Comment by omnicognate

I think at least in the UK the lack of "mathematical maturity" among early undergraduates is partly the result of this very coyness about mathematical concepts. Enormous time at A-Level is spent rote learning algorithms, and very little on grasping the basic concepts of mathematics, so it's hardly surprising students turn up unprepared for such simple notions as "vector space".

I don't have first hand experience of the French system, but from what I understand the approach there is more along the lines I'm thinking of, and the relative over-representation of French graduates among my more mathematical colleagues suggests it may be rather effective in practice.