| Chronology | Current Month | Current Thread | Current Date |
| [Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
Enjoy
______________________________ Forward Header __________________________________
Subject: Barometer Test
Author: Jonah Winters <jwinters@chass.utoronto.ca> at INTERNET
Date: 9/21/96 1:01 PM
[ I sure hope this is a true story. -J ]
Barometers and Analog Design by Alexander Calandra.
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 his answer to a physics question, while the student
claimed he should receive a perfect score and would if the system were not
set up against the student. The instructor and the student agreed 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 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."
I pointed out that 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. 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 when the student
did. 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 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. 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=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. In 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. "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 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 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."
"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, to use the "scientific method," and to explore the deep
inner logic of the subject in a pedantic way, as is often done in the new
mathematics, rather than teaching him the structure of the subject. With
this in mind, he decided to revive scholasticism as an academic lark to
challenge the Sputnik-panicked classrooms of America.