Studies in mathematics education have led to the construction of various theoretical lenses to identify and explain crucial didactical phenomena in the learning and teaching of mathematics. In this seminar, through the analysis of students' processes involved in mathematical activities, I will introduce some explanatory frameworks based on a duality of mathematical concepts that can be a source of cognitive gaps for students. The importance of considering the intertwining of different perspectives - epistemological, cognitive and didactic - will be highlighted.