  Successful teaching entails a complex interaction between a teacher and a
learner. The teacher must select and convey information based on what they
think the learner perceives and believes. Teaching always involves misaligned
beliefs, but studies of pedagogy often focus on situations where teachers and
learners share perceptions. Nonetheless, a teacher and learner may not always
experience or attend to the same aspects of the environment. Here, we study how
misaligned perceptions influence communication. We hypothesize that the
efficacy of different forms of communication depends on the shared perceptual
state between teacher and learner. We develop a cooperative teaching game to
test whether concrete mediums (demonstrations, or "showing") are more robust
than abstract ones (language, or "telling") when the teacher and learner are
not perceptually aligned. We find evidence that (1) language-based teaching is
more affected by perceptual misalignment, but (2) demonstration-based teaching
is less likely to convey nuanced information. We discuss implications for human
pedagogy and machine learning.
