Principles, conditions and means of forming the competence of plausible reasoning of pedagogical university mathematics students

This article highlights the actual problem of modern education, aimed not only at transferring knowledge, but also at preparing students for life difficulties, adapting to changes and actively participating in the development of society. The approaches to the formation of the competence of plausible reasoning among students of mathematics at pedagogical universities, as well as the principles, conditions and means necessary for its development are considered. The purpose of the study is to analyze various methods and strategies that contribute to the development of the competence of plausible reasoning, and describe the basic principles, conditions and means to ensure its successful formation. The methodological basis of the research is the theory of the gradual formation of mental actions by P. Ya. Galperin, the theory of the development of thinking, as well as systematic and constructive approaches. These theories play an important role in shaping students' plausible reasoning, as they are directly related to cognitive activity. The article presents and analyzes the main approaches to the formation of competence of plausible reasoning, such as theoretical-semantic, inductive and analog, computational, constructive, problem-oriented, modeling and design, as well as provides examples of each of them. Special attention is paid to the use of open tasks as an important tool in the development of this competence. The article provides examples of the use of open problems for the formation of plausible reasoning competence in mathematics students, as well as describes the basic principles, conditions and means of its effective formation. As a result of the research, the importance of integrating various approaches into the educational process and the need for further study of methods for forming the competence of plausible reasoning is emphasized.