Wednesday, February 27, 2008

A Commentary On The Teaching Of Mathematics

I just had to share with you this piece: A Commentary on the Teaching of Mathematics, by James Jackson of Carlisle, Ind. It appeared in "Echoes" (winter 1994), published by Rose-Hulman Institute of Technology, Terre Haute, Ind. "Echoes" took it from the 1993-94 issue of "21st Century" (not otherwise identified).

The commentary takes the form of a series of story problems:

In 1960: A logger sells a truckload of lumber for $100. His cost of production is four-fifths of this price. What is his profit?

In 1970: A logger sells a truckload of lumber for $100. His cost of production is four-fifths of this price, or $80. What is his profit?

In 1970 (new math): A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100, and each element is worth $1.00. Make 100 dots representing the elements of the set M. The set C of the costs of production contains 20 fewer points than set M. Represent the set C as a subset of M, and answer the following question: What is the cardinality of the set P of points?

In 1980: A logger sells a truckload of wood for $100. His cost of production is $80, and his profit is $20. Your assignment: underline the number 20.

In 1990 (outcome-based education): By cutting down beautiful forest trees, a logger makes $20. What do you think of this way of making a living? (Topic for class participation: How did the forest birds and squirrels feel?)

In 1996: (profit-driven education): By laying off 40% of the 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 stock options at $80? Assume capital gains are no longer taxed, because Republicans feel this encourages investment.

In 1997: A company out-sources all of its loggers. The firm saves on benefits, and when demand for its product 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 $50 an hour. Was out-sourcing a good move?

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's 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?

In 1999: A laid-off logger serving time in Folsom 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?

In 2000: (internet in every classroom) Do a web search on forest, trees and logger using two different search engines. E-mail your results to the teacher.

In 2008: A logger sells a truckload of lumber for $100. His cost of production is four-fifths of this price. What is his profit? First, tell us what your strategy will be to solve the problem. Form a hypothesis based on the rubric to test your strategy. Perform a calculation based on your hypothesis, and then discuss why you came to the answer that you arrived at.

It would be funny if it weren't so true!

(H/T Mike A.) More math humor here.