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Re: Derivations



Jim Green replied:

>
I think you're being optimistic, Jim.

Perhaps you misunderstand me, Hugh. People are complaining that it takes
up so much time to do the copious derivations, that they don't have time to
tech in discussion (ie Socratic) mode. I say that by far most required
derivations are simple enough that they should not take very much time to
show on the board. So do them and move on. Students are not dumb -- only
lazy. Few of them are even as difficult as SR.

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. Although I never intentionally try a derivation that I
have not prepared in advance, every so often a question comes up that
makes is worth while to do one that I hadn't anticipated, and those
often are the most instructive. Since I haven't prepared it, they are
seldom done in a linear fashion. There will sometimes be two or three
false starts before we get where I want to go. After it is done, I
usually reprise the process and show them how I worked from a general
thought to the correct route (or a correct route, for there is seldom
only one), using some very general ideas and seeing where they led.
If they don't show progress fairly quickly, I abandon them for
another possible route. My goal is to let them know that this isn't
all cut and dried, and that the final result that gets published
never (unless the author is Feynman) shows any of the blind alleys
that the author struggled with. It is important for students to see
that the process of discovery is not a straightforward logical one,
and that there is a lot of "noodling around" that goes on. I also
point out that doing a problem using the "brute force and ignorance"
method is often a good way to go, and that once completed by that
method a simpler and more elegant way is often suggested by what they
have been through. Doing problems the hard way is often a valuable
learning experience.

As a teacher, it seems to me, we are caught between two goals: to
show, or to help the students find the way from the beginning to the
end in some fairly efficient way (after all, we have only so much
time to take them through several hundred years of development), but
at the same time, show them something about how science is really
done. We all know that a textbook is the distillation of a lot of
hard work, false starts and mistakes, but if that's all the students
see, they often despair that they could never do something like that
themselves, and they don't realize that nobody has. It is important
for them to see and to experience the frustrations of "real science"
even if only vicariously.

It isn't necessary that they see it every time, only that they see it
often enough to know what is hidden behind the stuff they read in the
textbooks.

Hugh
--

Hugh Haskell
<mailto://hhaskell@mindspring.com>

Let's face it. People use a Mac because they want to, Windows because they
have to..
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