Subject: More about how people think

From: "Nadav Har'El" <[email-masked]>
Date: Fri, 5 Jan 2001 21:38:48 +0200

I just saw the following joke on rec.humor.funny.reruns (it was first posted
on rec.humor.funny in 1989), which is somewhat relevant to our discussion on
how to teach science to kids :)

Newsgroups: rec.humor.funny.reruns
Subject: Food for thought
From: [email-masked] (George Moore)
Keywords: heard it, funny, originally appeared in third quarter, 1989
Date: Fri, 5 Jan 2001 7:20:00 PST

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".'

-- 
Nadav Har'El                        |        Friday, Jan 5 2001, 11 Tevet 5761
[email-masked]             |-----------------------------------------
Phone: +972-53-245868, ICQ 13349191 |War doesn't determine who's right but
http://nadav.harel.org.il           |who's left.

---

From: Shlomi Fish <[email-masked]>
Date: Sat, 6 Jan 2001 09:25:55 +0200 (IST)

Well, I remember that joke, probably some time from the early 90's.
Anyway, I don't consider the original answer as valid, because the
question did not specifically said he had a rope available. And one cannot
assume more than what is given.

Anyway, it is true that in Math there is more than one way to do it(Tm),
and teachers often are not able to cope with this. Recently, in Analog
Communications I solved a question in which I had to fine the Fourier
transform of a trapezoid-like signal, by taking the derivative,
transforming and then multiplying the result by j*w. What I did not do was
convert sin(w)/w into sinc(w), which confused the T.A.

You can find my own solution to the famous Bugs in a Square problem on my
web-site at the Math-Ventures section. I did not see it anywhere but I
know at least 4 or 5 other solutions, one of which I also came by myself.
I read once that solving a problem in three different ways is in a way
better than solving three problems, each in one way.

Regards,

	Shlomi Fish

----------------------------------------------------------------------
Shlomi Fish        [email-masked] 
Home Page:         http://t2.technion.ac.il/~shlomif/
Home E-mail:       [email-masked]

The prefix "God Said" has the extraordinary logical property of 
converting any statement that follows it into a true one.