- Jun 18, 2013
I agree with you. With English imo being the best example here: the act of memorising an essay and regurgitating it for an exam is rote-learning, but the initial conception and construction of that essay itself requires a level of critical thinking and understanding on the part of the student.....
This is actually an interesting point, and I'm going to assert that integration is the quintessence of rote-learning. The only real understanding one has for integration is the whole "area under the curve" thing, which is fine. But to analytically solve integrals, that understanding is useless and it only really comes down to "how many integrals have you seen?", and bashing as many familiar integrals and rules you know against the problem until (a) by some measure-zero chance you solve it, (b) give up, or (c) realise the integral is impossible and then give up.In regards to the integral example, we have it committed to memory due to the sheer amount of practice that we do. However, I would think most top students would understand where it comes from and know how to derive it, so I personally wouldn't call it rote learning.
Perhaps this is just my own views on maths here, but particularly with respect to analytical integration, I doubt that there is a real "understanding", and that the top integrators approach the problem with a mechanical blindness and brute-force that is the quintessence of rote-learning. When a difficult integral is solved analytically, the correct approach is almost always discovered by trial-and-error from a history of practice, not deliberated understanding.