|
| > Some interesting questions. IMO there is a lot useful
| mental exercise
| > and useful practice in methodical problem solving skills in going
| > through the algebra which you don't get by just setting up the
| > equations in the typical "toy" problems one uses to learn
| the material
| > in high school or introductory courses.
|
|
|
| I'm not entirely convinced of the relative value of the
| "mental exercise" in doing algebraic manipulations. Since
| they can be done by actual robots it seems that a human doing
| them is also acting like a robot, brainlessly performing
| trained manipulations without thinking.
|
|
Hopefully not sinking into the morass of a long debate, so I may just
leave my opinion with the following:
I've noticed over the years that students who were comfortable with
doing the math (algebra and calculus of these problems) tended to have
less problems with doing the physics set-up of the problems as well and
those that didn't had difficulties with the other as well. So there
seems to be something important about going through those exercises IMO.
Does the fact that all of the math manipulations of elementary, middle
and high school can be done by "robots" mean we shouldn't bother
teaching mathematical manipulations?