Classroom interactions between students and teachers form a two-way or dyadic network. Measurements such as days absent, test scores, student ratings, or student grades can indicate the "quality" of the interaction. Together with the underlying bipartite graph, these values create a valued student-teacher dyadic interaction network. To study the broad structure of these values, we propose using interaction factor analysis (IFA), a recently developed statistical technique that can be used to investigate the hidden factors underlying the quality of student-teacher interactions. Our empirical study indicates there are latent teacher (i.e., teaching style) and student (i.e., preference for teaching style) types that influence the quality of interactions. Students and teachers of the same type tend to have more positive interactions, and those of differing types tend to have more negative interactions. IFA has the advantage of traditional factor analysis in that the types are not presupposed; instead, the types are identified by IFA and can be interpreted in post hoc analysis. Whereas traditional factor analysis requires one to observe all interactions, IFA performs well even when only a small fraction of potential interactions are actually observed.