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 her answer to a physics question, while the student claimed she should be given a perfect score and would, 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.
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 the barometer to the street, and then bring it up, measuring the length of the rope. The length of the rope is equal to the height of the building.”
I pointed out that the student really had a strong case for full credit, since she 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 her 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 that the student did.
I gave the student six minutes to answer the question, with the warning that her answer should show some knowledge of physics. At the end of five minutes, she had not written anything. I asked if she wished to give up, but she said no. She had many answers to this problem; she was just thinking of the best one. I excused myself for interrupting her and asked her to please go on. In the next minute, she dashed off her answer which read: “Take the barometer to the top of the tall building and lean over the edge of the roof. Drop the barometer, timing its fall with a stopwatch. Then, using the formula S = 1/2 at2, 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. On leaving my colleague’s office, I recalled that the student had said she had other answers to the problem, so I asked her 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 a simple proportion, determine the height of the building.”
“Fine,” I said. “And the others?”
“Yes,” said the student. “Here is a very basic method of measurement 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, she concluded, there are many other ways of solving the problem. “Probably the best,” she said, “is to take the barometer to the basement and knock on the superintendent’s door. When he answers, you speak to him as follows: “Mr. Superintendent, here I have a fine barometer. If you will tell me the height of this building, I will give you this barometer.”