Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: plug and chug



The minimal change is to say "the friend pushes forward on the skier",
thereby avoiding the implication that the skier actually moves. However,
this wording easily activates the misconception that forward force implies
forward motion. This might be a good thing, as the misconception can then
be discussed later. By carefully wording a problem you can deliberately
trigger a misconception that needs to be brought out into the open. The
properly worded problem is indeed not p&c. However I would be tempted to
make it slightly richer in context. Perhaps giving the mass of the friend
and both coefficients of friction might be a good idea plus a few
descriptive adjectives about the snow condition and weather. This would
bring in other possible misconceptions and also make the problem much richer
in context. Trying different variations might be an interesting
microexperiment.

The idea of making problems non p&c is good, but richer context also is very
beneficial. The big trick is to challenge the students enough without
totally overloading them. The usefulness of rich context is explained in
the Hellers' papers.

John M. Clement
Houston, TX


Hi John-
Are you really declining to take "yes" for an answer? I've
already said that I'm happy with any rewording of the problem that makes
the intent clearer. You clearly understand that the skier is at rest and
will remain at rest, which is the expected answer. Your wording, which
you believe more clearly describes the situation, is fine with me. Next
time I use the problem I will probably reword it.
The point that the students clearly failed to understand
("clearly" in the light of after-quiz discussions) is that the coefficient
of static friction is defined by an inequality.
Hopefully, the main point of the present exercise is getting
across, namely, that non p&c problems may be directed to concepts, that
they invite erroneous answers from students who don't understand
the concepts,
and that they should be simply stated for reasons already discussed.
Regards,
Jack


On Mon, 29 Jul 2002, John Mallinckrodt wrote:

Hi John-
IMO both John Clement's and this amusing problem have too much
detail, so
that the real point of the problem may easily get lost in the
p&c aspects.

I understand and agree. Since p&c problems occupy a very specific
and narrow range on the spectrum, "non p&c" only tells us what the
problem *isn't.* What we are really talking about are problems that
are *very* simple, but that will not yield to the mindless
application of formulas.

If you get hung up on whether the "friend" pushes the skier
"forward" or
pushes "on the skier's back", where the real issue is whether the push
force is hard enough to overcome static friction, ...

I still don't consider my objection to be "getting hung up." The
first issue in the skier problem *has* to be whether or not the skier
is moving and which way. There are at least three different answers
to this problem depending on that piece of information. Only after
one has established that the skier is at rest is the real issue
whether or not the push is hard enough to overcome static friction.

I know that you mean for the students to understand that the skier is
at rest, but I think you are sending them needlessly contradictory
messages. Why use the phrase "pushed forward" if the skier is at
rest? Why not simply eliminate the ambiguity by using the wording I
suggested? Do you *really* not agree that a student could read your
problem and decide that the skier is moving?

--
John Mallinckrodt mailto:ajm@csupomona.edu
Cal Poly Pomona http://www.csupomona.edu/~ajm


--
"But as much as I love and respect you, I will beat you and I will kill
you, because that is what I must do. Tonight it is only you and me, fish.
It is your strength against my intelligence. It is a veritable potpourri
of metaphor, every nuance of which is fraught with meaning."
Greg Nagan from "The Old Man and the Sea" in
<The 5-MINUTE ILIAD and Other Classics>