How do teachers learn about what learners already know? How do learners aid teachers by providing them with information about their background knowledge and what they find confusing? We formalize this collaborative reasoning process using a hierarchical Bayesian model of pedagogy. We then evaluate this model in two online behavioral experiments (N = 312 adults). In Experiment 1, we show that teachers select examples that account for learners' background knowledge, and adjust their examples based on learners' feedback. In Experiment 2, we show that learners strategically provide more feedback when teachers' examples deviate from their background knowledge. These findings provide a foundation for extending computational accounts of pedagogy to richer interactive settings.