Preparatory Stage of Teaching the Theory of Limits Section in the Mathematical Analysis Course in Higher Pedagogical Schools

Limit theory is a fundamental section of mathematical analysis, as finding a limit underlies the definition of most of its key concepts. In the context of higher pedagogical education, mastering this section is crucial for developing both the subject knowledge and professional competencies of future university graduates. This article substantiates the need for a special preparatory stage in teaching limit theory, preceding work with formal definitions and proofs. The main goal of this stage is to develop students’ intuitive and practical understanding of the importance of the concept of a limit and to create a foundation for a conscious understanding of the rigorous theory of the basic concepts of mathematical analysis. The methodological objective consists of purposefully modeling typical cognitive conflicts through a system of specially selected examples and problems. Using this approach, students learn to identify and analyze problematic situations and gain experience solving problems that lay the foundation for introducing formal concepts. The set of heuristic questions and problems developed during the preparatory stage contributes to the development of research skills and methodological thinking, which are an important component of the professional training of future mathematics teachers. To effectively teach this concept in higher education institutions, it is advisable to conduct practical preparation before introducing rigorous definitions, theorems, and proofs. The goal of this study is to gain a practical understanding of the essence of the “limit” operation during the preparatory stage, construct alternative examples for conflict situations, teach solutions, and develop a system of practically unsolvable or difficult-to-solve questions.