I find that _writing code_ for a rote procedure helps me understand things. Then applying various kinds of standard computer optimizations to see what happens. The computer is merciless at reminding you not to divide by zero, etc. If you also have access to Maxima/Mathematica/Maple, etc., with good plotting capabilities, then you can learn even more. I think that math education could be vastly improved by incorporating a lot more computer computations into early math. This would replace most of the mindless repetition -- e.g., 4x4 matrices. At 10:45 AM 10/22/2014, Andy Latto wrote:
The thing I disagree with most strongly is the praise for rote learning. I would have learned so much more mathematics if I wasn't required to spend hundreds (thousands?) of hours in rote repetition of things I already knew perfectly well how to do. And not just at the multiplication table level! What possible benefit was their, in an honors-level linear algebra class at a good university, of wasting my time making me do Graham-Shmidt orthogonalization of 4x4 matrices by hand?