharply, and overall performance was improved. Acknowledgment of the success of the training is consistently high points of the Unified State Exam on mathematics of the lyceum graduates, and, subsequently, high rating indicators of their academic performance at the university.

Gamova N.A., Kulish N.V., Sikorskaya G.A.
PEDAGOCICAL SUPERVISION IN LEARNING MATHEMATICS ^{[№ 2 ' 2018]}
Demand for graduate degrees are growing, thus necessity for more effective educational supervision occurs. Better the supervision, better result of students. If organization of students’ studying process improves, their abilities will mount. With correction and diagnosing problems in studying it`s possible to improve students` self-awareness in education process. Main aim of educational supervision is to get information about process as whole. In the studying process pedagocical supervision was created by providing all students variety of tasks with character oriented studying. In particular, it’s provided by tests and quizzes with public access, using modern technology, including possibility of real time remote studying. Pedagogical supervision of students has improved feedback for teacher’s work on consecutive steps of educational process. With character oriented studying students got mathematical skills for tackling practical tasks. They learnt how to use mathematical language and its symbols to construct managerial models and they have learnt how to improve their methods of studying on each steps of educational process.

Gamova N.A., Kulish N.V., Shepherds D.I.
INFLUENCE OF INDEPENDENT WORK ON FORMATION OF PROFESSIONAL QUALITIES OF FUTURE BACHELORS ^{[№ 6 ' 2017]}
One of the main objectives of professional education is training of the skilled worker of appropriate level and a profile, competitive in labor market, competent, responsible, owning the profession, ready to the constant professional growth, social and professional mobility. According to FGOS of the 3^rd generation the role of independent work increases in educational process of bachelors. More than a half of all school hours is allowed for her. Modern requirements to process and results of independent work on formation of professional qualities of bachelors speak about need of her special organization. Educational and nonlearning independent work of the student has been built so that to develop ability to study. Practically she was implemented by providing all students with the educational and methodical materials, such as an electronic course of lectures solved by standard options of tasks, questions for independent studying of the specified subjects, tasks which model separate stages of individual research work and tasks on work with literature in the specialty. Formation of the professional abilities allowing to apply creatively gained knowledge happened when carrying out independent work in teams, during the work on the project, with the assistance of students in the formulation and realization of the problem connected with future profession. Control of results of independent work took place in the written, oral or mixed form. The correcting of the gained knowledge was carried out after holding an interview, testing, protection of projects and the presentations as from the teacher, and the student. Independent work on formation of professional qualities has allowed to teach students to set the educational purposes, to choose optimum ways of their achievement. To work in collective. I promoted increase in motivation of training. I developed the aspiration to continuously increase the knowledge at the bachelor. I developed abilities to independent creative activity.

Gamova N.A., Kulish N.V., Tomina I.P.
EDUCATIONAL OPPORTUNITIES INDEPENDENT WORK OF STUDENTS ^{[№ 2 ' 2016]}
Organization of educational activity should be considered in the context of the success of the introduction of independent work of students in the innovative elements aimed at the formation of new connections and relationships of cognitive activity, which create space for their development. To form the experience of independent work of students, need orientation in the flow of information. This creates the following opportunities for developing training: increasing demand of students in the self; are prerequisites for the coordinated work of teachers and students; activates the intrinsic motivation of educational activity; assimilated the logic of the study (data management and analysis, allocation problems, hypotheses, hypothesis testing, formulation of conclusions). Independent work of students under the guidance of the teacher allows them to become the subjects of education. There is a development initiative and activity of students, there is understanding of the development of scientific knowledge. Developing the capability of independent work of students under the guidance of a teacher in the study of mathematical analysis is to gain experience of the students' independent work, competence, responsibility, readiness for professional growth and competitiveness in the labor market. In this respect, the growing importance of classroom organization and students' independent work in the learning process for the formation of skills of self-education that is the basis for postgraduate education and further training.

