From shashidhar@protocol.ece.iisc.ernet.in Tue Apr 20 15:57:39 1999
Date: Mon, 19 Apr 1999 21:31:20 +0530 (IST)
From: Shashidhar V
To: Kaushik Ghose ,
Diptendu Mitra
This is probably fictitious, but it sure is fun :
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.
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