This article considers the search for new methodological approaches to teaching high school students mathematics that will promote the development of their logical thinking. Based on the analysis conducted by the authors of the study identified an urgent need to develop the logical thinking of students in mathematics lessons through various methods of solving problems. The authors of the article set out to investigate the factors that will ensure the implementation of a problem-based approach to teaching mathematics. These factors include the choice of a certain type of mathematical problem; selection of a method for solving mathematical problems; compiling a system of problems of one type that require the selection of methods for solving them. The authors reveal the introduction of the problem approach as a method of developing students’ logical thinking in the article on the example of solving irrational equations with parameters. The authors of the study explain the value of problems with parameters by the fact that the process of solving them contributes to the formation of students’ research skills. In the study, the authors focused on the analytical method of solving problems with parameters. Structural analysis of problems allowed the authors to formulate the following didactic requirements for the system of mathematical problems such as compliance with the problems of the course content and the principle of gradual increase in complexity; the rational relationship between the logical and heuristic components of educational activities; the presence of ideological and technical complexity, etc. To confirm the effectiveness of the introduction of the problem-based approach to the educational process, as a method of developing students’ logical thinking, an experiment was conducted. The main objectives of the experiment were to identify the level of logical thinking of students; development and implementation in the educational process of a system of problems with parameters in the study of the topic “Irrational equations”, which contribute to the development of logical thinking of students; analysis of the results of the experiment. The obtained results and their statistical processing confirmed significant differences in the levels of development of logical thinking in the control and experimental groups, respectively. This proved the effectiveness of a problem-based approach to teaching mathematics and the development of logical thinking of students.