The Evolution of Math Teaching

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1960's: "A farmer sells a bag of potatoes for $10.  His costs amount
to 4/5 of his selling price. What is his profit?" 

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1970's: "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?" 

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1970's (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 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 find its complement, the set of profits. 
What is the cardinality of the set of profits?" 

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1980's: "A farmer sells a bag of potatoes for $10.  His costs are $8 and
his profit is $2.  Underline the profit and discuss the fairness of this
amount with your classmates."

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1990's: "A farmer sells a bag of potatoes for $10.  His or her production 
costs are 0.80 of revenue.  On your calculator, graph revenue vs. costs.
Run the POTATO program to determine the profit. Write a brief essay that
analyzes this example in the context of the real world of economics." 

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(anonymous, adapted from The American Mathematical Monthly, Vol. 101, No. 5)

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