Angels
on a Pin
by Alexander Calandra
1. Some time ago, I received a call from a colleague who asked
if I would be the referee on the grading of an examination
question. He was about to give a student a zero for his answer
to a physical question, while the student claimed he should
receive a perfect score and would if the system were not set
up against the student. The instructor and the student agreed
to submit this to an impartial arbiter and I was selected.
2. I went to my colleague's office and read the examination
question. "Show how it is possible to determine the height
of a tall building with the aid of a barometer."
3. The student had answered: "Take the barometer to
the top of the building, attach a long rope to it, lower the
barometer to the street, and then bring it up, measuring the
length of the rope. The length of the rope is the height of
the building."
4. I pointed out that the student really had
a strong case for full credit, since he had answered the question
completely and correctly. On the other hand, if full credit
were given, it could well contribute to a high grade for the
student in his physics course. A high grade is supposed to
certify competence in physics, but the answer did not confirm
this. I suggested that the student have another try at answering
the question. I was not surprised that my colleague agreed,
but I was surprised that the student did.
5. I gave the student six minutes to answer the question,
with the warning that his answer should show some knowledge
of physics. At the end of five minutes, he had not written
anything. I asked if he wished to give up, but he said no.
He had many answers to this problem; he was just thinking
of the best one. I excused myself for interrupting him, and
asked him to please go on. In the next minute, he dashed off
his answer which read:
6. "Take the barometer to the top of the building and
lean over the edge of the roof. Drop the barometer, timing
its fall with a stopwatch. Then, using the formula S = ½at2, calculate
the height of the building."
7. At this point, I asked my colleague if he would give up.
He conceded, and I gave the student almost full credit.
8. In leaving my colleague's office, I recalled that the
student had said he had other answers to the problem, so I
asked him what they were. "Oh yes," said the student.
"There are many ways of getting the height of a tall
building with the aid of a barometer. For example, you could
take the barometer out on a sunny day and measure the height
of the barometer, the length of its shadow, and the length
of the shadow of the building, and by the use of a simple
proportion, determine the height of the building."
9. "Fine," I said. "And the others?"
10. "Yes," said the student. "There is a
very measurement method that you will like. In this method,
you take the barometer and begin to walk up the stairs. As
you climb the stairs, you mark off the length of the barometer
along the wall. You then count the number of marks, and this
will give you the height of the building in barometer units.
A very direct method.
11. "Of course, if you want a more sophisticated method,
you can tie the barometer to the end of a string, swing it
as a pendulum and determine the value of g at the street level
and at the top of the building. From the difference between
the two values of g, the height of the building can, in principle,
be calculated."
12. Finally he concluded, there are many other
ways of solving the problem. "Probably the best,"
he said, "is to take the barometer to the basement and
knock on the superintendent's door. When the superintendent
answers, you speak to him as follows: "Mr. Superintendent,
here I have a fine barometer. If you will tell me the height
of this building, I will give you this barometer."
13. At this point, I asked the student if he really did
not know the conventional answer to this question. He admitted
that he did, but said that he was fed up with high school
and college instructor trying to teach him how to think, to
use the "scientific method," and to explore the
deep inner logic of the subject in a pedantic way, as is often
done in the new mathematics, rather than teaching him the
structure of the subject. With this in mind, he decided to
revive scholasticism as an academic lark to challenge the
Sputnik panicked classrooms of America. ■■
Source:
Calandra, Alexander. "Angels on a Pin." Quick
Takes: Short Model Essays for Basic Composition. Elizabeth
Penfield and Theodora Hill. 67-69.
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