Re: plug and chug

[John Clement <clement@HAL-PC.ORG>]

> 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.
> 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, think of the
> opportunities that these problems provide for failing to test on the real
> issue.
>
> John Clement's problem is a p&c problem in disguise.  I agree that it is
> better than a p&c problem and has merit as a vehicle for group solution.
> It would tend to lead the group to "discover" the underlying p&c.  The
> Anent problem would probably best be used as a vehicle for discussion in a
> lab setting.
>
> I suggest that the KISS principle should be used for the design of non-p&c
> problems.  Here is another example, taken from TMU.

Actually neither problem is mine, but rather comes from the cited sources.
The first one is definitely not plug and chug because it is not actually
supposed to be solved.  The students must write down how they would solve
it.  This was just a random selection from the cited source, and perhaps
someone may be able to come up with even better examples from the same
source.  The first problem is intended for college use and is way too
difficult for a regular HS course.

The second one is also not plug and chug because it requires some analysis
such as drawing a graph before writing down an equation.  Indeed at the
point in which the second problem is introduced, students have not been
given any equations at all, but have been introduced to graphs and strobe
diagrams, so plug and chug is impossible.  A given problem can be non plug
and chug if the students are not given specific equations that make it easy
to solve.  Incidentally they have been introduced to some of the equations
in math, but it the math has zero feedthrough.  This means that timing can
be important in determining whether or not a problem is plug and chug.  This
problem is intended for HS use.  The cited reference is a very nicely
formatted worksheet that is designed to take about 45 minutes or so.  The
MOP series does not introduce the 4 SVT equations, but introduces the use of
graphs and strobe diagrams as an alternate solution method along with the
basic equations for position, and velocity in 1 dimension.  The second
problem (Merinda and Joey) is actually designed to help break students of
the habit of just searching for the relevant equation, as 98% of the
students are not capable of using equations on that problem.

As far as KISS is concerned, the whole point of rich context problems is
that students have to wade through information to find the relevant stuff.
This is an attempt to simulate real life problems.  Another strategy that is
employed is distributing the information around the problem in different
places without specifically telling the student where to look.  For example
some information is in the statement, some in the picture (drawing), and
some can be in the graph.  Obviously the amount of detail in a problem must
be adjusted for usage.  Very rich problems are only suitable for group
problem sessions or for group tests.  Sparser problems must be used for
individual tests, but even there it is advisable to add in some irrelevant
or redundant detail, or even have some missing detail.

Rather than concentrating on just the 2 examples I presented, I would
recommend going to the references and reading the material there.  In
addition both web sites have posted papers explaining the philosophy with
references to the published papers.

One may also categorize problems as being numerical or descriptive.
Descriptive require an explanation, and are by nature not p&c.  Numerical
problems can be p&c or not depending on the information given, the
information the student currently has, and the way in which the problem is
presented.