THE METHODOLOGY OF STUDYING THE AREAS OF GEOMETRIC SHAPES IN THE MATHEMATICS COURSE OF GRADES 5-9

ABSTRACT

The modern development of mathematical knowledge has determined the relevance of school mathematics education, where geometry occupies a special place. This contributes to the development of thinking, spatial imagination and logical reasoning, as well as the education of intellectual qualities of a person. The topic of "Square" is fundamental in the course of mathematics, but its study causes difficulties for students. Despite the purposefulness of the research, the theoretical and methodological aspects of calculating the areas of geometric shapes have not been sufficiently developed. The relevance of the research lies in the need to define methods and approaches to teaching the topic "Square", including the development of a theoretically sound

Keywords: mathematical education, development of spatial imagination, teaching methods, teaching problems, modern methods, organizational forms of teaching.

Relevance of the study. The modern era owes many achievements to the level of development of mathematical knowledge, therefore, at the turn of the century, school mathematical education is in the center of attention of specialists of various profiles. Geometric education as a separate direction of mathematical education has an independent value not only from the point of view of development and enrichment of mathematical knowledge, but also from the position of humanization of education. This is explained by the fact that it is the geometric material that allows for more harmonious mental activity of schoolchildren, which is especially important at the initial stage of teaching mathematics. Therefore, many domestic scientists (A.D. Alexandrov, G.D. Glazer, V.M. Tikhomirov, I.F. Sharygin, etc.) sought to create their own original concepts of teaching geometry at school, taking into account not only the specifics of the subject and method of geometry, but also containing one or another answer to the possibility of psychological development of children by means of geometry. Currently, many researchers are engaged in the search for new models of teaching geometry, linking the solution of methodological problems with certain provisions and patterns of educational psychology. This led to the creation of new systematic and propaedeutic courses in geometry, the authors of which are V.A. Gusev, G.A. Klekovkin, V.A. Panchishina, N.S. Geometry, being a phenomenon of universal human culture, is distinguished by its own method of understanding the world. Geometry studies objects of the surrounding world, idealized in simple and visual concepts, which contributes to the development of spatial imagination and logical thinking. That is why geometry has the potential to cultivate intellectual qualities of personality in a child. The works of B.P. Belotserkovsky, V.G. Boltyansky, V.A. Gusev, V.A. Zharov, Yu.M. Kolyagin, F.F. Nagibin, A.D. Semushin, Z.A. Skopets, D. Polya are devoted to the problem of teaching students the elements of geometry and solving geometric problems, forming rational methods of educational work in solving problems. This problem is also considered in the dissertation research of E.G. Gotman, G.B. Kuznetsova, L.M. Nozdracheva, E.V. Potoskueva, Yu.A. Rozka, G.I. Sarantseva, E.E. Ovchinnikova and others. One of the important sections of the school curriculum is geometric quantities. A number of candidate dissertations are devoted to the methods of studying geometric quantities in secondary school. Dissertations of M.S. Matskin, V.N. Shishlyannikova are entirely devoted to the detailed development of the content and methodology of presentation of the main sections related to the measurement of geometric quantities. In the studies of A.F. Spassky and I.S. Klimov, methods for instilling practical measurement skills in students are developed: a methodology for working with measuring instruments and a system of practical work on measuring geometric quantities are given. Mathematical justification of the theory of scalar quantities, and in particular geometric quantities,is presented in the dissertation of K.F. Rubin. The topic "Area" is basic, fundamental and is studied throughout the entire mathematics course, starting from elementary, and then in grades 5-6, continuing up to grade 11. The issues of studying the theory of areas in the school geometry course have been comprehensively analyzed by many teachers and methodologists. The fundamental importance of this topic for the further study of mathematics was established, the ways and means of forming this concept were indicated. In the dissertation of Z.I. Turlakova, a methodology for studying such sections as "Length of a segment", "Length of a curve" and "Area of ​​a geometric figure" in senior grades is presented. On the other hand, the theoretical justification for calculating the areas of geometric figures and the use of area as a tool for solving problems has not been sufficiently studied in modern methodological literature. E.G. Gogman, I.A. Kushnir, N.D. Novikov, V.V. Prasorov, I.F. Sharygin demonstrates methods of calculating areas in his works, but they do not form a theory and a system of teaching this method. However, despite quite serious research in the field of methods of teaching mathematics, the assimilation of the topic "Area" by schoolchildren causes certain difficulties. This is evidenced by the experience of teachers, a systematic study of the quality of students' knowledge and the results of entrance exams. Thus, the analysis of theory and practice involves the search for effective methods, means and organizational forms of teaching elements of geometry. This justifies the relevance of the chosen research topic. Therefore, the search for ways to improve the methodology for studying the topic "Area" is considered as a research problem.systematic study of the quality of students' knowledge and the results of entrance examinations. Thus, the analysis of theory and practice involves the search for effective methods, means and organizational forms of teaching elements of geometry. This justifies the relevance of the chosen research topic. Therefore, the search for ways to improve the methodology for studying the topic "Area" is considered as a research problem.systematic study of the quality of students' knowledge and the results of entrance examinations. Thus, the analysis of theory and practice involves the search for effective methods, means and organizational forms of teaching elements of geometry. This justifies the relevance of the chosen research topic. Therefore, the search for ways to improve the methodology for studying the topic "Area" is considered as a research problem.

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