A Mathematical Model on the Dynamics of Teacher Adoption of Problem-based Learning in Mathematics Education

Abstract

This study develops a compartmental model to analyze the dynamics of Problem-Based Learning adoption among Ghanaian mathematics teachers. The model is framed within the SEIR structure and classifies teachers into susceptible, exposed, hesitant, and active adopter compartments. Stability analysis of the derived nonlinear system establishes a threshold for sustainable adoption via the basic reproduction number, R0 Positivity and boundness of solutions in the region Ω are established. This reveals that the model has epidemiological significance and is well-posed. Stability analysis reveals two stable equilibria: a PBL-free equilibrium and an endemic equilibrium. Sensitivity analysis identifies teacher attrition and hesitancy as the primary barriers to adoption, while peer influence and recruitment are key facilitators. Numerical simulations visualize the temporal dynamics of each teacher compartment. Simulations highlight slow PBL adoption rates and significant congestion in the hesitant group under baseline conditions. The findings indicate the need for policymakers to design targeted interventions such as training, mentorship, and incentives to promote PBL adoption and improve mathematics education outcomes in Ghana.