There are a number of skills needed in maths (I'm teaching undergraduate pure maths) that are not really topics on their own, such as interpreting a definition, taking negation, or giving counter-examples. Part of me thinks that it's useful, while covering the official content of a course, to also bring in these ideas, so that the students get some practice. On the other hand, part of me thinks this risks confusing the students, by bringing in more than one idea that they are not comfortable with at once. Is there any evidence for which, if either, is better?
Ideally I'd like research papers, but I'm also open to personal experience. I'm also more interested in the case where there are time constraints (ie there is a quantity of material that must be covered that fills the available time).
(A connected question: what about bringing in ideas from earlier courses that students are expected to remember but don't?)