Sikorskaya G.A.
SELF-COMPILATION OF SUBJECT TEST AS EDUCATIONAL FACTOR OF UNIVERSITY STUDENT ^{[№ 3 ' 2025]}
Modern university student education is characterized by the level of formation of key subject competencies, the ability to choose a rational approach to solving educational and life problems, and the ability to acquire knowledge independently. The goals of the educational process are determined by the requirements of state educational standards, the degree of implementation of which is fixed by various forms of assessment, in particular, testing. A test is a set of standardized control tasks with the necessary system–forming statistical characteristics that provide reliable and valid estimates of a measurement variable. Testing in mathematical disciplines serves not only to assess the subject theoretical knowledge of students, but also to assess the ability to solve mathematical problems of various levels of complexity. In general, the search for ways to solve problems is a process of creative thinking, the main component in building a research understanding of the problem–solving process. An effective way of learning how to solve problems is their construction – a set of mental operations that, according to a given abstract situation, allow you to formulate a task and complete its solution. The process of creating a test consists of constructing a task (question); observing the proportions between the task condition and the answer; building distractors, taking into account balancing the ratio with the correct answer. Independent preparation of a subject test by a university student contributes to the formation of the ability to identify life problems and find solutions to them; the development of inquisitiveness of mind, inventiveness of thinking, which is especially in demand in the professional development of a future engineer.

Sikorskaya G.A., Tomina I.P.
THE ATTITUDE OF A HIGH SCHOOL STUDENT TO COGNITIVE INDEPENDENCE AS A NECESSARY QUALITY OF PERSONALITY ^{[№ 3 ' 2024]}
The strategic goal of the Russian state policy in the field of education is defined as improving the quality of education that meets the requirements of innovative economic development, modern needs of society and every citizen. In this regard, the main goal of individual human progress is the development of cognitive independence, which contributes to the disclosure of personal capabilities and abilities. The study, conducted using the methods of questionnaires and statistical analysis, identifies the main goals of educational activities from the point of view of high school students, including theoretical readiness for a future profession, the desire to be successful in life, interest in new knowledge, as well as interest in the very process of cognition. The reasons for choosing the priority of independent work opportunities are determined, such as the presence of a problem in which he is personally interested; choosing his own way to solve the task; obtaining his own result, significant for himself; having your own point of view. Thus, the main task of the development of cognitive independence, in the opinion of students, is the disclosure of their personal potential, the inhibiting factors in this case are, respectively, a large overload during the educational process, lack of opportunity for self-expression, lack of attention to individual work on the part of the teacher. Based on the analysis of the results of measuring the level of development of cognitive independence of high school students, motivation and readiness of high school students for independent activity, their assessment of the importance of independent work, as well as studying the attitude of high school students, teachers, parents to cognitive independence, the reasons for the development of cognitive independence as a necessary personality quality, now a high school student, later a university student, a professional in production, successful in human life.

Sikorskaya G.A.
PERSONALITY-ORIENTED TASKS AS A MEANS OF DEVELOPING COGNITIVE INDEPENDENCE OF A HIGH SCHOOL STUDENT IN A SPECIALIZED SCHOOL (MATHEMATICAL PROFILE) ^{[№ 2 ' 2024]}
The development of cognitive independence of high school students is most in demand in a specialized school, since at this educational stage, high school students are being trained to study at a university, according to new standards aimed at increasing the proportion of independent work. Over the past 10–15 years, school teaching teams have been increasingly using the basics of personality-oriented education in their practice. Students enter the class with a certain profile orientation from the position of continuing their studies in higher education. Basically, by the 9th–10th grade, the inclinations, abilities of students, their motivation are fully manifested, in accordance with the vector of their further education. Thus, for a high school student of a specialized school, his personal experience is increasingly important, focused on his valuable, vital meanings, obviously, for him, lying in the sphere of motivational priorities. For this reason, an axiological approach is completely justified in the personality-oriented education of high school students of a specialized school, as it expands the boundaries of learning material acquisition determined by the program, actualizes the voluntary choice of the student, the independence of his position on setting goals, highlighting obstacles. This approach involves the manifestation of will, personal experience, and, therefore, requires the manifestation of active independent cognition of a high school student. The process of developing independent cognition of high school students of specialized classes is possible, in particular, as a result of the organization of educational activities of schoolchildren through personality-oriented tasks involving the use of personal, subjective experience created by the student himself as a leading element of the content. One of the possible ways to form the cognitive independence of a high school student in a specialized class of a mathematical direction is based on the application of personality–oriented tasks of mathematical content — tasks with a parameter. When solving a rather complex problem with a parameter, a high school student is faced with the need to independently search and apply knowledge from various mathematical fields, choosing, based on his personal experience, the most rational trajectory to achieve the goal. As a result of research and experimental work on the development of cognitive independence of high school students of specialized mathematical classes through personality-oriented tasks in the form of mathematical problems with a parameter, the steady development of cognitive independence of students was revealed. The positive aspect accompanying the experiment was a significant improvement in the cognitive component of teaching high school students in the specialized mathematical field, which provided a fairly solid knowledge of solving problems with the parameter included in the Unified State Exam.

Sikorska G.A., Dzhukashev K.R., Kryuchkova I.V.
ABOUT THE PROBLEM OF IMPROVING THE MATHEMATICAL EDUCATION QUALITY AND PROPOSALS FOR ITS OVERCOMING ^{[№ 3 ' 2020]}
The concept of the development of mathematical education in the Russian Federation has set the task — to bring Russian mathematical education to a leading position in the world; the role of mathematics is determined — the most important component of world scientific and technological progress; a direct dependence of the success of Russia of the 21st century on the level of mathematical science, mathematical education and mathematical literacy of the entire population is recorded. The article reveals the conditions of graduate competitiveness upon admission to any universities of the country; the shortcomings of the educational system of the Orenburg region are revealed; the relevance of developing the theory, concept and methodology of the process of innovative improving the quality of mathematical education of high school students is substantiated. The necessity of creating an educational center, a methodological association for the development of effective forms of achieving results, contributing to the dissemination of experience in the accumulation and transfer of best practices for the development of mathematical education of high school students, updating and transferring the best methodological experience of training teachers teaching mathematics in specialized physics and mathematics classes is substantiated. The planned project will allow updating educational programs, creating an educational product based on modern information technologies. The purpose of the educational product is the development of students' mathematical thinking, providing high school students with high-quality mathematical preparation for the exam at a profile level.

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.

A.V.Kostryukov, G.A.Sikorskaya
ON PRINCIPLES OF UNINTERRUPTED EDUCATION AND THEIR REALIZATION AT SCHOOL-COLLEGE STAGE ^{[№ 2 ' 2002]}
The article defines the role of education at the present stage of the country's development, on the one hand, through tasks and goals of Russia's becoming a legal state with market economy and, on the other hand, as the basic society-forming factor.