STUDYING COORDINATES AND VECTORS IN 8TH GRADE OF NUS ACCORDING TO THE AUTHOR’S TEXTBOOK OF THE INTEGRATED COURSE OF MATHEMATICS: ВИВЧЕННЯ КООРДИНАТ І ВЕКТОРІВ У 8 КЛАСІ НУШ ЗА АВТОРСЬКИМ ПІДРУЧНИКОМ ІНТЕГРОВАНОГО КУРСУ МАТЕМАТИКИ - Shkolnyi, Oleksandr (Physical and Mathematical Education, 2026)
Formulation of the problem. The New Ukrainian School (NUS) reform is aimed at developing key competencies in students that will facilitate their further education in higher education and self-realization in future professional activities. According to this reform, the learning process in Ukrainian schools is organized as follows: according to the approved State Education Standards and the basic educational plan, model educational programs have been developed in all educational fields, in particular, in mathematics, and textbooks and other teaching aids are created based on these model programs. The goal of the article is to highlight the methodological features of studying coordinates and vectors in the 8th grade of the New Ukrainian School according to the textbook of the author team, Oleksandr Shkolnyi, Yevhen Nelin, Andrii Mylianyk, and Yulia Prostakova, created according to the model program of the author team led by Maria Vasylyshyn. According to this program and textbook, vectors and coordinates are studied in the 8th grade. This will make it possible to study the topic “Geometric transformations of the plane” at the beginning of the 9th grade, and future study of this topic will contribute to a more accurate presentation of the material on constructing a graph of a quadratic function using geometric transformations. In addition, coordinates and vectors are needed in the 8th grade, particularly for physics teachers to solve many problems in this field. Materials and methods. Theoretical analysis of methodological literature, comparative analysis, systematization, and generalization of existing theoretical research on the topic of the article were used, as well as pedagogical observation and generalization of one’s own pedagogical experience in teaching mathematics in the 8th grade of the New Ukrainian School. Results. In the work, we describe in detail the methodology for studying coordinates and vectors, which involves studying the following subsections: “Coordinate system on the plane. Coordinates of the midpoint of a segment. Distance between two points with given coordinates. Equation of a circle”, “Vector. Absolute value of a vector. Collinear and equal vectors. Operations on vectors”, “Vector coordinates. Operation on vectors in coordinate form”, “Equation of a line. Mutual location of a circle and a line and two circles”, “Dot product of vectors and its application.” In particular, it is important for studying vector coordinates to introduce the concept of a basis, which corresponds to a given coordinate system on the plane. This makes it possible to introduce the concept of vector coordinates as coefficients in an expansion using basis vectors in a fairly simple, traditional way for a mathematics course. Conclusions. Testing of the textbook of the aforementioned author team during the 2024-2025 academic year in Ukrainian schools shows that students quite positively perceive the place and method of studying coordinates and vectors on the plane and properly use them in their educational activities. However, the proposed method for students in 8th grade at NUS to master this material requires further research. However, we are convinced of the feasibility and prospects of the described approach and will continue to use it to develop students’ key competencies.