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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 physics 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.
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."
The student had answered: "Take a 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."
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 was 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.
I gave the student six minutes to answer the question with the warning
that the 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:
"Take the barometer to the top of the building and lean over the edge
of the roof. Drop that barometer, timing its fall with a stopwatch.
Then using the formula S = Żat▓, calculate the height of the building.
At this point I asked my colleague if he would give up. He conceded,
and I gave the student almost full credit.
In leaving my colleague's office, I recalled that the student had said
he had many other answers to the problem, so I asked him what they
were. "Oh yes," said the student. "There are a great many ways of
getting the height of a tall building with a barometer. For example,
you could take the barometer out on a sunny day and measure the height
of the barometer and 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."
"Fine," I asked. "And the others?"
"Yes," said the student. "There is a very basic 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."
"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 of the two values of `g' the height of
the building can be calculated."
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 tell me the
height of this building, I will give you this barometer."