Methodological features of studying the logical basics of mathematics in the integrated course “Mathematics” for students of the 7-th grade of NUS.

Abstract

Currently, the reform of the Ukrainian school is aimed at ensuring that its graduates become fulfilled and happy citizens of a prosperous country in adulthood. For this reason, the basis of the “New Ukrainian School” (NUS) reform was chosen to be a competency-based approach to learning, which focuses the entire process of learning at school not on the formal acquisition of knowledge, skills and abilities by students in one or another subject area, but on the formation of relevant such personality characteristics that will allow them to ensure their successful self-realization in the future. The stages of implementation of the Ukrainian school reform were the approval of State Education Standards and model programs, in particular, in mathematics. According to these programs, appropriate textbooks were created, in particular, the textbook of the integrated course “Mathematics” for the 7-th grade of the author’s team Oleksandr Shkolnyi, Yevhen Nelin, Andrii Mylianyk and Yuliia Prostakova. This textbook is innovative and involves an evolutionary update of the content of school mathematics in the 7-th grade, in particular, the introduction of the adaptation topic “Concepts and their definitions, statements and their proofs”, which concerns the logical foundations of mathematics immediately before studying geometric material on an axiomatic basis.

The purpose of the article is to highlight the methodological features of studying of math logical foundations in the 7-th grade mathematics course of NUS. In particular, in the article we show how to adapt seventh-graders to studying abstract geometry material, which has always caused difficulties. This adaptation is achieved by explaining the logical essence of concepts and statements using simple examples from everyday life. Students begin to understand why certain concepts are not defined, but only modeled in some way, and certain concepts are defined through undefined concepts and concepts whose definitions have already been given. It also becomes clear to seventh-graders how the truth of statements is established (on the basis of life experience and some agreements), why some statements are accepted without proof, and some of them are proved.

Approbation materials of the mentioned textbook on mathematics for the 7-th grade testify to the students’ interest in the logical foundations of mathematics, and also show that after mastering this material, they more easily perceive studying of the simplest geometric figures properties. In the future, we plan to continue research in this direction, since this textbook is recommended by the MES of Ukraine for teaching mathematics in the 7-th grade of the New Ukrainian School.