Re: plug & chug (not)

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

Hugh Haskell wrote:

> ... 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.

I agree 1000% about the importance of having a "feel for
the numbers".  I agree with everything Hugh said, except the
notion that getting a feel for the numbers is necessarily
or even preferentially associated with plugging and chugging.

Since a fraction of the readership perceives a shortage of
examples, here's one we can discuss:

  1) "I buy milk in ordinary standard one-gallon plastic
  jugs.  I have a picnic cooler with inside dimensions
  12"x12"x12".  How many such milk jugs can I fit in the
  cooler?"

IMHO this requires people to have a "feel" for how big
a milk jug is.  Not all students know that initially.
If you ust ask them, straight out,
  2) "How big is a one-gallon milk jug?"
you'll get a lot of answers around one cubic foot.  Note
that I prefer question (1) to question (2).

NOTE!  The teacher has to make a style decision here, namely
to decide how to present question (1).  Plan A would be to
just assign it, see how well they do, and follow it up with
the important philosophical discussion below.  (The
discussion is mandatory.)  Plan B is to have the discussion
_before_ assigning the problem.  I recommend plan B because
otherwise lots of students would be severely irritated by
the question, and once they're irritated and defensive it's
hard to get 'em turned around.

The philosophical discussion goes something like this:  I am
quite aware that milk jugs have not been discussed in class.
They are not covered in the textbook either.  But you must not
whine about it.  Your mission, should you decide to accept it,
is to figure out how big a milk jug is.  Don't raise your hand,
but each of you please answer the following questions for
yourself:  Do you own no rulers at all?  Are you unable to
afford a ruler?  Are you unable to get to a store where you
can at least touch a milk jug?  I suspect most of you could
figure out the size of a milk jug if you really wanted to.

On rare occasions in this class I will ask you to solve a
problem using a particular method.  On those rare occasions,
I'll let you know.  Otherwise, the rule in this class (and
in the real world) is that you should solve every problem as
expeditiously as you can, using every bit of information and
every technique you can come up with.

More generally, there is an issue of personal responsibility.
You are presumably here because you want to learn something.
This is primarily and almost entirely your responsibility.
My job is to help you meet that responsibility.  I cannot meet
it for you.  Possibly some stuff you read in the textbook (and
elsewhere) is erroneous.  Possibly some of it is irrelevant.
Certainly it is incomplete, in the sense that what you learn
in school is at most 10% of what you need to function in the
real world.  Learning is your responsibility;  all I can do
is help you get started in the right direction.

Whining about problems that seem underspecified is not helpful.
In the real world, virtually every problem you will ever
encounter will be underspecified.

So now you see that the point of question (1) is that you
need to measure the size of a milk jug, even though there
is no explicit instruction to do so.  Now I've spoiled it
by telling you this, but don't worry, there are plenty more
questions where that one came from.