Re: Equation hunting instead of concept hunting (was: Loss of KE)

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

>       While lecture may exacerbate the situation, I think we are dealing
> with a "conditioning" problem with the students.  That is this: throughout
> their high school, and even college careers, memorization, rather than
> understanding principles, has gotten them much success.  In most
> situations
> memorizing an equation, or an example, or a set of facts, has gotten them
> A's; then they run into a particular teacher or course and the technique
> fails.  Going to different styles of Intro Physics courses will help some,
> but I now believe we must be extremely explicit in teaching "principle
> thinking".  Just yesterday I ran across a technique in which during the
> first two weeks of the semester on a weekly quiz the students are asked to
> draw a picture of the problem, then list the variables.  That's it! As the
> the semester goes along the quizzes require more steps to be added
> in to the
> solution of the problems, thus by repetition, the students are conditioned
> into a better mode of thinking through a problem.  We may all have to
> revert to this sort of training.
>
>                    Mike Monce
>                    Connecticut College

Be very careful here.  Just listing variables can actually be a form of
equation hunting.  If you wish to explore a very productive explicit
training method go the web site where the Heller's show their successful
methods.

http://groups.physics.umn.edu/physed/Research/CGPS/CGPSintro.htm

Traditionally textbooks have emphasized writing down the variables, then
selecting the equations, and finally turn the crank to get the answer.
Listing the variables is the first step in this very low level method.  A
more productive approach is to use rich context problems or even missing
information problems where the students are asked whether it is possible to
solve the problem and then either to produce the solution or state why there
is no solution.  If students a low enough, consider using the techniques in
Minds on Physics, Leonard et al, Kendall-Hunt.  And remember that math
research shows that students taught explicit methods usually can not apply
them to similar but different problems, while students taught to understand
can apply the methods to different problems.  If you teach both
understanding and explicit procedures, the students still can not bridge to
other problems.

Certainly I would agree that conditioning is part of the problem, but this
form of condition has been around all along.  We really have no evidence
that students in the 50s are any better than students today.  Indeed there
is a lot of evidence that they were very similar.  The 50s students were a
select group because the low ones dropped out at age 16 in 8th grade.  Only
the very best went to college.  Now all of them at least try to go to
college.  The evidence from IQ tests actually argues that students are
better today than in the 50s.  The raw scores on certain sections of IQ
tests have been rising steadily during this century.  This is disguised by
renormalizing the test.  I forget the figure but it seems to be a certain
number of points per decade.

There is also evidence that the percentage of students who exhibit formal
operational reasoning skills has not changed much.  The average for HS
graduates is around 20% in England, and I think the figure may be similar in
the US.

John M. Clement
Houston, TX

This posting is the position of the writer, not that of SUNY-BSC, NAU or the AAPT.