>The students I taught were performing this calculation by the end of the unit, but it was of course a joke. On their exam, they were asked to do this calculation (in differential equations language), and most of them were able to do it because they were good students and had memorized the procedure.
This is a prime example of what I believe is wrong with traditional education (i'm not judging your teaching ability of course), as you are obviously aware, this is more of a box ticking activity than learning in the sense of having any actual understanding.
This has always personally caused me a great deal of trouble, for whatever reason I can only learn substantially through understanding - attempting to memorise procedures when I don't have time to understand the underlying workings is like trying to eat cardboard for me, in that sense I am a bad student and am exiled to purely self taught methods.
Although I am quite content learning on my own, it makes me feel like much of my formal education was a big waste of time, If I could go back in time knowing this I would avoid it altogether.
My experience is hopefully a more dated view by now, I also hold out hope that the new exposure the internet has given courses through MOCs who provide no kind of certification will by proxy refocus traditional education more on the value of learning than certification.
Also in the UK at least there are some new ranking systems emerging for universities that are more focused on learning like TEF, although indirect that is at least a step in the right direction.