Development of a prototype intelligent web-based system for learning mathematics through an adaptive scenario

Abstract

The subject of the study is the architecture and functional implementation of a prototype web-oriented intelligent tutoring system for adaptive mathematics learning in an online environment. The purpose of the work is to develop and substantiate the concept of an intelligent web-based system that provides parameterized generation of mathematical problems, automated answer validation, a multi-level hint mechanism, and an individual learning trajectory based on a probabilistic knowledge mastery tracing model. To achieve the goal, the following tasks were addressed: the analysis of modern approaches to building intelligent tutoring systems and knowledge tracing models; the formation of a domain model using a knowledge graph with prerequisite links; the development of modules for template-based problem generation and automated answer validation; the formalization of an adaptive learning scenario based on Bayesian updating of mastery probability; the design of a three-level contextual hint mechanism; the creation of interface solutions for entering mathematical expressions and providing immediate formative feedback; and the evaluation of the potential use of generative artificial intelligence for automating learning content creation. The research methods include systems analysis, functional decomposition, a comparative literature review on intelligent tutoring systems and computer-aided mathematics assessment, the implementation of the classical probabilistic knowledge tracing model, and prototyping of a client-server web system (with an Angular frontend). Conclusions. The developed prototype implements a closed-loop adaptive learning cycle that includes dynamic problem generation, answer input and validation, the provision of contextual hints, the updating of knowledge mastery assessment, and the selection of the next learning step. The system is already operational as a public web prototype and creates a foundation for the empirical evaluation of the effectiveness of adaptive mathematics learning. The scientific novelty lies in the comprehensive integration within a single web platform of: template-based problem generation, automated validation of mathematical expressions, a hierarchical hint mechanism, a probabilistic knowledge tracing model for trajectory management, a knowledge graph with prerequisites, and the justification for the use of generative artificial intelligence in automating content creation and error diagnostics.