  Infant-directed speech (IDS) has distinctive properties that differ from
adult-directed speech (ADS). Why it has these properties -- and whether they
are intended to facilitate language learning -- is matter of contention. We
argue that much of this disagreement stems from lack of a formal, guiding
theory of how phonetic categories should best be taught to infant-like
learners. In the absence of such a theory, researchers have relied on
intuitions about learning to guide the argument. We use a formal theory of
teaching, validated through experiments in other domains, as the basis for a
detailed analysis of whether IDS is well-designed for teaching phonetic
categories. Using the theory, we generate ideal data for teaching phonetic
categories in English. We qualitatively compare the simulated teaching data
with human IDS, finding that the teaching data exhibit many features of IDS,
including some that have been taken as evidence IDS is not for teaching. The
simulated data reveal potential pitfalls for experimentalists exploring the
role of IDS in language learning. Focusing on different formants and phoneme
sets leads to different conclusions, and the benefit of the teaching data to
learners is not apparent until a sufficient number of examples have been
provided. Finally, we investigate transfer of IDS to learning ADS. The teaching
data improves classification of ADS data, but only for the learner they were
generated to teach; not universally across all classes of learner. This
research offers a theoretically-grounded framework that empowers
experimentalists to systematically evaluate whether IDS is for teaching.
