A friend of mine showed me a pretty practical Java example. It was a riddle. I got excited and quickly solved the problem. After it, he showed me the mathematical explanation of my solution (he proved why is it good), and it was completely clear for me.

This seems like natural approach for me: solve problems, and generalize. This is very familiar to me, I do it all the time when I am programming: I write a function. When I have to write a similar function, I generalize the problem, grab the generic parts, and refactor them to a function, and solve the original problems as a specialization of the general function.

At the university (or at least where I study), things work backwards. The professors shows just the highest possible level of the solutions ("cryptic" mathematical formulas).

My problem is that this is too abstract for me. There is no connection of my previous knowledge (== reality in my sense), so even if I can understand it, I can't really learn it properly.

Others are learning these formulas word-by-word, and get good grades, since they can write exactly the same to the test, but this is not an option for me. I am a curious person, I can learn interesting things, but I can't learn just text. My brain is for storing toughts, not strings. There are proofs for the theories, but they are also really hard to understand because of this, and in most of the cases they are omitted.

What is the reason for this? I don't understand why is it a good idea to show the really high level of abstraction and then leave the practical connections (or some important ideas / practical motivations) out?