  Much effort and research has been invested into understanding and bridging
the gaps which many students experience in terms of contents and expectations
as they begin university studies with a heavy component of mathematics,
typically in the form of calculus courses. We have several studies of bridging
measures, success rates and many other aspects of these entrance transition
problems. In this paper, we consider the inverse transition, experienced by
university students as they revisit core parts of high school mathematics (in
particular, calculus) after completing the mandatory undergraduate mathematics
courses. To what extent does the advanced experience enable them to approach
the high school calculus in a deeper and more autonomous way? To what extent
can capstone courses support such an approach? How could it be hindered by
deficiencies in the students' advanced experience? In this paper, we present a
theoretical framework for an analysis of these questions, as well as a number
of critical observations and reflections on how they appear in our own
institutional context.
