Informal teaching is a ubiquitous social behavior with a rich evolutionary history. We model teaching as the decisionmaking problem of planning a sequence of actions to convey information to a naive learner. We compare humans intuitiveteaching actions in a simple collaborative game to the optimal solution of a Partially Observable Markov Decision Process(POMDP). In a teaching POMDP, the current state is the latent, unobservable knowledge of the student and pedagogicalactions may yield changes in that knowledge or provide partial information about the students state. In our experiment,human teachers balance assessment and instruction while incorporating prior information about student knowledge. View-ing teaching as a POMDP suggests specific predictions for when different teaching actions (e.g., testing versus instruction)should be preferred under different conditions. Improving our understanding of the decision making strategies that underlieintuitive teaching has a range of implications from education to clinical rehabilitation.