Schools are in the business of knowledge, and so it follows that school leadership should draw on theories of knowledge. This chapter lays out some components that might begin to form a body of curriculum theory, to allow insight, bring clarity to thought, create a common language for discussion, and allow the differences between the subjects to be seen more clearly. In this way, leadership of curriculum can be strengthened and a more productive discourse developed. Over a curriculum, semantic waving might be built in over many timescales. In some places the cycle might be completed in a single lesson; in others it might be over a unit, in other places ideas might be developed across months or years. Concrete particulars might be given as temporary scaffolds or developed for fluency, depending on the requirements of the curriculum in question, before moving to abstraction.