Graph-theoretical framework for analyzing student interaction networks: a formalized approach to classroom collaboration

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Abstract A thorough graph-theoretical framework for studying student interaction patterns in educational environments is presented in this work. Inspired by ideas from network science and social network analysis, we create a formal mathematical model in which students represent nodes and their interactions create weighted, undirectional edges. The approach comprises fresh measures measuring how network topology influences knowledge exchange and group cohesiveness: the Collaborative Efficiency Theorem and Information Diffusion Potential. By means of empirical analysis of classroom data gathered from thirty secondary school students over several weeks, we confirm our technique by exposing notable correlations between network architecture and cooperative outcomes. Our results show that roughly 15% of students show risk indicators for academic disengagement depending on network positioning and that student networks show non-random community forms with modularity scores of $$Q = 0.45 \pm 0.07$$ . We present a cohesiveness indicator that significantly associates with group performance ( $$r = 0.72$$ , $$p = 0.05$$ ), therefore offering teachers a useful diagnostic tool. This work provides mathematical rigor and pedagogical value to improve classroom cooperation dynamics, hence bridging the gap between abstract graph theory and useful teaching tools.

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