Are you a scientist?

[Andrew (imported)]

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 = {frac 1/2}a{sp 8}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".'

[Paolo]

For some reason, this made me think of Glenn, a student of mine in freshman math some 10 years ago when I was teaching.

Glenn was one of those average students who, if left to his own devices, might or might not come up with answer and get his work all done. He wasn't a dull boy, but he wasn't a genius either. He WAS however, a bit of a smartass.

One day I decided to throw a quiz on towards the end of the term, for extra credit, as the class had hit introductory algebra and everyone was feeling sort of confident about their ability to solve equations with ONE variable. So, being the evil sort that I was, I threw the Quadratic Equation at them and told them to solve it for X. "Take as long as you need," I said.

Now, the equation is A*x-squared + B*x + C = 0. The answer is -B+or-the square root (b Squared - 4a*c) all divided 2a.

During the first few steps, things were fine, on Glenn's paper. Then I see the line ... "Divine Intervention" .... he skips a few steps, obviously knowing the answer but not sure how he got there. A few lines later, when the radicals began to get sticky, he writes "A Miracle Happened." A few lines later, he hands it in.

I gave him 10 of 20 points, noting in red ink that he had violated The Separation of Church and State in the public school system by accepting God's help on a math quiz, and told him to take THAT one up with his Social Studies teacher.:p