The Evolution of an Arithmetic Problem
1950:
A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is the profit?
1960 (traditional math):
A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price, or in other words $80. What is his profit?
1970 (new math):
A lumberjack exchanges a set L of lumber for a set M of money. The cardinality of set M is 100, and each element is worth $1. Make 100 dots representing the elements of set M. The set C is a subset of set M, of cardinality 80. What is the cardinality of the set P of profits, if P is the difference set MC?
1980 (equal opportunity math):
A lumberjack sells a truckload of wood for $100. His or her cost of production is $80, and his or her profit is $20. Your assignment: Underline the number 20.
1990 (outcome based education):
By cutting down beautiful forest trees, a lumber person makes $20. What do you think of his way of making a living? In your group, discuss how the forest birds and squirrels feel, and write an essay about it.
1995 (entrepreneurial math):
By laying off 402 of its lumberjacks, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his stock options at $80? Assume capital gains are no longer taxed, because this encourages investment.
1998 (motivational math):
A logging company exports its wood-finishing jobs to its Indonesian subsidiary and lays off the corresponding half of its US workers (the higher-paid half). It clear-cuts 95% of the forest, leaving the rest for the spotted owl, and lays off all its remaining US workers. It tells the workers that the spotted owl is responsible for the absence of fell-able trees and lobbies Congress for exemption from the Endangered Species Act. Congress instead exempts the company from all federal regulation. What is the ROI (return on investment) of the lobbying?
The answer to the problem was "log(1+x)". A student copied the answer from the student next to him, but didn't want to make it obvious that he was cheating, so he changed the answer slightly, to "timber(1+x)".
1950:
A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is the profit?
1960 (traditional math):
A lumberjack sells a truckload of lumber for $100. His cost of production is 4/5 of this price, or in other words $80. What is his profit?
1970 (new math):
A lumberjack exchanges a set L of lumber for a set M of money. The cardinality of set M is 100, and each element is worth $1. Make 100 dots representing the elements of set M. The set C is a subset of set M, of cardinality 80. What is the cardinality of the set P of profits, if P is the difference set MC?
1980 (equal opportunity math):
A lumberjack sells a truckload of wood for $100. His or her cost of production is $80, and his or her profit is $20. Your assignment: Underline the number 20.
1990 (outcome based education):
By cutting down beautiful forest trees, a lumber person makes $20. What do you think of his way of making a living? In your group, discuss how the forest birds and squirrels feel, and write an essay about it.
1995 (entrepreneurial math):
By laying off 402 of its lumberjacks, a company improves its stock price from $80 to $100. How much capital gain per share does the CEO make by exercising his stock options at $80? Assume capital gains are no longer taxed, because this encourages investment.
1998 (motivational math):
A logging company exports its wood-finishing jobs to its Indonesian subsidiary and lays off the corresponding half of its US workers (the higher-paid half). It clear-cuts 95% of the forest, leaving the rest for the spotted owl, and lays off all its remaining US workers. It tells the workers that the spotted owl is responsible for the absence of fell-able trees and lobbies Congress for exemption from the Endangered Species Act. Congress instead exempts the company from all federal regulation. What is the ROI (return on investment) of the lobbying?
The answer to the problem was "log(1+x)". A student copied the answer from the student next to him, but didn't want to make it obvious that he was cheating, so he changed the answer slightly, to "timber(1+x)".