"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
S=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.
"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 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."
"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, 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.