The article is correct in the insight part, however it misses(or doesn't state explicitly) the fact that insight comes from the definition of the problem, what you are trying to do. Every concept is a solution to a problem, and to get the insight, my approach is to go through a list What am I trying to accomplish (this is where visualizing comes) What are the other ways of doing it How does this method work, and why Why is this method better then others *Where will this method not work.

After this solving any problem in the problem set is a piece of cake. Reduce the problem to subproblems, check applicability of the concept to the subproblems, apply the method, enjoy the result.