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Jack comments on You don't need Kant - Less Wrong
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I actually think that math teaching might work better if people spent time learning who though what as a result of asking what questions and how they first conceptualized their insights by building on what else.
Memorizing anything anywhere ever except as practice for understanding how memory works is always an indication that something has gone wrong however.
When I was in school, we were given proofs of certain geometry theorems, and we were told that we might have to prove the same theorems in the exam. Most of my classmates simply memorised the proof as given; since I'm better at on-the-spot analysis than at memorisation, I used to re-prove the theorems from basic principles instead. The result of this was that my proof, while (usually) correct, would look nothing like everyone else's proofs. Because of this, the maths teachers would have to actually evaluate my proofs step by step, instead of simply ticking off the well-recognised general proof. Apparently this makes marking slower.
This implies that there may be some pressure from the teachers for memory-learning, as it leads to easier marking.