Either:

a) an attempt in the mid-50's through the 70's to update the K-12 and undergraduate math curriculum by incorporating ideas from set theory, abstract algebra, topology and other topics from "modern" (that is, < 200 years ago) mathematics including modulo arithmetic, the binary system, linear algebra and the like....

OR

b) an attempt to totally swindle innocent schoolchildren out of a grasp of ordinary arithmetic and undergraduates out of the good old fashioned calculus by clouding the issue with such superfluities as Venn diagrams, Möbius strips, alternate-base arithmetic, symbolic logic, signs like < and > and other trivia.

The reasoning was sound. Mathematics, as taught at anything but a graduate level had become a fossilized and sterile discipline, in which almost no discovery had been made in at least 200 years. Math books tended to use the same examples and problems from edition to edition, and some, the infamous A, B, and C problems, had been knocking around for at least a century. Math, and math teaching, therefore, tended to be a rather staid collection of unchanging rules, facts, and processes that were often given piecemeal with little explanation: innovation in math education was limited to such minutiae as audio vs. visual memorization methods for addition and multiplication tables (my private nemesis -- before I learned to put them on a grid, it made no sense), and the like. Even worse, very little of this curriculum was all that applicable to mathematics, as such: proofs, of the sort used in papers on the subject, were hardly seen until the last year or two of study. However, it was easy to teach, and easy to grade, and if anyone had problems with it, well...math is hard.

At the same time, mathematics was rapidly expanding, and concepts that were once considered hopelessly esoteric, such as linear and abstract algebra, topology, and computer programming (considered, for a time, to be a wholly mathematical exercise), were rapidly becoming important in industry, business administration, economics, and defense, as well as the sciences. Moreover, at least parts of many of these fields did not call for much in the way of skill in calculation, but were more akin to problems in logic, the humanities, and even ordinary common sense than the usual counting-to-the-calculus round.

With this in mind, it seemed logical to make at least the rudiments of higher math part of everyday parlance, to reveal a bit of the structure underlying arithmetic and algebra, and to thoroughly overhaul math teaching methods. Many textbooks were given color and more pictures and diagrams, age-appropriate word and story problems replaced the creaky legacy time/distance and steam-engineering conundrums, and various props, such as Cuisenaire rods and abacii came to the fore, as well as games like Wff'n'Proof and Tuf. The prime example, and still the gold standard of this kind of teaching is/was the freshman-level Introduction to Finite Mathematics, which moves seamlessly from compound expressions to game theory in one semester, punctuated by various speculations on such things as the intelligence of blondes and jocks, baseball, and Lewis Carroll.

When taught well, the New Math program was a resounding success -- I went from being inept in the times tables to multiplying matrices in a year's time, and would have gone much further if I'd stayed in similar programs. As it was, I went back to Old Math next year (taught by an uninspired fossil) and crashed and burned, consoling myself with rumors of the DoD of the day practically kidnapping able "young" minds...heheheheheheh....to Points Unknown out West. Hey it was the Seventies.

The truth was, most elementary- and high school teachers didn't want to have to learn a lot of weird concepts just to be able to get kids to deal with long division and trigonometry. Parents hated not being able to help kids with their homework, and although kids loved it, there was little follow-up on the really good parts. Consequently, after 1971 or so, many school programs again became "traditional with a gloss of New Math", retaining the new, glossy textbooks, some props and "enrichment activities", and token coverage of Venn diagrams. This has led to a dismal situation that has not been helped by time...

More fun from Tom Lehrer. Best performed at high speed. It mocked a trend in arithmetic teaching that tried to make it less "by rote" and based more closely on an understanding of the meaning of numbers. This is explained in teleny's w/u elsewhere here.

Some of you who have small children may have perhaps been put in the embarrassing position of being unable to do your child's arithmetic homework because of the current revolution in mathematics teaching known as the New Math. So as a public service here tonight, I thought I would offer a brief lesson in the New Math. Tonight, we're gonna cover subtraction. This is the first room I've worked for a while that didn't have a blackboard, so we will have to make do with more primitive visual aids, as they say in the ed biz. Consider the following subtraction problem, which I will put up here: 342 minus 173. Now, remember how we used to do that:

Three from two is nine, carry the one, and if you're under 35 or went to a private school, you say seven from three is six, but if you're over 35 and went to a public school, you say eight from four is six ...and carry the one, so we have 169.

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. Here's how they do it now:

You can't take three from two,
Two is less than three,
So you look at the four in the tens place.
Now that's really four tens
So you make it three tens,
Regroup, and you change a ten to ten ones,
And you add 'em to the two and get twelve,
And you take away three, that's nine.
Is that clear?

Now instead of four in the tens place
You've got three,
'Cause you added one,
That is to say, ten, to the two,
But you can't take seven from three,
So you look in the hundreds place.

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've got thirteen tens
And you take away seven,
And that leaves five...

Well, six actually...
But the idea is the important thing!

Now go back to the hundreds place,
You're left with two,
And you take away one from two,
And that leaves...?
Everybody get one?
Not bad for the first day!

Hooray for New Math,
New-hoo-hoo Math,
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Now, that actually is not the answer that I had in mind, because the book that I got this problem out of wants you to do it in base eight. But don't panic! Base eight is just like base ten really - if you're missing two fingers! Shall we have a go at it? Hang on...

You can't take three from two,
Two is less than three,
So you look at the four in the eights place.
Now that's really four eights,
So you make it three eights,
Regroup, and you change an eight to eight ones
And you add 'em to the two,
And you get one-two base eight,
Which is ten base ten,
And you take away three, that's seven.

Ok?

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, ya ask a silly question, ya get a silly answer!"

From the three, you then use one
To make eight ones,
You add those ones to the three,
And you get one-three base eight,
Or, in other words,
In base ten you have eleven,
And you take away seven,
And seven from eleven is four!
Now go back to the sixty-fours,
You're left with two,
And you take away one from two,
And that leaves...?

Now, let's not always see the same hands!
One, that's right.
Whoever got one can stay after the show and clean the erasers.

Hooray for New Math,

New-hoo-hoo Math!
It won't do you a bit of good to review math.
It's so simple,
So very simple,
That only a child can do it!

Come back tomorrow night...we're gonna do fractions!

© Tom Lehrer; First appeared on That Was the Year That Was (1965). Lyrics appear with his written permission. CST Approved.

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