Rote Drill has its place. Its a great tool. I highly recommend it.
By rote drill, I mean being able to solve a problem or recite a theorem on demand with no hesitation and at the fastest speed possible.
To survive Very Hard tests in college, I had to have some things down cold. I took advanced thermo and stats classes that required us to derive methods to solve general classes of problems then solve specific cases. All the math had to be second-nature. And we ended up using ALL our math skills - from calculus, diff-eq, Linear Algebra, theorems from RA, Stats, etc. Those kids who did could not slam out the math or reach for a theorem, were left behind.
The first week, the instructor told us we had to take this "easy" week to get up to speed. He told us how to do it.
I had already been doing rote drill for calculus and Linear Algebra prior to the semester to get warmed up. But he upped our game. Every night I spent 12 hours outlining all my other texts, categorizing problems, setting up flash cards, then just started going through it. I had over 200 flash cards with theorems and problems - both pure and applied - on them. Once I had all the subjects down, I shuffled the cards, then took 50 with me on the bus each morning. As the class progressed, I added cards from that class.
After I started this method, I usually finished the finals in one hour vs four most of the other students needed. It all came down to that rote drill. A friend of mine started using it when he was in the math program and from then on he got A+ in classes.
To this day, I can look at most applied math problems and do them in my head. And I can usually look at something that is not right and be able to grasp the theorem being used and which of its givens are being violated.
When you look at other human pursuits - such as sports or marksmanship or cqb - rote drill is a key part of the training method. Sure, there are unstructured problems - but the solution to them often involves pieces taken from actions which are down cold. Academics - and problem solving - are no different.
