Schools tend to present generalizations before specifics. But a generalization is really only valuable if you make it yourself. The reason for this is simple enough. The generalizations we remember are those we make ourselves.
If someone teaches you a generalization (a formula, for example, is a type of generalization that is typically taught) then it better be useful nearly every day, or you will most likely forget it. Generalizations come from cases, lots of cases. When we're faced with lots of cases, we are forced to make generalizations as a way of tying together what we know in a useful form. When we make such generalizations, we can be sure to remember them because we obviously needed them in the first place.
Generalization and understanding are intimately connected. Generalizations that are simply told to us have no place to sit in memory, no cases they tie together, are quickly forgotten from lack of use. They are "lean" generalizations, isolated from the knowledge that would answer questions like "Why is it so?," "Why do I want to know it?," "What are the exceptions?" and "How does this impact on other things that I know?"
The Problem with Expert Systems
Where am I in the content of the book?