One is that teachers, especially elementary teachers, are so under-prepared in mathematics that the curriculum must do everything for them. It must tell them exactly what to do, when to do it, and in what order. Once this was called "teacher-proof" curriculum. Now, of course, that term is no longer fashionable, so teacher-proof-ness, when it is espoused at all, is couched in other terms. For example, a textbook representative recently described to me the lessons in their teacher's guide by saying, "And it's all scripted for the teacher, so that they know what questions to ask." This view of curriculum assumes that there is a Right Way to organize and teach the curriculum, and that, if we have a curriculum that embodies this right way, students will learn mathematics well.