New Math

My parents’ generation was the first to really be subjected to this horror known as "New Math," a replacement for decades of institutionalized memorization and recitation. Starting in the 1960s, schools began to roll over into the space age by converting their mathematical syllabi to a modern system.

Tom Lehrer brought us the simplest, and most singable, example of New Math instruction with his aptly-named song, "New Math," complete with the honest admission, "but in the new approach, as you know, the important thing is to understand what you're doing rather than to get the right answer." His example was to calculate 342 - 173, resulting in a musical description of the process:

From the three you then use one
To make ten ones...
(And you know why four plus minus one
Plus ten is fourteen minus one?
'Cause addition is commutative, right!)
And so you have thirteen tens,
And you take away seven,
And that leaves five...

Well…SIX actually.
But the idea is the important thing.

Lehrer was smarter than simply making New Math sound complex. In the second half of the song he admits his original intention was to do the calculation in Base 8 (Base eight is just like base ten really…if you're missing two fingers). He uses this to strike an honest point home: under New Math, simply memorizing math tables only helps you with what you memorize. Learning the meaning of math allows you to drop into a new situation without breaking stride, if you know what rules to use.

Now instead of four in the eights place
You've got three,
'Cause you added one,
That is to say, eight, to the two,
But you can't take seven from three,
So you look at the sixty-fours.

"Sixty-four? How did sixty-four get into it?" I hear you cry.
Well, sixty-four is eight squared, don't you see?
(Well, you ask a silly question, and you get a silly answer.)

Unfortunately, Tom Lehrer, thanks to his advocacy of poisoning pigeons and pornography, wasn’t immediately thought of to advocate the cause of New Math with the general public. Instead, the public was given an informational pamphlet, published in 1965 by Birk & Co of New York, called "What Parents Want to Know About NEW MATH".