On the rare occasion I can get him to slow down ever-so-slightly, his quality and accuracy go through the roof. I just haven't figured out a way to get him to hit the brakes.
Have him imagine that one day he will design an airplane or a giant skyscraper. What would happen if he makes an error in his calculations or assumptions?
At some point in his life, he will assume a great deal of responsibility and in order to be ready, he needs to have a lot of practice at checking his work and generally being careful.
Speed should be used to give yourself time to check your work on key things IF there is a time crunch!
--
As for home work, there are lots of guides on studying.
But, what I like to do for technical stuff is to:
1. Read the chapter, taking notes.
2. Make flash cards of all theorems and example problems.
3. Memorize those in 2.
4. Do the assigned problems.
5. Do all the problems - omitting the trivial ones.
6. Add cards from 2 to my stack for the class and carry around for 5 minute power sessions.
7. When finals approach:
a. Go through notes from 1 and consolidate.
b. Do randomly selected problems all over again- omitting the easy ones.
c. Do hard problems for speed.
d. Review problems solved 30 min before test.
8. When the class is over with, move notes from 7a into an "archive" notebook for future reference.
If you have time, you can get another book on the subject and work the harder problems in it.
The same can be adapted to humanities type classes. Problem solving is replaced by synopsis of the read passages. I try to totally memorize key passages if doing lit.
If you are reasonably bright, you should be able to do the final with a 100% every time given the above preparation. The speed drill is there to give you time for either very hard problems OR time to check your work.
