[viddi]

This is something I've always observed. But to be fair, there are many different types of pupils, especially on a high school. If you were to explain things in a way, that they actually mean something, some of your students would do really well, while the rest is unable to grasp the essence. Nowadays schools teach in a way that works for all: Just give recipes, and hope that a few students will motivate themselves to actually understand what they're doing. Or, let them do it for so long, that they get the idea the better, the more often they apply the recipe.

In my case I was one of the lucky few who actually understood derivations after the first class. At home, I thought about half an hour about it, and was able to tell the next "recipe" on the lesson plan. (Side note: Students get rewarded for memorizing algorithms, not understanding them. So even people who are "good in maths" are - even in college - not always good at understanding them.)

Now in university I'm still a bit disappointed. This could be because of my engineering course. We're still just being taught how to do what, but not in a descriptive way. This became extremely bad at differential equations. We weren't even told what differential equations are, and when you use them. It was a mere "you have this, then you have to do that". It seemed very difficult to me, but many other students had no problems. They told me because "it's just: you have this, then you do that".