Aleksandra Kypera

This article presents an experimental study of the influence of a specially designed didactic prompt on the level of students' learning proficiency in the course "Additional Chapters of Mathematical Analysis". The prompt is considered a tool for pedagogical support of independent learning activities, providing a step-by-step organization of problem-solving, the actualization of theoretical principles, and the development of self-assessment skills. The relevance of the research problem is determined by the need to develop new tools for pedagogical support of students' independent work in the context of the active integration of artificial intelligence technologies into the educational process, especially when studying complex mathematical disciplines that require developed abstract thinking and stable learning skills. The aim of the article is to experimentally evaluate the influence of a specially designed didactic prompt on the level of students' learning proficiency in the course "Additional Chapters of Mathematical Analysis". The leading research method was a pedagogical experiment with the formation of control and experimental groups and the application of repeated measurements of learning outcomes. Statistical data analysis was performed using parametric (Student's t-test) and non-parametric (Wilcoxon test) methods, as well as effect size calculation. The obtained results indicate that the use of the didactic prompt leads to a more pronounced increase in the learning proficiency levels of students in the experimental group and to the growing number of students with higher levels of mastering the educational material. This allows us to consider didactic prompts as an effective tool for developing sustainable learning skills in the context of integrating artificial intelligence technologies into the teaching of mathematical disciplines. The theoretical significance of the work lies in developing ideas about the didactic potential of prompt engineering in relation to teaching mathematics and substantiating the possibilities of using structured text instructions as a tool for pedagogical support of students' independent work. The practical significance of the study is determined by the possibility of applying the methodology of prompt-oriented preparation in teaching mathematical cycle disciplines that require intensive independent work of students. The proposed approach does not require complex technical solutions and can be easily scaled within various educational programs.