A computational approach to functional specialization suggests that brain systems can be characterized in terms of the types of computations they perform, rather than their sensory or behavioral domains. We contrasted the neural systems associated with two computationally distinct forms of predictive model: a reinforcement-learning model of the environment obtained through experience with discrete events, and continuous dynamic forward modeling. By manipulating the precision with which each type of prediction could be used, we caused participants to shift computational strategies within a single spatial prediction task. Hence (using fMRI) we showed that activity in two brain systems (typically associated with reward learning and motor control) could be dissociated in terms of the forms of computations that were performed there, even when both systems were used to make parallel predictions of the same event. A region in parietal cortex, which was sensitive to the divergence between the predictions of the models and anatomically connected to both computational networks, is proposed to mediate integration of the two predictive modes to produce a single behavioral output.