Formation of mathematical competence of students by implementing methods of finding non-standard algorithmic solutions

The purpose of the study is to analyze the effectiveness of using methods for finding non-standard algorithmic solutions in the process of teaching mathematical disciplines during the professional training of future mathematics teachers and to determine the conditions for the formation of the ability of higher education students to independently and variably solve problems. Theoretical methods of analysis, synthesis, abstraction, induction and deduction were applied to systematize scientific approaches to the development of mathematical thinking and the competencies of higher education students, thereby allowing us to identify key principles for organizing educational activities aimed at activating students' creative potential. Pedagogical conditions that ensure the development of mathematical competence were determined, including the organization of problem-based learning, stimulation of creative activity, interactive forms of control and the use of visualization, which allows combining clarity with the development of analytical skills. The article proposes an author's selection of problems from mathematical disciplines, the key feature of which is a departure from standard solutions and an orientation towards the search for non-standard methods of solution, which contributes to the formation of students' ability to abstract, logically structure solutions and find relationships between different mathematical objects. The results obtained demonstrate that the use of non-standard algorithmic approaches contributes to students' transition to a more productive level of educational activity, the development of logical and critical thinking, and the ability to independently assess the effectiveness of the methods used and choose optimal strategies for solving problems. The pedagogical conditions for the development of students' mathematical competence through the systematic use of non-standard algorithmic approaches in teaching are substantiated. The results of the study can be used by teachers at higher education institutions to improve the professional training of future mathematics teachers, by fostering students' complex professional skills and readiness to act effectively in various educational and non-standard situations.