  Theories developed by Tinto and Nora identify academic performance, learning
gains, and involvement in learning communities as significant facets of student
engagement that, in turn, support student persistence. Collaborative learning
environments, such as those employed in the Modeling Instruction introductory
physics course, provide structure for student engagement by encouraging
peer-to-peer interactions. Because of the inherently social nature of
collaborative learning, we examine student interactions in the classroom using
network analysis. We use centrality---a family of measures that quantify how
connected or "central" a particular student is within the classroom
network---to study student engagement longitudinally. Bootstrapped linear
regression modeling shows that students' centrality predicts future academic
performance over and above prior GPA for three out of four centrality measures
tested. In particular, we find that closeness centrality explains 28 % more of
the variance than prior GPA alone. These results confirm that student
engagement in the classroom is critical to supporting academic performance.
Furthermore, we find that this relationship for social interactions does not
emerge until the second half of the semester, suggesting that classroom
community develops over time in a meaningful way.
