In mathematics, courses are arguably conceived and structured around significant ideas. But, for many (interesting) reasons, the final organization (or fine-structure) of the course looks more like a coherent set of technical fragments. This is particularly true at the school level, but is also evident in introductory service courses at university. Of course the ideas orchestrate these fragments into an elegant whole, but little of that is apparent to most students and the impression of the subject that they carry forward is narrow and technical. I will argue for an alternative model based on interesting examples.