Teaching Knowledge during Lectures in Mathematics Analyses and ExamplesWe investigate several issues tied to the moments when the teacher introduces in his classroom the general, formal mathematical knowledge (the "course"). These issues are especially explained with reference to a theoretical hypothesis stated in terms of "pseudoconcepts". Our didactical analyses take into account the contents of the course and its sequence of events. In particular we clarify several discursive "proximities" that may or may not appear during the sequence of events. Such proximities are particularly associated to explicit "closenesses" between students' work over contextualized activities and the underlying general non-contextualized statement. These analyses are first illustrated on examples extracted from a course about graphical representation of functions (14-16 years old students). Secondly, we compare three types of courses on sequences and functions' limits given to first-year university students: a textbook, a video and a lecture. The study reveals differences between diverse courses. It leads to clarify the issue about the specificity of the courses' input in the students' learning.