Theoretical aspects of studying the theme “trigonometric transformations” in class 9

Аннотация

The purpose of this article is to consider the theoretical aspects of studying the subject of "trigonometric transformations" in grade 9. Keywords: aspect, trigonometry, study, method, tasks. At present, our education system is more and more focused on the humanization of the learning process in schools. Humanization in the field of teaching mathematics is understood as the focus of the entire educational process on the development of a comprehensively developed personality of the student. In this regard, in the new educational system, the means and methods of teaching are organized in such a way thatstudents are given the opportunity to show wit, resourcefulness, and the originality of their thinking to the subject material. One of the effective didactic tools that provide such an orientation of learning is differentiation, which is understood as a way of organizing the educational process, which takes into account the individual psychological characteristics of each student [1]. An orientation toward building a comprehensively developed personality in teaching mathematics requires the improvement of teaching methods and changes in the methodology, using the results of the latest achievements of mathematics, pedagogy and psychology. The reorganization of the structure of school educational system makes it possible not only to monitor the level of knowledge, skills and abilities of students, but also to shift the emphasis from narrow-subject knowledge to meta-subject knowledge, contributing to the development of new methods for studying mathematics at school. The consequences of the transition to a new education system entail not only the emergence of additional subjects of study in high school, but also a change in the methods and methods for studying already established subjects, in particular mathematics. At this point in time, the main task of the learning system is to develop new teaching methods at school, to implement the concept of specialized education at the secondary level of general education. The use of the fundamental ideas of the concept on practical application in school raises the question of the incomplete preparation of methodological knowledge for teaching specific mathematics topics in the education system, including in the section “Trigonometric transformations” in a secondary school in 9th grade [2]. It should be noted that the initial trigonometric knowledge of students is often presented abruptly, fragmentarily. The attitude of modern students 176 Scientific research results in pandemic conditions (COVID-19) to trigonometry is due to a lack of understanding of its role and significance. In the old days, until 1966, trigonometry was shown to schoolchildren as a clear and understandable example of improving mathematical science. The place of trigonometry in school education was rated very highly, in the ninth and tenth it was studied as an independent discipline "Trigonometry", allocating two hours a week for this lesson. Since 1966, the attitude towards trigonometry has changed dramatically and has changed dramatically over time. The reform of school mathematical education, the so-called “reform of A.N. Kolmogorov. " First of all, this was manifested in the fact that the program goals of studying "Trigonometry" in schools have changed. This branch of mathematics has lost its “significance” as a teaching tool used to develop thinking, stage-by-stage and directed familiarization of the child with the foundations of the scientific fundamental world through mastering the elementary practice of constructing this fundamental one. Summing up, the trigonometric material began to gradually “disappear” not only from the main school, but also from the course of the senior level of education at school. The course of trigonometry of the basic school continues to have considerable weight in practical application, which involves the assimilation of basic concepts, the ability to transform various kinds of expressions, study the function and graphing students. Studying the concepts of trigonometry is not limited to the framework of one school subject, since they reflect a fairly wide area of human life, causal relationships, embodying the ideas of actual and potential infinity, continuity, etc. Schoolchildren must have strong knowledge of trigonometry, because they are part of a huge chain of concepts and are of great importance in the implementation of intersubject communications. Studying the elements of trigonometry in high school is associated with a number of difficulties: a high level of abstraction of concepts, a complex logical structure of their definitions, insufficient study time to comprehend the complexity of questions and other issues [3]. Currently, trigonometric material is losing its general educational value. In connection with the growing need of students for a good organization of training in this section, it becomes necessary to consider the issue of the applied orientation of t