Journal of Advances in Mathematics and Computer Science

The interaction between teachers and students is an important determinant of learning outcomes and the overall effectiveness of an education system. In this paper, we formulate and analyse a nonlinear ordinary differential equation model to study the dynamics of teacher–student interaction and student learning. The student population is divided into two categories: students needing additional academic support and students with relatively higher levels of learning achievement, while teacher effectiveness is treated as a dynamic variable. The model considers student progression due to effective teacher intervention, student disengagement, teacher performance, and the negative impact of heavy workload on teaching effectiveness. Positivity and boundedness of the model solutions are established, and possible equilibrium states are identified. We analyse the local stability of the equilibria using standard dynamical-systems techniques and obtain a threshold quantity that characterises the conditions for the persistence of effective learning. Sensitivity analysis is conducted to determine which parameters have the greatest influence on student learning outcomes. Numerical simulations are presented to demonstrate the effects of teaching effectiveness, student workload, and learning transition rates on the long-term behaviour of the system. The findings suggest that improved teacher effectiveness and an appropriate teacher–student ratio can make a substantial difference to learning gains. The proposed model provides a mathematical framework for understanding educational dynamics and may help to evaluate strategies aimed at improving teaching effectiveness and student achievement.