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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 sure where the answer lies, but I suspect that the product
of what would come out of a curriculum where the "robot" does all the math
won't be a skilled problem solver, but rather a person who gives up when
problems get frustrating.
taught arithmetic on a calculator for example. I don't think it would be a
disaster if students weren't allowed to touch calculators until high school;
and even then only under adult supervision. :-)
department at our university is beginning to be less enamored with graphing
calculators and using them for teaching the algebra and calculus classes. I
think this is happening for a reason.
If you think that the math classes and
the physics classes should be reinforcing each other (I do) then I'd say its a
mistake. (Not to mention the Chemistry and the Biology and English
classes).
SDSU