“Show how it is possible to determine the height of a tall building with the aid of a barometer.”
As far as the teacher was concerned, it was a simple enough concept. A student’s response to the above prompt would reveal whether the student properly understood the concept of how barometric pressure changes with elevation. Much to the teacher’s surprise, he was the one who had a lesson to learn.
The professor at Washington University, St. Louis, Missouri, had posed the above question to the class, expecting the correct answer that the height of the building can be estimated in proportion to the difference between the barometer readings at the bottom and at the top of the building.
One student gave a different answer that wasn’t wrong, but it wasn’t what the professor expected. His response: “Take the barometer to the top of the building. Attach a long rope to it, lower the barometer to the street, then bring it up, measuring the length of the rope. The length of the rope is the height of the building.”
The professor declined to give the student credit for the answer, but the student protested. The student pointed out that nothing in the question required a specific approach to get the answer and that his approach did, indeed, provide the correct answer to the question that was presented.
The professor asked his colleague, Alexander Calandra, to help resolve the dilemma. The issue, of course, was that a correct answer should earn the student full credit. At the same time, the purpose of the exercise was to establish whether the student understood the concepts taught in the class. Awarding full credit did not seem appropriate, but it also felt wrong to deny credit for an answer that was not incorrect.
Calandra proposed giving the student another opportunity to answer the question, but with the stipulation that the answer must demonstrate a knowledge of physics. He gave the student six minutes to provide his answer.
Calandra recalled, “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.”
With one minute remaining, the student began to write hurriedly. This is the answer he submitted: “Take the barometers 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 = 1⁄2at2, calculate the height of the building.
Again, the student had not provided the expected answer by the professor, but again the answer was correct. Since the student had met the revised requirements of the examination, the professor grudgingly agreed to award “almost full credit.”
Bemused by the experience, Calandra asked the student about the other answers that he had considered.
“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.”
“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 baiometer 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, “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 I have a fine barometer. If you will tell me the height of this building, I will give you this barometer.’”
Calandra asked the student if he really did not know the conventional answer to this question. The student readily admitted that he did, but he said that he was rebelling against high school and college instructors trying to teach him how to think.
Calandra’s experience has attained near-urban legend status in educational circles. The story has been retold as having occurred at MIT, Harvard, and many other centers of education. The student has been identified Niels Bohr, among others. In truth, it happened in the heartland of the USA with an unidentified student. Calandra wrote about it in “Angels on a Pin,” and it was published in 1959 in Pride, a magazine of the American College Public Relations Association. It has since been reprinted in different publications.
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