Keyword: «nlu»

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.