Working memory is a central topic of cognitive neuroscience because it is critical for solving real world problems in which information from multiple temporally distant sources must be combined to generate appropriate behavior. However, an often neglected fact is that learning to use working memory effectively is itself a difficult problem. The "Gating" framework is a collection of psychological models that show how dopamine can train the basal ganglia and prefrontal cortex to form useful working memory representations in certain types of problems. We bring together gating with ideas from machine learning about using finite memory systems in more general problems. Thus we present a normative Gating model that learns, by online temporal difference methods, to use working memory to maximize discounted future rewards in general partially observable settings. The model successfully solves a benchmark working memory problem, and exhibits limitations similar to those observed in human experiments. Moreover, the model introduces a concise, normative definition of high level cognitive concepts such as working memory and cognitive control in terms of maximizing discounted future rewards.