In the same way maybe what most people are "actually practicing" when they do math homework is flipping though the textbook until they find an example problem that looks analogous to the one they're working on and imitating the structure of the example problem solution in order to do their homework.

That would explain why story problems seem to be perceived as hard by average students at the high school level. I remember being confused by that, since mathematically they were usually the easiest problems in a set -- but they wouldn't be trivially pattern-matched to sample problems.