# Let ε < 0.

## 02.4.09

### Evolution of mathematical teaching

Filed under: Diff'rent strokes, Lower-division jokes — Travis @

#### Version 1: the potato problem

1960s:

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

1970s:

A farmer sells a bag of potatoes for \$10. His costs amount to 4/5 of his selling price, that is, \$8. What is his profit?

1970s (new math):

A farmer exchanges a set P of potatoes with set M of money. The cardinality of the set M is equal to 10, and each element of M is worth \$1. Draw ten big dots representing the elements of M. The set C of production costs is composed of two big dots less than 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 your classmates.

1990s:

A farmer sells a bag of potatoes for \$10. His or her production costs are 0.80 of his or her revenue. On your calculator, graph revenue versus costs. Run the `POTATO` program to determine the profit. Discuss the result with students in your group. Write a brief essay that analyzes this example in the real world of economics.

Adapted from The American Mathematical Monthly, Vol. 101, No. 5, May 1994.

#### Version 2: the logging problem

1960s:

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?

1970s:

A logger cuts and sells a truckload of lumber for \$100. His cost of production is four-fifths of that amount, i.e. \$80. What is his profit?

1970s (new math):

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?

1980s:

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

1990s:

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?