This study develops a mathematical framework to evaluate the effectiveness of peer learning relative to traditional instructional approaches. The proposed Traditional–Peer Learning (TPL) model provides a structured, quantitative method for analysing learning outcomes across instructional modes. The model partitions students into four learning states: skilled via traditional learning (ST), unskilled via traditional learning (UT), skilled via peer learning (SP), and unskilled via peer learning (UP). Transitions between these states capture the dynamics of knowledge acquisition. A central feature of the model is the Knowledge Reproduction Rate (K₀), a parameter analogous to the basic reproduction number in epidemiological models, used to quantify the extent to which knowledge propagates through peer interaction. Consistent with this analogy, when K₀ 1, knowledge spreads more effectively, enhancing peer learning outcomes. In cases where K₀ < 1, the model introduces a secondary parameter, the Specific Threshold (SP), which defines the minimum proportion of knowledgeable students required to sustain effective peer-driven learning. The model is applicable during the instructional period prior to curriculum completion and assumes that all students initially begin as unskilled and rely solely on traditional learning methods. Students who do not engage in either traditional or peer learning are excluded from the analysis. The study further outlines a systematic procedure for applying the TPL model in educational contexts. As an exploratory study, the focus is on model development, with empirical validation left for future research.

Authors:
Godfrey Nkululeko Mazibuko, University of Technology, South Africa

About the Presenter(s)
Dr. Godfrey Nkululeko Mazibuko is a Mathematics Lecturer at the Durban University of Technology, where his research focuses on curriculum evaluation models like RCUSP and the integration of APOS

Connect on Linkedin
https://www.linkedin.com/in/nkululeko-mazibuko-518664230

See this presentation on the full schedule – Sunday Schedule

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