Optimising curriculum design using Bayesian structure learning

Abstract

Mathematics education is vital in developing students’ analytical and problem-solving skills. However, in South African schools, many students opt for Mathematical Literacy over Pure Mathematics, often due to the latter being perceived as overly abstract and challenging. This study investigates the poten- tial of Bayesian Networks and score-based structure learning algorithms to optimise curriculum design, making Pure Mathematics more accessible, structured, and student-centered. Mathematical concepts were modelled as a Bayesian Network, enabling the extraction of prerequisite relationships using probabilistic graphical models. The study evaluated the performance of several struc- ture learning algorithms, including the Chow-Liu algorithm, the Tabu Search algorithm, the Simulated Annealing algorithm, and the Hill Climbing algorithm. The accuracy of the learned structures was as- sessed against a known ground truth using Structural Hamming Distance (SHD) and Kullback–Leibler (KL) Divergence. Results show that learned structures consistently recover the main prerequisite structures, with SHD and KL Divergence improving as sample size increases. Sparse learners (Hill Climbing, Chow–Liu) yield interpretable backbones that align well with expert expectations and are effective for auditing scope and sequence. Denser searches (Tabu, Simulated Annealing) surface additional cross-topic dependencies that highlight remedial and enrichment routes, although they’re less simple. Applied to ASSISTments data, the pipeline confirms meaningful prerequisite relations. It repeatedly elevates “connector” concepts (e.g., factorisation skills, numerical representation, symmetry) as influential bridges whose targeted re- inforcement can lower downstream difficulty. This research provides a foundation for data-driven curriculum modelling that ensures students mas- ter foundational topics before progressing to more advanced content. By leveraging adaptive learning frameworks informed by structural learning, educators can personalise instruction based on learners’ knowledge gaps, reduce cognitive overload, and enhance engagement. This approach holds particular promise in South Africa, where it can support efforts to shift perceptions of Pure Mathematics from abstract and intimidating to relevant and achievable. Limitations include sensitivity to skill tagging, priors, and static modelling of time. Overall, BN struc- ture learning emerges as a viable instrument for evidence-aligned curriculum design, supporting iterative “learn–validate–refine” improvement cycles in mathematics education.