Oksana V. Bleikher

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.

Educational chat-bots are becoming important tools for supporting students’ independent learning. In case of teaching higher mathematics, the architecture of chat-bots becomes particularly significant: moving from rigid linear scenarios that ensure a strict sequence of topic study to more flexible navigational models. It allows students to independently build their own learning flows. However, fully free navigation is associated with the risk of fragmented and superficial assimilation of the material, disruption of the course logic, and loss of methodological integrity. This highlights the necessity of transitioning to a graph-based model that combines the structure of the course with the possibility of personalized choice and adaptation depending on the level of knowing the material. The aim of the study is to substantiate the methodological and technological feasibility of implementing a graph-based chat-bot architecture capable of taking into account semantic links between concepts, typical student's difficulties, and natural language queries. The theoretical part builds on contemporary research in the field of personalized higher mathematics education, the use of graph structures in pedagogy, and natural language processing technologies. The empirical study, conducted in 2024–2025 at the Yerevan branch of Plekhanov Russian University of Economics, included a comparison of the effectiveness of two types of educational chat-bots – those with sequential (linear) and free navigational organization. The collected data showed that chat-bots with free navigation flow were perceived as more convenient and structurally flexible, but they also came with the risk of insufficient learning of the material due to the lack of reliance on internal course logic. Based on the analysis of student feedback and theoretical premises, the necessity of introducing a flexible graph-based model has been substantiated. This model ensures not only variability in navigating the learning material but also contextual returns to key topics, adaptation of the pace and content of learning, and support for self-assessment processes. Such a model allows achieving a balance between freedom and logical coherence of the learning material, which is particularly important for disciplines with a hierarchical structure of concepts, such as mathematical analysis. The results of the proceedings can be used in designing digital solutions for teaching higher mathematics and in creating chat-bots aimed at personalizing the educational flow.