This paper concerns a puzzle about teachers' knowledge. That special knowledge of academic subjects is an essential asset in teachers' work, for the more they know the greater their resources for helping learners. Yet that knowledge also is a liability, for the more accomplished teachers are in a field, the more finished their knowledge is. That finished material properly represents teachers' intellectual accomplishments, but it typically is quite remote from learners' tentative and often puzzling formulations. How can teachers use such knowledge to help learners who are only beginners? (Contains 22 notes and 1 table.)