The Evolution of Math Teaching
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?"
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?"
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?"
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."
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."
(Anon. Adapted from the American Mathematical Monthly, Vol 101, No.5 May,