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'plug & chug' problems



While there is an almost universal distaste for 'plug & chug' problems the
reality of the situation is more complex than a simple sneer conveys.

1) We probably include problem solving in too many courses. Most (non AP)
high school courses would probably better serve the students with 'active
engagement', conceptually focused courses. The same could be said for many
College courses for 'General Education' students, although here other types
of courses might be appropriate ('Physics and Society', Energy or other
focused topics are examples). That leaves AP and Honors HS courses and
science & engineering College courses as those served best by major problem
solving components. [I'm sure some will disagree violently with this.]

2) Sophisticated (real-world) problem solving is the goal, but we have to
recognize that often the students come ill-prepared--that is, they come with
little skill or practice at solving 'word problems'. This means that
students can have a difficult time with even the most simple back-of-chapter
(boc) problems. Part of the problem here is reading skills, but mostly just
a lack of experience with the kind of critical thinking necessary to turn
words into math. While boc problems are probably not ideal, the simple ones
can offer an entry point into this kind of thinking and this kind of math.

3) I consider the rap on boc problems to be somewhat of a 'straw-man'. The
intermediate and difficult levels of problems found in books are seldom
really plug & chug. The real difficulty in using boc problems is that
Chapter 6 problems tend to deal only with Chapter 6 concepts--although even
here I'm seeing more problems that incorporate concepts from previous
chapters. Carefully choosing the problems to be assigned can diminish the
ability of students to just plug & chug the solutions.

4) One can, of course, write their own problems, or (as I do) supplement
the book problems with more 'real-world' ones (the Heller's problems are a
good model). In doing this, one can include enough material from previous
chapters to get the students to have a wider focus. Tests require such a
focus since the problems are not labeled (or even ordered) by chapter.
Another 'trick' is to use test problems that span the whole course (to date)
in the same way one usually does on the final. That is, the second test
will include materials covered for the first test. The fourth test covers
everything up to that point. This coverage can be in a single problem or by
writing test problems that span topics--calculate the electric field to find
the force on a charge to get the acceleration and the final velocity, a
problem type that CAN even be found in text books!

5) The main concern here is two-fold. In which courses should one spend
the considerable effort to teach problem solving. Once it is decided to
include problem solving as a major component of a course, how best to
develop student skills and what types of problems to use. How to 'teach'
problem solving is a complex topic, but it does seem to me that many current
text books have problem sets that should not be dismissed out of hand. It
would be difficult to work up a set of real-world problems that are simple
enough to introduce the basic concepts of problem solving to those students
with little skill and practice with word problems. The simple boc problems
can provide an entry point. The more difficult boc problems are often not
the simple 'plug & chug' variety and should not be dismissed out of hand.

6) A great place to move toward true real-world problem solving is the lab,
especially for classes of higher math abilities. For example, I use our
Pasco Ballistic Launchers (mounted on special bases) in an exercise where I
have the students write an equation for the range of the launchers--in terms
of the spring constant. Since the projectile is launched from a height
above the floor but strikes the floor, the kinematics part of the equation
is somewhat complex. Students must devise an experiment to measure the
spring constants--they end up with vertical shots and energy considerations.
When they get it all combined, they put their equations into a spreadsheet,
develop theoretical range curves (function of angle at a fixed spring
compression, function of spring compression at a fixed angle) and then fire
the launchers to get data to compare to their theory.

In other words, moving away from cook-book experiments to more open
investigations and asking for analyses that include developing equations
from the collected data, can provide really useful problem solving
activities. Of course these can't come 'out of the blue'. You need to know
that student can handle simple systems and simple problems before you hit
them with something like the above.

Rick

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Richard W. Tarara
Professor of Physics
Saint Mary's College
Notre Dame, IN 46556
219-284-4664
rtarara@saintmarys.edu

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