Re: [math-fun] Why Tough Teachers Get Good Results
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?
* Henry Baker <hbaker1@pipeline.com> [Oct 23. 2014 16:46]:
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.
Agreed. You may have forgotten: programming is a splendid way to learn to concentrate! (I find this important because bad students often have a rather shocking inability to concentrate.)
If you also have access to Maxima/Mathematica/Maple, etc., with good plotting capabilities, then you can learn even more.
This can be dangerous if no peer with superior knowledge is available. I know, because I went down this route! The problem being (the danger of) "mindless numerology".
I think that math education could be vastly improved by incorporating a lot more computer computations into early math.
_early_ math, sure? Most important is having a good teacher, and no amount of multi-media foobar will make any teacher significantly better.
This would replace most of the mindless repetition -- e.g., 4x4 matrices.
Indeed 4x4 sounds silly to me, but... Would you agree that letting students compute eigen-values/vectors for 2x2 matrices (with tiny integer entries) so they a grip on it? I observe a lack of very basic skills in students that should have been learned much earlier. Many of these are usually learned by doing sufficiently many exercises. Best, jj
At 10:45 AM 10/22/2014, Andy Latto wrote: [...]
participants (2)
-
Henry Baker -
Joerg Arndt