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Re: More on (Derivations)



I am trouble by a couple of the comments on derivations:

e.g.

This avoids the need to rely on derivations which are
mysterious and tedious to algebra-challenged students

One of the more important reasons for covering derivations (besides helping
in learning where a lot of the stuff comes from, and fits into the scheme
of
things, and isn't just a collection of facts), assigning some derivations
as
HW and even having them every now and then on tests (not to be memorized,
because often its a similar but different derivation from the assignment;
in
fact as long as there aren't numbers most students view a problem as a
derivation, or worse as "theory"): is to address the "algebra-challenged"
nature of the students. Derivations requires that they try to develope and
enhance their skills with algebra and algebraic reasoning to solve
problems.
If nothing else, I hope my students develope these kind of skills and the
cognitive abilities that come from developing them.

I agree with that. I never do a derivation that I can't complete in a
few minutes. If it's longer than that they forget even what we were
trying to do.

This means that those students never have to attempt to grapple with a
longer derivation and develope their skills in dealing with such. I'd hope
that one of the purposes of higher education is to develope these very
skills. I know attention spans are such that this is difficult; but its
for
that very reason students should be forced to confront such tasks, even as
a
freshman, where I believe it should start.

Naturally I don't mean that the bulk of the intro course should be half
hour
derivations or any such nonsense; just that every now and then a longer
than
few minute derivation should be dealt with (by whatever means); following
long arguements is an important higher level coginitive skill and the
developement of that skill should beging sooner than later.

My comments are not necessarily meant to be appropriate in high school
contexts.

Joel Rauber
Joel_Rauber@sdstate.edu