An institutional point of view of the secondary-university transition: the case of duality

Novice students at the university encounter many difficulties, linked with the secondary-tertiary transition. But what does 'transition' mean exactly? We consider it here from an institutional point of view, which leads us in particular to distinguish between two types of transition. We propose a specific perspective, and apply it to the case of duality in linear algebra. After describing the structure of the mathematical content concerning this theme, we discuss a survey that we have developed for the follow-up of knowledge and difficulties of students enrolled in first-year university mathematics or physics programmes, concerning duality. We present its results categorizing students' difficulties. We explain why it is possible to interpret students' difficulties with duality in terms of transition.