Message-ID: <333726BC.6906@continet.com>
Date: Mon, 24 Mar 1997 18:13:33 -0700
From: Rich Lemert <RLemert@continet.com>
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Subject: Re: Grades and credentials
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Herman Rubin wrote:
> 
> In article <33360773.400E@nospam.wanted>,
> sockeye  <sockeye@send.no.spam> wrote:
> >       When I was in high school, I took the New York State Regents exam in
> >algebra. At that time, it was considered to be a fairly difficult exam
> >by high school standards, today, only about 35% of students take the
> >test and pass it. I got a score of 88%. I can say with complete candor
> >that I knew no math beyond arithmetic when I took the test. How did I
> >pass? The exam was multiple-guess, with questions like, "If 5x - 3 = 0,
> >what is x?". I knew that my answer would be (+/-)5/3 or (+/-)3/5 just by
> >inspection, so I could usually eliminate at least two answers, like 4/7
> >or 0. I would then plug in the remaining answers for x, multiply, and
> >mark whichever one "fit" the equation.
> >       If anyone thought they were testing me for my ability to solve linear
> >equations they were sorely mistaken. Had this exam not been
> >multiple-guess, I would have been lost. I would have had to generate
> >likely-looking answers, then try them one by one. Bear in mind, I got a
> >fairly high score.
> 
> 
> This same problem holds, even more so, for formulating word problems.
> 
> I believe this to be THE most important part of algebra for most
> students, and frankly I doubt that most of our graduates in
> mathematics can do it.  This is the mathematical equivalent
> of being able to read and write sentences and paragraphs.
> 
> Notice that I said formulate, not solve, not see if there is
> enough to get a solution, or if a solution exists.  This is
> what is needed before putting the problem on a calculator or
> computer, or calculating the solution in the more common ways
> usually tested.
> 

  I once attended a lecture by Sheila Tobias, a respected author in the
field of technical education and how students learn. She described a
test that was causing the physics community a great deal of 
consternation. The physics professors were all convinced that the test
was meaningless because there was no way anyone could fail it. They
were then surprised because so few people passed.

  The problem was the test was not the typical physics test, but more
like an essay test. There were NO questions such as the following:

  "A baseball player hits a 0.5 kg ball with a force of 125 Newtons
at an angle of 35 degrees above the horizontal. Neglecting wind
resistance and assuming a flat field, does he hit a home-run if the
outfield is 350 ft from home plate?"

Instead, the questions were more along the lines of the following:

  "Hank Aaron has just hit the homerun that broke Babe Ruth's career
record. When the ball is at the peak of its arc, what are the forces
that are acting on it?"

She said it was amazing how many people claimed that the bat was still
acting on the ball even though they were a couple of hundred feet
apart.

  What this points out is that too often we fall in the trap of 
figuring the students understand the material if they can solve the
typical word problem (i.e. indentify the equation that uses all the
variables, and solve for the unknown). To try to combat this, I would
always put what I call "concept" questions on my tests. These were 
similar in thought to the second example above, although in a different
field. The students hated them, in part because I had trouble coming
up with good homework problems that would let them practice the
necessary skills, and in part because they really forced them to think
about the material.

Rich Lemert
