What was the purpose of teaching new math in grade schools, early 70s? Usefulness?

Question

"Elfs", "twelfs", "base 7", and similar garbage. Tom Lehrer's song didn't come to my attention till AFTER bad math phobia/hatred had set in, bigtime.
Why were they trying to teach NM to grade school kids, what on earth can you DO with it (practically speaking), and can any math whizzes here give me a VERY, VERY, VERY simple grade-school-level explanation (remember, math dummy here!) of how the $%#$# thing is **supposed** to work? I'm still wondering, years later.
Thanks, all!

Answer 1

Um, the idea is just that counting can happen with any group size. When you count using the normal decimal (base-10) system, you bump up to the next level of group whenever you get ten of the previous size.

Like, if you had a pile of marbles, you could fit ten of those in a small bag. Then, you have a larger bag that holds ten small bags. And a larger yet bag which holds ten of THOSE. And so on.

Well, who's to say the bags couldn't go by nested 11's, or 12's?
We have special names for the nested bags. A ten bag is called "ten". A ten tens bag is called a "hundred." A ten ten tens bag, which is a ten hundreds bag, is called a "thousand". And so on.

Anyway, what's important about this is that it's the basis for place value, and the reason why you need only the figures{0,1,2,3,4,5,6,7,8,9} to write any number, versus an infinity of them. When writing a number, each bag size gets its own column, so that you just have to write the number of the bag size. You only need the ten digits because any more than 9 in a column means jump to the next column. Eg: 1,043 means one 1,000, no 100's, four 10's, and three 1's.

In base-11 you'd need another symbol for "ten" because "10" takes up two places and would read "one eleven and no ones."
In base-12 you'd need two more, because "10" would read "one twelve and no onse," and "11" would read "one twelve and one 1."

"New math" was (I think--I never experienced it) a failure because of the way in which it was implemented--a simple idea, which everyone understands, presented in an overly-generalized form forced upon them by fearful bureaucrats beholden to misguided textbook companies.

Answer 2

The only thing it did was confuse us all. Older math teachers
were teaching something they had never learned.
Simple answers took a complicated formula to arrive at. So once you figured out the answer the easy way, you had to
put it into the formula.
Just another way of taking something easy and making it
so complicated NO ONE could understand it.

Answer 3

what you describe is hardly NEW... it is actually quite old. As for being hard... it is not hard, and very useful, base 12 is used every day, that is the way we count the hours, it is also the way we count the months of the year, base 7 is how we count the days of the week, etc etc.
the more you understand the better is going to be your life...