STUDYING ELEMENTS OF SPACE GEOMETRY IN THE INTEGRATED COURSE OF MATHEMATICS FOR GRADES 7-9 OF THE NEW UKRAINIAN SCHOOL

Abstract

Problem formulation. The formation of students’ spatial imagination is one of the important components of the formation of mathematical competence of modern students, in particular, in the context of the implementation of the New Ukrainian School (NUS) project. In the model mathematics programs for grades 7-9 of NUS, the study of spatial geometric solids is either not provided for at all, or is carried out indirectly during the study of other topics of the mathematics course. Such study is provided only in grades 10-12. Therefore, there is a violation of the principle of continuity in the process of forming students' spatial imagination, which leads to difficulties in mastering space geometry in senior specialized schools. The purpose of the article is a detailed presentation of the methodological features of studying the elements of space geometry in mathematics lessons by students of grades 7-9 of NUS using author’s educational aids. Materials and methods. To achieve the goal of the research, a theoretical analysis of methodical literature related to the topic was used, as well as observation of the educational process in schools during the approbation. We also use methods of scientific knowledge: comparative analysis to clarify views on a problem; systematization and generalization for the formulation of conclusions and recommendations regarding the study of elements of space geometry by students of grades 7-9. Results. According to the author’s methodological aids, the study of the elements of space geometry begins in the 7th grade with the topic “Nets of polyhedrons”, continues in the 8th grade with the topic “Nets of rotation solids" and ends in the 9th grade with the topic “Areas of surfaces of polyhedrons and rotation solids”. With this approach, spatial solids are studied not fragmentarily, but systematically. At the same time, the corresponding material in each grade is combined with traditional material: in the 7th grade, the nets of polyhedrons are studied after studying the properties of triangles; in the 8th grade, the repetition of the nets of polyhedrons and the study of the nets of rotation solids are carried out after studying the properties of quadrilaterals; in the 9th grade, the study of the areas of the surfaces of polyhedrons and rotation solids is one of the applications of the newly mastered topics “Areas of polygons” and “Area of ​​a circle and its parts”. In this way, a natural integration of the elements of space geometry into the traditional course of mathematics in basic secondary school is achieved. Conclusions. As shown by surveys of students and teachers during the approbation of the author’s methodical materials, the given approaches to teaching students the elements of space geometry are well received by teenagers. Although the number of students who studied using the author’s aids does not yet provide statistically substantiated grounds for claiming that the study of elements of space geometry in the 7-9 grades of NUS contributes to the formation of their spatial imagination, we believe that the methodological approaches described in the article are useful. In the future, these approaches should ensure the formation of students of 7-9 grades mathematical competence and other key competences, provided for by state documents in the field of education.