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Re: teaching 'em to learn, to think, and to decide what's important



At 16:02 -0400 7/24/02, John S. Denker wrote:

Similarly, "plug and chug" homework problems should not be
assigned, because they foster the foolish expectation that
problems can be solved in the obvious way. As an example of
something better, include two or three irrelevant factoids
in the statement of the problem. Someone who takes the
childish, greedy approach of exploiting the given factoids
in the order they are presented will get stuck.

Students who expect only "plug & chug" problems are the bane of any
teachers existence. The question that routinely drove me up the wall
was "What equation do I need to solve this problem?"

Neverthless, P&C does have a useful, if limited, role. Get the
students to make some simple calculations of, for example momenta for
many different items, or rest energies for lots of things of wildly
varying sizes. Doing one or two of these sorts of problems at the
very beginning gives the student a "feel for the numbers." What is a
typical energy range for a car, for a human, for an atom, for the
Exxon Valdez (now that it's back at sea), for a comet, whatever. If
they have no feel for the numbers then they have no benchmarks to
compare their answers to for reasonableness. If, for instance, the
student has no idea of how far it is from here to New York, then if
they get an answer to a problem of local dimensions that is
comparable to the distance to New York or more, they will not be able
to see instantly that their answer is unreasonable. If they don't
know that the mass of a typical car is 1000-2000 kg, when they find
20,000 kg as their answer, they won't know enough to question it.

I'm not saying these things should be a big deal, but I usually have
one or two multi-part problems at the beginning of any new subject
that are basically P&C, but which give them their necessary context
for appreciating the numbers they will be dealing with as they study
the subject at hand. And they may get one such question (single part,
usually), on a test, just to see if they have, in fact, developed
that feel for the numbers.

I like to throw new ideas to students on homework problems. Ideas
they may not have heard of, but for which the same tools they are
using at the moment are suitable, although the vocabulary is new. My
experience has been that students usually hate such questions, even
if it is just a P&C with new words. But the students have to be
stretched, even if they think it is being done on a rack.

Hugh
--

Hugh Haskell
<mailto:haskell@ncssm.edu>
<mailto:hhaskell@mindspring.com>

(919) 467-7610

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