Gamova N.A., Kulish N.V., Tomina I.P.
PERSONAL INDEPENDENT WORK OF STUDENTS IN MATHEMATICS ^{[№ 1 ' 2016]}
Multi-level training of students, as well as the individual style of educational activity of each of them all at the same time does not allow to go to a particular level of competence (information, mathematical, foreign language, etc.). It requires a special organization of independent work, the development of its methodological support in a tiered system of higher education. Based on work practices, we believe that the individual independent work will be more effective if students will work in groups of 2-3 students, which allows the direct result of the process of knowledge sharing, creates favorable conditions for their active personal involvement in the educational process. Students thus serve as members of the mutual control and mutual motivation as a factor, creative, communicative, socio-cultural activities, providing a significant increase in the effectiveness of the cognitive activity of each participant. Independent work university students in teaching mathematics should be improved, using a personally and professionally — oriented approach, the score-rating system, modern information technology, etc., that will determine the student's individual route to self-employment, improve the quality of his mathematical education. The presented theoretical and practical recommendations to make the individual independent work available for analysis and projected in academic and extracurricular activities.

Gerasimenko S.A., Gamova N.A., Zubova I.K., Ostraya O.V.
ON THE DIRECTIONS OF EDUCATIONAL ACTIVITY IN HIGH SCHOOL (ON AN EXAMPLE OF THE ORENBURG STATE UNIVERSITY) ^{[№ 2 ' 2014]}
The article reflects the experience of teachers in the Faculty of Mathematics and organizing educational activities, presents the structure, functions, principles and the role of educational activity in the formation of socially mature personality.

Korabeynikov I.N., Gamova O.N.
THEORETICAL SUBSTANTIATION OF CONVERSION OF THE ECONOMICS TO THE INFORMATION-ORIENTED SOCIETY ^{[№ 4 ' 2012]}
In this article theoretical foundation of conversion of the economics to the information-oriented society is determined. Cases of conception of the information-oriented society, attainments-economics, derivative economics, theory of technological modes, social networks conception are afforded here. The author's conception of transformation of socio-economic progress by conversion to the information-oriented society is suggested.

Gamova N.A., Kazakova O.N.
SPHERE OF PEDAGOGICAL ACTIVITY OF THE FACULTY ^{[№ 2 ' 2011]}
The article depicts math's faculty staff and lecturers experience in educational area building; it's structure, functions, principles of faculty's educational area building and educational area's in socially mature personality forming

Korabeinokov I.N., Inevatova O.A., Dmitrenko O.V., Gamova O.N.
PECULIARITIES OF SCIENTIFIC AND INNOVATION SPHERE DEVELOPMENT IN ORENBURG REGION ^{[№ 2 ' 2009]}
This article is devoted to the studying of peculiarities of scientific and innovation sphere development in Orenburg region. The complex analysis of this sphere as a totality of interactive elements produced knowledge and provided their commercialization is given in this work. Also factors influenced on forming of scientific sphere are analyzed and suggestions effectiveness increase of scientific and innovation sphere functioning are formed.

Korabeinikov I.N., Gamova O.N., Inevatova O.A., Chernova E.V.
MODERN ASPECTS OF INFORMATION TECHNOLOGIES DEVELOPMENT ^{[№ 8 ' 2008]}
This article is devoted to the studying of modern aspects of effective development of information technologies. Existing interpretations of such conceptions as "net economy", "information economy", "information society" and some others are analyzed in this work. The analysis of worldwide and native approaches determined perspectives of information technologies development is given here. Also the problems of effective introduction of information technologies into economy are analyzed and classified in this article.

Gamova N.A.
PEDAGOGICAL POSSIBILITIES OF DEVELOPING UNIVERSITY STUDENTST INTERSOCIAL COMMUNICATION CULTURE ^{[№ 7 ' 2002]}
Such rapid events of the 21 century as growing intercultural contacts throughout the world, the world wide consolidation against terrorism, financial and economic consolidation of Europe, integrating processes in CIS countries, strongly depend on a new generation of active young people, having a profound scientific knowledge, easily using modern means of communication and information, speaking foreign languages, familiar with different peoplesT culture, being highly qualified professionals, meeting the world standards. Hence, the global education is to cultivate in young people the sense and awareness of being responsible for the present and future of the world they live in. This becomes possible with the system of education adopting new intersocial principles, regularities, providing the ihsubject - subjectls relations on the innovative base.