[Phys-L] critical reasoning (was: suspended metal rod)

[John Denker <jsd@av8n.com>]

On 05/11/2013 06:10 PM, John Mallinckrodt wrote:

> Nothing wrong with the question.

I disagree.  I consider the question to be ill-posed.

They guy who originally posed the problem essentially told us it was 
ill-posed, at the start of this thread!  What more do you need?

> The torque equation will tell you where the center of mass of the rod
> is.  However, it is probably easy to make an unwarranted assumption
> about the position of the CM and get inconsistent answers.

I still disagree.  Words are supposed to have meaning.  The statement 
of the problem spoke of a "metal bar" and "rod".  Unless otherwise
specified, is not IMHO "unwarranted" to assume it is an ordinary rod, 
i.e. a slim cylinder, in accordance with the conventional meaning of 
the words.

Similarly, diagrams are supposed to have meaning.  In a technical
drawing, if the left half and the right half of an object are made
of wildly dissimilar materials, you are supposed to indicate that
on the diagram.  Hatching or shading are conventional indications.
Also if the left half and the right half have dramatically different 
diameters, you are supposed to indicate this.  In the absence of 
such indications, it is by no means "unwarranted" to assume it is 
an ordinary uniform cylinder.

Perhaps more importantly, if you are going to play lawyer games
with the mass distribution, beware that other people can play the 
same games.
 -- The bar could be in motion.  The horizontal state could be
  just a momentary snapshot.  The statement of the problem did 
  not explicitly say that the bar was at equilibrium.  Is it 
  "unwarranted" to assume static equilibrium?
 -- In the real world, cables are sometimes rather stiff.  The 
  statement of the problem said the cables were massless, but did 
  not explicitly say they were flexible.  Is it "unwarranted" to 
  assume flexibility?
 -- The statement of the problem did not specify g.  It gave the
  mass of the bar but not the weight.  The easiest way to account
  for the dangle is assume weightlessness.  Is it "unwarranted" to
  assume standard terrestrial gravity?
 -- etc. etc. etc.

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

On 05/11/2013 05:34 PM, LaMontagne, Bob wrote:

> > The moral of the story is don't make up
> > quickie problems for an exam.

I think there are additional morals, some of which are more positive
and more interesting.

Sometimes I run into teachers who consider /critical thinking/ to
be important, but say they don't know how to teach it.  Well, the
rod example is a golden opportunity.  It is a teachable moment.

1) The cornerstone of critical thinking is to /check your work/.
This is "supposed" to be emphasized in third grade and every grade 
thereafter.  There are usually many checks that can be made.  For
one thing, if there are two ways of solving the problem, solve it 
both ways and compare the results.  Always look for additional
lines of analysis.

  --> When designing quiz questions, provide enough context to 
  permit multiple lines of analysis.  In other words, overspecify
  the problem.

2) Another element of critical thinking is to check the data against
*all* the plausible hypotheses.   Among other things, this includes 
recognizing that the problem could be ill-posed.

3) Another element of critical thinking is to check that each hypothesis
accounts for *all* of the data.  This is related to item (1), and is the 
mirror image of item (2).  In the rod example, this includes accounting 
for the y-component of force as well as the x-component of force.

> > don't make up quickie problems for an exam.

I assume "quickie" means "quick and dirty" ... but we should be careful
how we express this idea.

"Quick" is not necessarily synonymous with "quick and dirty".  Actually,
other things being equal, quicker is better than slower.  The goal should
be to carry out the task quickly and accurately.  This includes doing the
initial work quickly and efficiently ... and then /checking/ the work 
quickly and efficiently.

We agree that trying to be /too/ quick can cause problems ... but that
does not mean slower is better.  Slow and sloppy is in no way better 
than quick and sloppy.

Teachers should insist that students do things properly.  The rule should
be
 -- show the work
 -- check the work
 -- show the checks
 -- design the work from the outset to facilitate checking

This includes taking off points, even if the solution is numerically 
correct, if the checks are not shown.  This should *not* be confined 
to one lesson during the year, on National Critical Reasoning Day, 
but instead should be a routine rule applied to every assignment.

Also:  Charity begins at home.  This means systematically checking your
own work.

Complacency is an occupational hazard for teachers.  If you spend 20 years
in a situation where you are the smartest guy in the room, it is easy to 
get complacent.  Furthermore, students are so accustomed to being taught
nonsense that even if you say something wrong, they're usually not going 
to call you on it.

  However, this does not make it OK!  Really not!  You should train the
  students -- and yourself -- to /think/ about what is being said.  If
  it doesn't make sense, somebody needs to blow the whistle.

As an example:  Before you talk about Baer's law as a real-world example of
the Coriolis effect, check it!  Crunch the numbers and figure out that it
doesn't make any sense.  (This takes about two minutes.)  Or just google 
it and come to the same conclusion.  (This takes about 30 seconds.)
  http://en.wikipedia.org/wiki/Baer%27s_law

As another example:  Before you claim that Kirchhoff's voltage law is a 
general principle, before you claim it is a necessary consequence of the
Maxwell equations, before you claim it is guaranteed on the basis of 
conservation of energy, check it!  (None of those claims is true.)

Note that working in the research lab can serve as a partial antidote to 
complacency.  You can see only so many ground loops before you learn not 
to put blind faith in Kirchhoff's laws.  If you get complacent in the lab, 
Mother Nature will call you on it, mercilessly.  On the other hand, this 
doesn't solve all the world's problems, because people have an amazing 
ability to be sloppy about some things, even while being fastidious about 
other things.