  Community-based professional development initiatives have been shown to
support physics faculty in their adoption of research-based instructional
strategies. Hoping to better understand these initiatives' mechanisms of
success, we analyze the results of two surveys administered to a faculty online
learning community teaching a common physics curriculum designed primarily for
pre-service elementary teachers. We use social network analysis to represent
the faculty network and compare members' centrality, a family of measures that
capture the prominence of individuals within a network, to their reported
experience in the community. We use a principal component analysis of different
centrality measures to show that closeness, a measure of how closely connected
a person is with every other person in their network, is the most appropriate
centrality measure for our network. We then compare regression models according
to Bayes factors to find relationships between participants' closeness and
their survey responses. We find that participants' self-efficacy, as well as
their sense of improvement to their teaching and sense of benefitting from the
community, are predictors of their closeness with other participants and thus
their breadth and depth of participation in the community. Our results are
consistent with other studies that have highlighted interactions among faculty
as key components of successful professional development initiatives. They may
also be useful for designers of similar communities as they decide how to
prioritize time and resources to meet specific goals.
