EXPLORING POTENTIAL APPLICATIONS OF THE METHOD OF CONTRADICTION

This paper is devoted to the identification of some possibilities for the effective implementation of the method by contradiction in the school mathematics course. At first the essence of the method by contradiction, the tools for its implementation are presented in the paper, and then the main difficulties, that pupils encounter when applying this method, are highlighted. Explaining and commenting the effectiveness of the application of the method by contradiction, the main tools are presented and interpreted in the form of methodological guidelines, thanks to which the use of this method in various problems of proof and/or refutation becomes easier. Accordingly, the essence of both the coloring method and the extreme rule, the possibilities of their application are presented and covered in detail, and it is also shown that for the effective implementation of the method by contradiction in various typical and atypical problems of proof and/or refutation encountered in the school mathematics course, both the coloring method and the extreme rule can be effective tools. Various typical and atypical problems of proof and/or refutation, selected from well-known problem books, are discussed in the present paper, according to the principle of gradual complication. For the latter, generalizations were made, as a result of which the method by contradiction was used to solve problems considered in a more general setting, and it was shown that both the coloring method and the extreme rule can be an effective tool for the successful implementation of the method by contradiction, which is the scientific methodological novelty of the article.