Shallow learning comes from shallow experiences

I love memes, as anyone who saw my artifact for the Coursera MOOC, E-learning and Digital Cultures would have seen. This one which I didn't generate captures what is not uncommon in students in maths and physics. Post-exam, crammed formulas are forgotten over a few beers.

It seems to me then, and this is as much a reflection on my own teaching as anything, is that shallow learning comes from shallow experiences. You learn a formula, you plug numbers into it or worse still, follow some long and tedious derivation you have to repeat, and then forget it afterwards. So what would a deep experience of a formula be such that not all of the details would be forgotten?

Of course it depends upon the subject, but number plugging means nothing unless you understand what terms mean, where they come from, their limits and so on. What happens if I ignore this term? How can I scale it such that other terms become unimportant? Can I relate it physically to real problems?

In the end of course, memorizing most formula isn't the point, but recognizing them and using them well. Still, the cry of 'I've forgotten everything' has too often been said with pride. Learning outcomes
need to be such that students see the point of what they are studying (like I'm telling you anything new? and are engaged enough to recall some of it afterwards - wanting to study for more than the sake of passing the exam.