The article examines the theoretical and methodological aspects of teaching school students to solve mathematical problems using non-standard methods. The relevance of the study is determined by the need for advanced mathematics instruction in lyceums and gymnasiums, the development of students’ logical, analytical, and creative thinking, as well as preparation for effective performance in mathematical olympiads and final assessment examinations (BBJM, ENT).

The study analyzes the works of foreign and domestic scholars and methodologists devoted to non-standard methods of solving mathematical problems and systematizes their classification. The stages and specific features of applying non-standard methods are illustrated through concrete examples, and their influence on students’ cognitive activity is analyzed. In addition, the article describes the organization and results of a pedagogical experiment conducted with students of grades 10-11 in a general secondary school. The experimental data confirm that the purposeful use of non-standard methods has a positive effect on the dynamics of students’ problem-solving skills, logical thinking, and cognitive independence. The effectiveness of the proposed methodological approaches is substantiated, and the possibility of using the research materials in classes with advanced mathematics instruction, elective courses, and olympiad preparation is justified.