This paper, on the central and distinctive contribution of knowledge to teaching, combines philosophical analysis with a discussion of work in research on teaching, student conceptions, and curriculum. The hierarchical argument contains two main points: (1) that content knowledge is a logical precondition for the activities of teaching; and (2) that the firm grasp of subject matter has to be relaxed to allow for its pedagogical, fluid control, that is, the extent to which teachers hold knowledge with ease and flexibility and keep the door open to different points of view. Lacks in the depth and assurance of teachers' knowledge of content can act as conceptual and behavioral traps that lead teachers and students away from education to outward forms of achievement, misconceptions, and procedural concerns. However, factual and conceptual control of subject matter is not enough for teachers. Given the pedagogical requirement for flexible control of subject matter, knowledge of epistemology and history of science is a specific preparation for teaching. Knowledge of this kind deepens understanding of subject matter, encourages the mobility of teacher conceptions, and yields pedagogical knowledge in the form of multiple and fluid conceptions. Policy implications of this argument for the curriculum of teacher education, selection into the profession, and conventional modes of classroom induction are discussed. (Author/JMK)