Аңдатпа
Elementary algebra forms the foundation of mathematical education and is at the same time a persistent source of learning difficulties: errors in handling variables, polynomials and expression transformations accumulate and block the mastery of later topics.Conventional assessment tools record only a final score and fail to reveal which specific knowledge elements and inter-concept links remain unlearned.This paper proposes intelligent learning and knowledge-control tools for elementary algebra that combine an ontological representation of the subject domain with a fuzzy assessment model.The domain is described by a semantic hypergraph whose vertices are concepts and whose arcs are structural prerequisite links.The mastery of each knowledge element is evaluated by a piecewise-linear membership function that filters out weakly confirmed results; individual estimates are then aggregated along the hierarchy knowledge element → topic → discipline → educational programme.Learning gaps are diagnosed through structural comparison of the reference and individual ontologies, and an adaptive planner selects tasks that restore broken prerequisites.The scope of the proposed model is deliberately limited to interpretable, structure-aware assessment and diagnosis rather than to maximising next-response prediction, in which neural and knowledge-tracing methods naturally excel.Within this scope, an experimental evaluation against binary assessment, a classical fuzzy model and Bayesian knowledge tracing showed the highest agreement with expert grading (Cohen's kappa 0.83), the lowest final-score prediction error (RMSE 0.094) and the most accurate localisation of structural gaps; the adaptive regime yielded faster growth of average topic mastery.The main contribution lies in unifying the ontological domain structure, interpretable element-level fuzzy assessment and multilevel aggregation within a single intelligent tutoring architecture targeted at elementary algebra.The model is accordingly presented as an interpretable ontology-fuzzy assessment model, complementary to prediction-oriented neural and knowledge-tracing approaches rather than a replacement for them.