The Evolution of Teaching Math

Up to the 1960s
A peasant sells a bag of potatoes for $10.
His costs amount to 4/5 of his selling price.
What is his profit?

In the early 1970s
A farmer sells a bag of potatoes for $10.
His costs amount to 4/5 of his selling price, i.e., $8.
What is his profit?

1970’s (new math)
A farmer exchanges a set P of potatoes with a set M of money.
The cardinality of the set M is equal to $10 and each element of M is worth $1.
Draw 10 big dots representing the elements of M.
The set of production cost is comprised of 2 big dots less then the set M.
Represent C as a subset of M and give the answer to the question:
What is the cardinality of the set of profits?

1980s
A farmer sells a bag of potatoes for $10.
His production costs are $8 and his profit is $2.
Underline, the word “potatoes” and discuss with our classmates.

1980’s (alternative math)
A kapitalist pigg undjustlee akires $2 on a sak of patatos. Analiz this tekst and sertch for erors in speling, contens, grandmar and ponctuassion, and than ekspress your vioos regardeng this metid of geting ritch.

1990’s
A farmer sells a bag of potatoes for $10.00.
His production costs are 0.80 of his revenue.
On your calculator graph revenue versus costs.
Run the “POTATO” program on your computer to determine the profit.
Discuss the result with the other students in your group.
Write a brief essay that analyzes how this example relates to the real world of economics.

Top 10 Excuses For Not Doing the Math Homework

1. I accidentally divided by zero and my paper burst into flames.
2. Isaac Newton’s birthday.
3. I could only get arbitrarily close to my textbook. I couldn’t
actually reach it.
4. I have the proof, but there isn’t room to write it in this margin.
5. I was watching the World Series and got tied up trying to prove
that it converged.
6. I have a solar powered calculator and it was cloudy.
7. I locked the paper in my trunk but a four-dimensional dog got in
and ate it.
8. I couldn’t figure out whether i am the square of negative one or
i is the square root of negative one.
9. I took time out to snack on a doughnut and a cup of coffee.
I spent the rest of the night trying to figure which one to dunk.
10. I could have sworn I put the homework inside a Klein bottle, but
this morning I couldn’t find it.

Subract 7 from 83

Question: how many times can you subtract 7 from 83, and what is left afterwards?

Answer: I can subtract it as many times as I want, and it leaves 76 every time.

13 Misunderstandings in the History of Mathematics

In the interest of historical accuracy let it be known that

1) Fibonacci’s daughter was not named “Bunny.”
2) Michael Rolle was not Danish, and did not call his
daughter “Tootsie.”
3) William Horner was not called “Little-Jack” by his
friends.
4) The “G” in G. Peano does not stand for “grand.”
5) Rene Descartes’ middle name is not “push.”
6) Isaac Barrow’s middle name is not “wheel.”
7) There is no such place as the University of Wis-cosine,
and if there was, the motto of their mathematics
department would not be “Secant ye shall find.”
8) Although Euler is pronounced oil-er, it does not follow
that Euclid is pronounced oi-clid.
9) Franklin D. Roosevelt never said “The only thing we have
to sphere is sphere itself.”
10) Fibonacci is not a shortened form of the Italian name that
is actually spelled: F i bb ooo nnnnn aaaaaaaa
ccccccccccccccccccccccccccccccccccc
iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii.
11) It is true that August Mobius was a difficult and
opinionated man. But he was not so rigid that he could
only see one side to every question.
12) It is true that Johannes Kepler had an uphill struggle
in explaining his theory of elliptical orbits to the
other astronomers of his time. And it is also true that
his first attempt was a failure. But it is not true that
after his lecture the first three questions he was asked
were “What is elliptical?” What is an orbit?” and “What
is a planet?
13) It is true that primitive societies use only rough
approximations for the known constants of mathematics.
For example, the northern tribes of Alaska consider the
ratio of the circumference to the diameter of a circle to
be 3. But it is not true that the value of 3 is called
Eskimo pi. Incidentally, the survival of these tribes is
dependent upon government assistance, which is not always
forthcoming. For example, the Canadian firm of Tait and
Sons sold a stock of defective compasses to the government
at half-price, and the government passed them onto the
northern natives. Hence the saying among these peoples:
“He who has a Tait’s is lost.”

Math Homework Assignment

A student, working on a rather long math homework assignment,
discovered that one problem was fairly easy to solve, except that it
required about three pages of fairly simple proof after the one or two
difficult steps. It being rather late at night, he did the difficult
steps and left the proof undone, along with a note:

“This proof is left as an exercise for the grader.”

Next week, he received his homework back. He noted that several extra
pages had been stapled to the back of it. Examining the extra pages,
he was surprised to find the entire proof written down step-by step.
At the end, in red pen, the grader had written:

“I made a minor math error. Minus 2.”

Two Math Professors in a Restaurant

Two math professors are in a restaurant. One argues that the average person
does not know any math beyond high school. The other argues that the
average person knows some more advanced math. Just then, the first one gets
up to use the rest room. The second professor calls over his waitress and
says, “When you bring our food, I’m going to ask you a mathematical
question. I want you to answer, ‘One third x cubed.’ Can you do that?”
The waitress says, “I don’t know if I can remember that. One thurr…
um…”
“One third x cubed,” says the prof.
“One thir dex cue?,” asks the waitress.
“One”
“One”
“Third”
“Third”
“X”
“X”
“Cubed”
“Cubed”
“One third X cubed”
“One third X cubed”
The waitress leaves, and the other professor comes back. They resume their
conversation until a few minutes later when the waitress brings their food.
The professor says to the waitress, “Say, do you mind if I ask you
something?”
“Not at all”
“Can you tell me what the integral of x squared dx is?”
The waitress pauses, then says, “One third x cubed.”
As she walks away, she stops, turns, and adds, “Plus a constant!”

The IBM Building

A small, 14-seat plane is circling for a landing in Atlanta. It’s
totally fogged in, zero visibility, and suddenly there’s a small
electrical fire in the cockpit which disables all of the instruments
and the radio. The pilot continues circling, totally lost, when
suddenly he finds himself flying next to a tall office building.

He rolls down the window (this particular airplane happens to have
roll-down windows) and yells to a person inside the building, “Where
are we?”

The person responds “In an airplane!”

The pilot then banks sharply to the right, circles twice, and makes a
perfect landing at Atlanta International.

As the passengers emerge, shaken but unhurt, one of them says to the
pilot, “I’m certainly glad you were able to land safely, but I don’t
understand how the response you got was any use.”

“Simple,” responded the pilot. “I got an answer that was completely
accurate and totally irrelevant to my problem, so I knew it had to be
the IBM building.”

“Standards are Falling”

My wife was at one of the math parties, getting rather bored.
A friend of mind explained to her that there was one conversation
line that always worked with professors. Just say
“Standards are falling.”
Another professor overheard this, and turned around to say that
this was absolutely true, and we spent the next half hour
complaining about how standards are falling.

Computer Science Students

A question is asked to CS department students. The question is: What is
the value of `2*2′?

(1st year student): says `4′, without any thinking.

(2nd year student): says `4, exactly’, after a moment of thinking.

(3rd year student): takes a pocket calculator, presses some buttons and
says `4′.

(4th year student): writes a program of about 100 lines, debugs it, runs
it and says: `4.0e+00′.

(5th year student): designs a new programming language that perfectly
fits for solving such problems, implemets it, writes a program, and
answers: `It says “4”, but I doubt if I really fixed that ugly bug last
night…’

(student just before the final graduation exams): cries in desperation:
`Why, why do you think I must know all that bloody constants by heart?!’