I've noticed that some math majors seem to have arrived at their junior or senior years with some pretty severe gaps in their knowledge of the basics. Ideally, students would be constantly looking back and filling in gaps in their knowledge as they progress through their major. (Probably this is something that the top students do automatically, which is part of the reason for their success.) However, many students seem not to spend enough time or energy on improving their understanding of the basics.
How could the structure of a degree program be modified in order to encourage or require students to keep honing their knowledge of the fundamentals?
Here are a few ideas (not necessarily good ideas, just ideas):
All math majors could be required to take a cumulative exam at the end of every semester or every year. The cumulative exam would cover everything the students have learned in their math classes up to that point (but focusing on the fundamentals).
Students could be required to work through the Khan Academy knowledge map and demonstrate proficiency in relevant subjects (as measured by the Khan Academy learning system).
Students could be enrolled every semester in a 2 unit review class which has homework assignments which review the fundamentals of courses they've already taken.
I'd be interested in hearing any non-traditional ideas for how to structure a degree program along these lines.