Graph theoretical methods for understanding student social interactions in physics classrooms

Social network analysis has become a common methodology within physics education research to quantify the impacts that student interactions and classroom structure have on student outcomes. These relationships are typically quantified using a degree centrality metric based on the number and range of connections a student has, such that a higher degree centrality would indicate a more central position in the network. However, when looking at these interdependent metrics as independent parameters, they do not consistently show any statistically significant relationship with motivational outcomes like self-efficacy or sense of belonging. In this study, we instead characterize students’ network positionality using various “network actor roles” and measure the strength of their connections through network paths, within the context of social capital. In this framing, we are less interested in the impact and importance of individuals than we are in the overall social integration of most students in the class. Using data from an interactive calculus-based physics 1 class, we find that students who are network isolates (no incoming or outgoing connections) or weakly connected report a lower sense of belonging compared with other students, but, consistent with prior research, the number of connections was not correlated with sense of belonging. Similarly, students who were strongly connected to at least one other person reported a higher sense of belonging compared to those who were weakly connected. This indicates the potential for graph theoretical methods to enhance our understanding of student interactions in physics classrooms.