I'm old enough to have heard of the "new math" but as far as I can tell that was what I was taught in school. I have asked people older than myself what exactly the "old math" was. They were definitely sure I must have been exposed to the newfangled stuff, but seemed puzzled when I asked them what the differences were. Personally, I really couldn't find any math that I was taught in high school or college that didn't have solid foundations before this century.
Here's my dad's answer:
"I remember the introduction of 'new math' way back in Scotts Valley. I really don't remember what it was except my impression is that it consisted more of talking about math rather than doing it. Most of the parents were worried sick, because they didn't understand it.
"As a help I can remember my youth in Dudley Elementary School (K, 1-7). It was called arithmetic not math. The first ten or fifteen minutes of every day for seven years consisted of excercises in adding, subtracting, multiplying, and dividing numbers. We were each handed a card with the day's problems on it. We each had a tablet of thin, translucent paper. The card went under the top page. We wrote the answers on the paper. Everybody hated this. On the other hand everybody who went through seven years of this could handle numbers without a calculator.
"Of course we also did the usual things in arithmetic class. One thing different was we learned logarithms in the seventh grade. Logarithms are not used anymore because of the computer and electronic calculator. I still love them, because they are real neat. ('Cool' is the new math word for 'neat.')
"The basic difference is that we did arithmetic, which is about numbers, and new math is more about ideas and concepts. Another is, 'This is the problem. What is the answer?' as opposed to, 'This is the concept. What does it mean?' Another attempt to making learning fun instead of work."
SDSTAFF Dex adds:
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.
