Parents' expectations for their children's ultimate educational attainment have been hypothesized to play an instrumental role in socializing academically relevant child behaviors, beliefs, and abilities. In addition to social transmission of educationally relevant values from parents to children, parental expectations and child characteristics may transact bidirectionally. We explore this hypothesis using both longitudinal and genetically informative twin data from the Early Childhood Longitudinal Study--Birth and Kindergarten cohorts. Our behavior genetic results indicate that parental expectations partly reflect child genetic variation, even as early as 4 years of age. Two classes of child characteristics were hypothesized to contribute to these child-to-parent effects: behavioral tendencies (approaches toward learning and problem behaviors) and achievement (math and reading). Using behavior genetic models, we find within-twin-pair associations between these child characteristics and parental expectations. Using longitudinal cross-lagged models, we find that initial variation in child characteristics predicts future educational expectations above and beyond previous educational expectations. These results are consistent with transactional frameworks in which parent-to-child and child-to-parent effects co-occur.