1960's 
A peasant 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, i.e., $8. What is his profit?

1970's (new math) 
A farmer exchanges a set P of potatoes with a set M of money. The cardinality of the set M is equal to 10 and each element of M is worth $1. Draw 10 big dots representing the elements of M. The set C of production costs is comprised of 2 big dots less t han 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?

1980's 
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.

1990's 
A farmer sells a bag of potatoes for $10.00. His production costs are 0.80 of his revenue. On your calculator graph revenue versus costs. Run the "POTATO" program to determine the profit. Discuss the result with students in your group, and write a brief joint essay that analyzes this example in the real world of economics. Each student shall grade the other members of his group (A+, A, or A-).

The validity of SET data is like the old joke about the three statisticians who go duck hunting. One rifle shot whizzes six inches above the duck; another shot flies six inches below it. The third hunter says, "We got him!"

Society for A Return to Academic Standards

Evolution of Teaching Math