Barometer

R.L. Loeffelbein, a physics teacher at Washington University in
St. Louis was about to give a student a zero for the student’s answer
to an examination problem. The student claimed he should receive a
perfect score, if the system were not so set up against the
student. Instructor and student agreed to submit to an impartial
arbiter, Dr. Alexander Calandra, who tells the story.
The examination problem 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, and lower the barometer to the
ground. Then, bring it back up, measuring the length of the rope and
barometer. The lengths of the two together is the height of the
building.”
I, as arbiter, pointed out that the student really had a strong case
for full credit since he had answered the problem completely and
correctly. On the other hand, of course, full credit would contribute
to a high grade for the student in his physics course, and a high
grade is supposed to certify that the student knows some physics, a
fact that his answer had not confirmed. So it was suggested that the
student have another try at answering the problem.
He was given six minutes to answer it, with the warning this time that
the answer should indicate some knowledge of physics. At the end of
five minutes, he had not written anything. Asked if he wished to give
up, he said no, that he had several answers and he was just trying to
think which would be the best. In the next minute he dashed off this
answer. “Take the barometer to the top of the building. Lean over the
edge of the roof, drop the barometer, timing its fall with a
stopwatch. Then, using the formula S=1/2at2, calculate the height of
the building. At this point, I asked my colleague if he gave up and he
conceded. The student got nearly full credit.
Recalling that the student had said he had other answers, I asked him
what they were. “Well,” he said, “you could take the barometer out on
a sunny day and measure the height of the barometer, the length of its
shadow, and length of the building’s shadow, then use simple
proportion to determine the height of the building. And there is a
very basic measurement method you might like. You take the barometer
and begin to walk up the stairs. As you climb, you mark off lengths of
the barometer along the wall. You then count the number of marks to
get the height of the building in barometer units.
“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.’ The height of the building can, in
principle, be calculated from this.
“And,” he concluded, “if you don’t limit me to physics solutions, you
can take the barometer to the basement and knock on the
superintendent’s door. When he answers, you say, ‘Mr. Superintendent,
I have here a fine barometer. If you will tell me the height of this
building, I will give you this barometer.'”
Finally, he admitted that he even knew the correct textbook answer —
measuring the air pressure at the bottom and top of the building and
applying the appropriate formula illustrating that pressure reduces as
height increases — but that he was so fed up with college instructors
trying to teach him how to think instead of showing the structure of
the subject matter, that he had decided to rebel.