To help students in school develop a flexible understanding of subject matter, teachers need to foster understanding of the relationships within and across disciplines, what specialists in a field do, how knowledge in a discipline is generated, tested, and revised, and how knowledge in the discipline relates to the learners' environment. Representations of subject matter (activities, examples, analogies, materials, etc.) used in teaching are the products of weaving understanding of the specific academic discipline together with knowledge of learners, learning, and the context. This paper describes the sources of representation and the knowledge on which teachers should draw in judging their appropriateness. Suggestions are made on what prospective teachers need to know about learners and learning based on research on learning in specific disciplines. Methods teachers should clarify students' views of teaching and learning, increase students' understanding of seminal topics and ideas, get students thinking about the kinds of understanding their pupils are likely to bring with them, evaluate various representations with their students, and model good representations. An annotated bibliography is included. (JD)