Graph modeling as a means to develop a methodological system for mathematics instruction and its integration with artificial intelligence technologies

Source abstract

The subject of this study is the conditions and means by which a methodological system for teaching mathematics generates a personalized content framework for engineering students, achieved through the integration of invariant and variable components at each vertex of the system's graph. The object of the research is the mathematics education of future engineers in the context of mass training. The author examines various aspects of the topic in detail, including the invariant framework of the methodological system defined by a five-vertex graph schema, the distinction between personalization and its related concepts of differentiation and individualization, as well as the necessity for a coordinated restructuring of the content of all components of the methodological system for each individual student. Special attention is given to the properties that the graph of the methodological system must acquire and to the differentiation of the functions of machine learning and neural network technologies in aligning the graphs of the subject area, the student, and the teacher. The research methodology is based on the concept of a mathematical teaching methodological system, employing systematic, activity-based, and competency-based approaches, along with graph theory, machine learning theories, and neural network technologies. Techniques utilized include system analysis, comparative analysis and generalization of educational system models and curricular content, graph modeling, and pedagogical design of the system architecture. This study is primarily theoretical in nature. The novelty of the research lies in the justification for the necessity of graph representation in the methodological system: by emphasizing the principle of personalized mathematics education, the system graph enhances the manageability of content across its components, reveals each vertex as a subgraph, and aligns the system with the graphs of the subject area, the student, and the teacher. A significant contribution of the author to the research topic is the differentiation of the functions of intelligent tools. Machine learning serves as a means for forming the student's graph vertices based on learning analytics and variable goal content, while large language models provide consultative support to learners and generate personalized methodological materials within scenarios defined by the teacher's graph. The main conclusions of the conducted research indicate that the methodological system for personalized mathematics education develops, rather than replaces, the classical five-component system. The personalized content is formulated through the alignment of three graph models, with artificial intelligence technologies operating within the boundaries established by the teacher. Future research will focus on the development of the student and teacher graphs and the experimental verification of the system.