Evolving the classroom: A mathematical and didactic exploration of teacher-guided peer learning

In this paper, we introduce a model involving group dynamics to investigate the intricate processes underpinning teacher-guided peer learning. This model seeks to pinpoint the optimal degree of teacher participation, thereby augmenting the effectiveness of peer learning experiences. Although peer learning inherently fosters enriched knowledge acquisition, the absence of a systematic approach or robust didactic analysis can impede its potential. Our model uniquely addresses this gap by facilitating a comparative investigation of peer learning under varying degrees of teacher participation, thereby illuminating the optimal range for this variable. To validate our model, we undertake comprehensive simulations that affirm its predictive power and practical applicability. Moreover, this study further contributes to the field by quantifying three distinct modes of facilitation, each characterized by different degrees of teacher participation. This is complemented by an in-depth didactic analysis. Our work synergizes the domains of educational research and network science, forging new pathways for understanding and enhancing classroom dynamics.