Аннотация
In the context of the rapid development of digital technologies, the issue of information security is becoming increasingly important. Cryptography is considered an effective scientific tool for protecting information, which is one of the most valuable resources of modern society. At the same time, in educational practice, particularly in school mathematics, students often face difficulties in understanding abstract concepts. In this regard, the use of cryptography elements can be seen as an effective way to address this problem. In other words, there is a growing need to teach mathematics through applied content. The integration of cryptography elements contributes to a deeper understanding of mathematical concepts. The aim of this study is to develop an effective methodology for teaching the Gauss method based on cryptography elements for solving systems of linear equations, as well as to assess its impact on the development of students’ cognitive abilities. The study employed both theoretical methods (analysis, modeling) and empirical methods, including a pedagogical experiment. The experiment was conducted at Secondary School No. 45 in the city of Semey and involved 22 ninth-grade students. During the implementation of the elective course, tasks of a cryptographic nature were transformed into systems of linear equations. These systems were then solved using the Gauss method. The results of the study showed that the use of cryptography elements contributes to the development of students’ algorithmic and logical thinking. In addition, it facilitates a deeper understanding of mathematical concepts and increases students’ interest in the subject. From a practical perspective, the proposed methodology can be implemented in the school mathematics curriculum as an elective course. It also promotes the strengthening of interdisciplinary connections.