The problem is that concrete skills are only a small part of learning. This sort of approach is great for teaching kids to pass math tests, but less great at turning kids into mathematicians.
Ah, I'm glad you agree. I suppose my reaction is that most people underestimate just how far you can go with this approach, and I am glad to see that you are not one of them; we agree that you can train someone to solve calculus problems, but not the skills of derivation.
Where we seem to disagree is about wether this approach should be used in isolation. Frankly, I think most people (successfully) trained in theory are bored by application so there is a use in multiple educational paths.
While application is a small subset of the available learning to someone interested in a field, it is often a sufficient subset to be a productively contributing member of society.
