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?

Adapted from Reader’s Digest, February 1996.

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