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Topic: Another Response to the Open Letter: An analogy
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Jerry P. Becker

Posts: 13,023
Registered: 12/3/04
Another Response to the Open Letter: An analogy
Posted: Dec 18, 1999 1:34 PM
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******************************************************
Note: Thanks to Denis Baker ... . Mr. Baker comments: The following
story highlights several of my reactions to the ongoing debate over the
Open Letter. The story uses a science example and speaks directly to using
problem solving instead of algorithms.
******************************************************

Sir Ernest Rutherford, President of the Royal Academy, and recipient of the
Nobel Prize in Physics, related the following story:

"Some time ago I received a call from a colleague. He was about to give a
student a zero for his answer to a physics question, while the student
claimed a perfect score. The instructor and the student agreed to an
impartial arbiter, and I was selected.

I 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 it 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."

The student really had a strong case for full credit since he had really
answered the question completely and correctly! On the other hand, if full
credit were given, it could well contribute to a high grade in his physics
course and certify competence in physics, but the answer did not confirm
this.

I suggested that the student have another try. I gave the student six
minutes to answer the question with the warning that the answer should show
some knowledge of physics. At the end of five minutes, he hadn't written
anything. I asked if he wished to give up, but he said 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.

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 x=0.5*a*t^2, calculate the height of the building."

At this point, I asked my colleague if he would give up. He conceded, and
gave the student almost full credit.

While leaving my colleague's office, I recalled that the student had said
that he had other answers to
the problem, so I asked him what they were. "Well," 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 simple proportion, determine
the height of the building."

"Fine," I said, "and others?"

"Yes," said the student, "there is a very basic measurement method 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 [gravity] 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, in principle, can be calculated."

"On this same tack, you could take the barometer to the top of the
building, attach a long rope to it, lower it to just above the street, and
then swing it as a pendulum. You could then calculate the height of the
building by the period of the precession".

"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 is a fine barometer. If
you will tell me the height of the building, I will give you this
barometer."

At this point, I asked the student if he really did not know the
conventional answer to this question. He admitted that he did, but said
that he was fed up with high school and college instructors trying to teach
him how to think.
--------------
The name of the student was Niels Bohr." (1885-1962) Danish Physicist;
Nobel Prize 1922; best known for proposing the first 'model' of the atom
with protons & neutrons, and various energy state of the surrounding
electrons -- the familiar icon of the small nucleus circled by three
elliptical orbits ... but more significantly, an innovator in Quantum
Theory.
*************************************************************

Jerry P. Becker
Dept. of Curriculum & Instruction
Southern Illinois University
Carbondale, IL 62901-4610 USA
Fax: (618) 453-4244
Phone: (618) 453-4241 (office)
(618) 457-8903 (home)
E-mail: jbecker@siu.edu

mailto://jbecker@siu.edu





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