So when I do math -- and I mean simple arithmetic -- I tend to make random goofy mistakes. This means I have to balance my checkbook every time I write a check, lest I find myself months later off by hundreds of dollars because one time I added (zig) when I should have subtracted (zag).
Everybody remember Tom Lehrer's "New Math"? It was a satirical song written in 1965 about changes in the way math was being taught to school-age kids. The subtraction problem under discussion is 342-173=169:
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 it to the two and get twelve
And you take away three; that's nine.
Is that clear?
And my brother and I always went "Well, yes, of course." Because that's exactly how we'd been taught, so it made complete sense to us, and we got that it had been funny in the 60's, but it didn't sound like nonsense to us at all.
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.
The spoken intro to the song, though, had the problem done with "old math".
Now, you remember how we used to do this: three from two is nine; carry the one, and if you're under thirty-five or went to a private school you say seven from three is six, but if you're over thirty-five and went to a public school you say eight from four is six; carry the one, so you have one hundred and sixty-nine.
And this? Makes
complete sense to me. I find myself balancing my checkbook and saying to myself, "three from two is nine, carry the one, nine from four is five ..." and ending up with an absolutely correct figure in dollars and fifty-nine cents. I make
fewer mistakes this way than the way I was taught in school. Can it be that the inventor of the jello-shot was right, that in the New Math it's more important "to understand what you're doing rather than to get the right answer"?
( For comedy value, he goes on to do the thing in base eight: )