The first rule "do not learn what you do not understand" is nonesense in the context of learning mathematics/physics/hard sciences. If you understand a subject, then it means that you have learned it effectively. In my experience with teaching at university, I have found that the wish of students to understand before learning is actually a great barrier to comprehend a subject. In order to build intuition on a subjec…
As a kid I cried at times because learning foreign words, lists of topological places, or events in history was so hard! If I don't get the structure or context I am so lost. At electrical engineering they still tried to teach me in the same way. Giving me assignments with little context. What saved me in the end were textbooks and the internet. The easiest way for me to understand new concepts are the subsequent gen…
Then, I get to Calculus III, and my instructor introduces each concept by showing us a complicated-but-ultimately-intuitive formula for something, then deriving the "shortcut" step-by-step. While most of the students griped that it was boring, I found it quite interesting, and for the first time in my university career I felt like I could grasp calculus. I made an A-.
There are other instances of this, as well, but that one was probably the most dramatic. I don't know what it is. I came up with a handful of analogies just now, but none of them seemed particularly satisfying, so I gave up. Perhaps it's just a quirk, I dunno :)