# There are many correct ways to answer a test question

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=½at2, 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 (p=p_{0}e^{-ay}) 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.

For my part, I seriously considered changing my grade to unequivocal full credit.

R.L. Loeffelbein has been a teacher and writer for 20 years. He was an assistant professor aboard the first voyage of the University of the Seven Seas.