Current research typically uses surveys to study parental preferences but examines the responses in isolation from each other. A key insight from the sociology of culture and political psychology, however, is that the meaning of responses in opinion data comes from their relationships with one another. To make progress in understanding the meaning of parental preferences, it is necessary to study their educational belief systems -- the structural configuration of their attitudes related to schools. Using data from Phi Delta Kappa's annual survey on education, I employ correlational class analysis to identify three subsets of parents whose members configure their beliefs about integration, standardized testing, and enhanced academics in distinct ways. These three groups of parents are "convergents," who see testing and integration as being aligned; "integration divergents," who see standardized testing and integration as being in opposition; and "academic divergents," who see standardized testing and enhanced academics as being in opposition. Compared to the full sample, these subgroups display more structure in the associations among their preferences. I also examine if the relationships between preferences and sociodemographic characteristics vary across subgroups and if political ideology predicts belief systems. I conclude with a discussion of implications for policy and future work.