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Food for Thought

(One of many versions of this story)

There are several ways to solve a problem. For example, consider the following from "The Teaching of Elementary Science and Mathematics" by Alexander Calandra:

The process of creativity is a mysterious and interesting one. It is brilliantly described in the following story. A student refused to parrot back what he had been taught in class. When the student protested, I was asked to act as arbiter between the student and his professor.

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 the height of the building.'

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 gave the student six minutes, with the warning that his answer should show some knowledge of physics. In the next minute he dashed off his answer, which read: '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 = 1/2a t(2), 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. 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. 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.'

'Finally, there are many other ways of solving the problem. Proably not the best 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."'

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