Measuring Conceptual Coverage Learning Resource with Respect to a Course Syllabus: A Set-Theoretic Approach

Learning resources (LRs) are widely used in higher education, but determining whether their content adequately covers the topics and concepts specified in a course syllabus remains a challenging task. Existing approaches for evaluating learning resources commonly rely on qualitative criteria, assessment rubrics, or expert judgments, which may make quantitative comparison and reproducibility difficult. This study proposes a set-theoretic model for quantitatively measuring the completeness of a learning resource with respect to a course syllabus. The proposed approach represents both the syllabus and the learning resource as sets of definitions organized according to their corresponding units and topics. Completeness is then quantified by comparing these sets using the asymmetric Tanimoto coefficient and the Jaccard index. The model was applied to syllabi and learning resources from university courses in Formal Languages and Automata and Computability, including resources developed by instructors and generated using artificial intelligence. The results show that both similarity measures can quantify the degree of correspondence between a learning resource and a syllabus, while the asymmetric Tanimoto coefficient provides a more direct measure of syllabus coverage because the syllabus definitions constitute the reference set. The proposed model provides a formal and reproducible approach for estimating the conceptual coverage of learning resources and can support instructors and instructional designers in evaluating and selecting educational materials.