Starting with the days of “new math”, the evolution of the teaching of mathematics probably goes like this:
The following examples may help to clarify the difference between the new and old math.
1960: A logger sells a truckload of lumber for $100. His cost of production is 4/5 of this price. What is his profit?
1970 (Traditional math): A logger sells a truckload of lumber for $100. His cost of production is $80. What is his profit?
1975 (New Math): A logger exchanges a set L of lumber for a set M of money. The cardinality of set M is 100 and each element is worth $1.
(a) make 100 dots representing the elements of the set M
(b) The set C representing costs of production contains 20 fewer points than set M. Represent the set C as a subset of the set M.
(c) What is the cardinality of the set P of profits?
1990 (Dumbed-down math): A logger sells a truckload of lumber for $100. His cost of production is $80 and his profit is $20. Underline the number 20.
1997 (Whole Math): By cutting down a forest full of beautiful trees, a logger makes $20.
(a) What do you think of this way of making money?
(b) How did the forest birds and squirrels feel?
(c) Draw a picture of the forest as you’d like it to look.
The indoctrinated pupils end up not even talking about mathematics at all.
Bttt.