The Evolution of Teaching Math
(Four variations of the same theme)

How a math problem changed its look ...
Variation #1:

Up to the 1960's

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 1970's

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?


1980's

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 your classmates.


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.


 

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Variation #2:

From the Feb. '96 Reader's Digest:

1960s arithmetic test:

"A logger cuts and sells a truckload of lumber for $100. His cost of production is four-fifths of that amount. What is his profit?"

'70s new-math test:

"A logger exchanges a set (L) of lumber for a set (M) of money. The cardinality of Set M is 100. The set C of production costs contains 20 fewer points. What is the cardinality of Set P of profits?"

'80s "dumbed-down" version:

"A logger cuts and sells a truckload of lumber for $100. Her cost is $80, her profit is $20. Find and circle the number 20."

'90s version:

"An unenlightened logger cuts down a beautiful stand of 100 trees in order to make a $20 profit. Write an essay explaining how you feel about this as a way to make money. Topic for discussion: How did the forest birds and squirrels feel?"

 

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Variation #3:

From issue #91 of Recreational & Educational Computing

Teaching Math in 1996

By laying off 40% of its loggers, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his options at $80? Assume capital gains are no longer taxed, because this encourages investment.

Teaching Math in 1997

A company "outsources" all of its loggers. The firm saves on benefits, and when demand for its products is down, the logging work force can easily be cut back. The average logger employed by the company earned $50,000, had three weeks vacation, a nice retirement plan and medical insurance. The contracted logger charges $30 per hour. Was outsourcing a good move?

Teaching Math in 1998

A laid-off logger with four kids at home and a ridiculous alimony from his first failed marriage comes into the logging company corporate offices and goes postal, mowing down 16 executives and a couple of secretaries, and gets lucky when he nails a politician on the premises collecting his kickback. Was outsourcing the loggers a good move for the company?

Teaching Math in 1999

A laid-off logger serving time in Folsom Prison for blowing away several people is being trained as a COBOL Programmer in order to work on Y2K projects. What is the probability that the automatic cell doors will open on their own as of 00:01, 01/01/00?

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Variation #4:

From John Funk and his daughter

Teaching Math in 1950:
~~~~~~~~~~~~~~~~~~~
A logger sells a truckload of lumber for $100.
His cost of production is 4/5 of the price.
What is his profit?

Teaching Math in 1960:
~~~~~~~~~~~~~~~~~~
A logger sells a truckload of lumber for $100.
His cost of production is 4/5 of the price, or $80.
What is his profit?

Teaching Math in 1970:
~~~~~~~~~~~~~~~~~~
A logger exchanges a set, "L", of lumber for a set, "M", of money.
The cardinality of set "M" is 100. Each element is worth one dollar.
Make 100 dots representing the elements of the set "M."
The set "C", the cost of production contains 20 fewer points than set "M"
Represent the set "C" as a subset of set "M" and answer the following question: What is the cardinality of the set "P" of profits?

Teaching Math in 1980:
~~~~~~~~~~~~~~~~~~
A logger sells a truckload of lumber for $100.
His cost of production is $80 and his profit is $20.
Your assignment is to - Write and underline the number "20".

Teaching Math in 1990:
~~~~~~~~~~~~~~~~~~
By cutting down beautiful trees and desecrating the precious forest a logger makes $20.
What do you think of this way of making a living?
Topic for class participation after answering the question:
How did the forest birds and squirrels feel as the logger cut down the trees? - There are no wrong answers.

Teaching Math in 2000:
~~~~~~~~~~~~~~~~~~~
A logger sells a truckload of lumber for $100.
His cost of production is $120.
How does an Enron Accountant determine that his profit margin is $275?

Teaching Math in 2010 (in California):
~~~~~~~~~~~~~~~~~~
"El hachero vende un camion cargapor 100,000 pesos.
La cuestade production es... "

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