Re: Fluff for the day

["John S. Denker" <jsd@MONMOUTH.COM>]

Hi --

This puzzle gives rise to some pedagogical / philosophical issues.

What is the purpose of posing a problem to students?  IMHO:
  1) The primary purpose is that the students should learn something by
working he problem.
  2) The secondary purpose is that the teacher should learn something
about the students' progress.
  3) On rare occasions the purpose is to lay the foundation for a later
discussion.

Note:
  1) The students usually learn the most from problems that are neither
too hard nor too easy.
  2) Similar considerations apply to evaluating the students:
   -- a question that everybody gets right tells me nothing
   -- a question that everybody gets wrong tells me nothing
   -- a question that people get wrong for random fluky reasons tells me
nothing.

======

For these reasons among others, I very rarely assign tasks where I expect
the student to get it wrong.  I certainly do it, but only on special
occasions, and with very systematic preparation and follow-up.  The
follow-up consists of a detailed discussion of why this situation is a
trap, why it is representative of real-life traps, how to recognize and
avoid such traps, blah, blah, blah.....

When I give flying lessons, there is one task I give students where
_nobody_ has ever gotten it right -- even though I discuss the situation
beforehand for about 30 minutes and make them promise three times that they
will do it right.   Afterwards we discuss it for another 10 minutes or so,
and we go try it again.  Almost everybody gets it right the second
time.  It's important to try it again, so that they can see that it really
is an easy maneuver if they are really prepared for it.

At 09:20 AM 5/4/01 -0500, RAUBER, JOEL wrote:
> Neat question, I think I have one of my final exam questions, now! Thanks!

IMHO the final exam is _not_ a suitable setting for a question like this,
where we expect most people to get it wrong --- because there is no
opportunity to follow up.  Without follow-up, such a question serves
neither purpose 1 (learning by doing) nor purpose 2 (evaluation) nor
purpose 3 (foundation-laying).




At 07:48 AM 5/4/01 -0700, John Mallinckrodt wrote:
> ... lack of an explicit specification of a reference point ...
> was decidedly not an issue for my students.

Are we sure about that?  Sometimes kids have a goodly amount of
horse-sense, even if they can't articulate it using fancy words like "gauge
invariance".  In particular, I can imagine a student using the following
nearly-logical argument:  "If the four charges don't add up to zero, the
energy can be anything you like.  Therefore the only way the question can
possibly make sense is to choose -Q as the answer."

Your situation may differ, but I would feel obliged to give nearly-full
credit for such an argument.  The reason is that I tell my students they
should generally assume that questions make sense.  If I give them a
circuit to analyze, they should assume it is a real circuit with a real
purpose, not a random hodgepodge of components.  I even give this a
name:  "The principle of reasonability".

In real life (unlike an exam), if a question doesn't make sense, you can
usually ask for clarification.

===========================

Here is a possibly constructive suggestion:  The question could be made
gauge-invariant by rephrasing it.  Perhaps something like this:


The following square object was assembled by bringing the four pointlike
components together from great distances.  Three of the objects have
specified charge +-Q as indicated.  Find the charge X on the fourth object,
such that the electrostatic binding energy of the assemblage is zero.

     -Q...........X
      .           .
      .           .
      .           .
      .           .
      .           .
      .           .
      Q...........Q


=============

Note: In chemistry it is conventional to measure binding energy relative to
widely-separated components.  But even this is somewhat ambiguous;  are the
components of CO2 considered C + O2, or C + O + O?