  A good teacher should not only be knowledgeable; but should be able to
communicate in a way that the student understands -- to share the student's
representation of the world. In this work, we integrate insights from machine
teaching and pragmatic communication with the burgeoning literature on
representational alignment to characterize a utility curve defining a
relationship between representational alignment and teacher capability for
promoting student learning. To explore the characteristics of this utility
curve, we design a supervised learning environment that disentangles
representational alignment from teacher accuracy. We conduct extensive
computational experiments with machines teaching machines, complemented by a
series of experiments in which machines teach humans. Drawing on our findings
that improved representational alignment with a student improves student
learning outcomes (i.e., task accuracy), we design a classroom matching
procedure that assigns students to teachers based on the utility curve. If we
are to design effective machine teachers, it is not enough to build teachers
that are accurate -- we want teachers that can align, representationally, to
their students too.
