The Barometer Story by Alexander Calandra – an article from Current
Science, Teacher's Edition, 1964.
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. It seemed
that 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 do so 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.
The Barometer Problem
I went to my colleague's office and read the examination question,
which was, "Show how it is possible to determine the height of
a tall building with the aid of a barometer."
The student's answer was, "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."
Now, this is a very interesting answer, but should the student get
credit for it? 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 that the student knows some physics,
but the answer to the question did not confirm this. With this in mind,
I suggested that the student have another try at answering the question.
I was not surprised that my colleague agreed to this, but I was surprised
that the student did.
Acting in terms of the agreement, 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, since I had another class
to take care of, but he said no, he was not giving up. 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 was:
"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."
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 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 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 between the two values of 'g', the height
of the building can, in principle, be calculated."
Finally, he concluded, "If you don't limit me to physics solutions
to this problem, there are many other answers, such as taking the barometer
to the basement and knocking on the superintendent's door. When the
superintendent answers, you speak to him as follows: 'Dear Mr. Superintendent,
here I have a very fine barometer. If you will tell me the height of
this building, I will give you this barometer.'"
At this point, I asked the student if he really didn't know the answer
to the problem. He admitted that he did, but that he was so fed up
with college instructors trying to teach him how to think and to use
critical thinking, instead of showing him the structure of the subject
matter, that he decided to take off on what he regarded mostly as a
Note that there are alternative versions circulating on the Internet
that do not reference the original author or publication. The above
version I declare is the definitive version.