Studying geometric transformations in 9th grade OF NUS according to the author’s textbook of the integrated course of mathematics

Abstract

The New Ukrainian School (NUS) is an education reform aimed at developing key competencies of students that will facilitate their further education in higher education institutions and self-realization in future professional activities. According to this reform, the learning process in schools is organized as follows: according to the approved State Educational Standards and the basic educational plan, model programs have been developed for all educational branches, in particular, mathematics, and textbooks and other teaching aids are created based on these model programs.

The purpose of the article is to highlight the methodological features of studying geometric transformations in the 9th grade of the New Ukrainian School according to the textbook of the author team Oleksandr Shkolnyi, Yevhen Nelin, Andrii Mylianyk, Yuliia Prostakova, created according to the model program of the author team led by Maria Vasylyshyn. According to this program and textbook, geometric transformations of the plane are studied at the beginning of the 9th grade. Among other advantages, this will contribute to a more correct presentation of the subsequent material of the 9th grade, which concerns the construction of graphs of quadratic functions, using not intuitive reasoning, but the method of geometric transformations.

In this work, we describe in detail the author's methodology for studying geometric transformations of the plane, which involves studying the following subsections: “Geometric transformations of the plane and their analytical representation”, “Movements and transformations of similarity; types of movements and their properties: parallel transfer, symmetry relative to a point, symmetry relative to a line, rotation”, “Equality and similarity of figures; solving draw problems using the method of geometric transformations”.

The probation of the textbook of the integrated course “Mathematics” for the 9th grade of the mentioned author’s team in the 2025-2026 academic year in Ukrainian schools shows that students quite positively perceive the place and method of studying geometric transformations of the plane and properly use them in their educational activities. However, the proposed method of mastering this material by 9th grade students of NUS requires further research. However, we are convinced of the feasibility and prospects of the described approach and will continue to use it to form key competencies of students.