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 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 the barometer to the top of the building,
attach a long rope to it, lower it 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 really answered the question completely and correctly. On
the other hand, if full credit were given, it could well contribute to a
high grade 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 when 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 the barometer, timing its fall with a stopwatch. Then,
using the formula x=0.5*a*t^2, calculate the height of the building."
At this point, I asked my colleague if he would give up. He conceded, and
gave the student almost full credit. In leaving my colleague's office, I
recalled that the student had said that he had other answers to the
problem, so I asked him what they were.
"Well," 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 simple proportion, determine the height of the
building."
"Fine," I said, "and others?"
"Yes," said the student." There is a very basic measurement method 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 between the two values of g, the height of the building, in
principle, can be calculated."
"On this same tact, you could take the barometer to the top of the
building, attach a long rope to it, lower it to just above the street, and
then swing it as a pendulum. You could then calculate the height of the
building by the period of the precession".
"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 is a fine barometer. If you
will tell me the height of the building, I will give you this
barometer.'"
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 instructors trying to
teach him how to think.