ABSTRACT
Learning, teaching, and understanding are complex tasks in complex domains like mathematics. Any teacher or student knows that there is rich complexity to the subject of conic sections or continuity. Knowing such domains demands much more than knowing formal statements of definitions, theorems, and proofs: It demands knowing examples, methods, exercises, pictures, graphs, and diagrams; rules of thumb; metaphors and analogies; folksy or informal formulations of ideas; a sense of what is important; a sense of what should follow what. This complexity exists whether the purpose is to learn or to teach.
