I was sad to hear of the recent passing of legendary jazz artist Bob Dorough, whose voice is probably still echoing in the minds of those of you who were children in the 1970s. While Dorough composed many excellent jazz tunes— his “Comin’ Home Baby” is still on regular rotation on my iphone— he is most famous for his work on Schoolhouse Rock. Schoolhouse Rock was a set of catchy music videos shown on TV in the 70s, helping to provide educational content for elementary-school-age children in the U.S. Apparently three minutes of this educational content per hour would offset the mind-melting effects of the horrible children’s cartoons of the era. But Dorough’s work on Schoolhouse Rock was truly top-notch: the music really did help a generation of children to memorize their multiplication tables, as well as learning some basic facts about history, science, and grammar. However, my favorite of the songs may have been the least effective, with lyrics that were mostly incomprehensible to kids who were not total math geeks. I’m talking about the song related to the number 12, “Little Twelvetoes.” I still chuckle every time that one comes up on my iphone.
Now, most of the songs in the Multiplication Rock series tried to relate their numbers to something concrete that the kids could latch on to. For example, “Three is a Magic Number” talked about a family with a man, woman, & baby; “The Four-Legged Zoo” talked about the many animals with four legs, and “Figure Eight” talked about ice skating. But Dorough must have been smoking some of those interesting 1970’s drugs when he got to the number 12. Instead of choosing something conventional like an egg carton or the grades in school, he envisioned an alien with 12 fingers and toes visiting Earth, and helping humans to do math. OK, this was a bit odd, but I think it could have been made to work— but he did his best to pile further oddities on top of that, with lyrics especially designed to confuse the average young child.
First, the song spends a lot of time introducing the concept that the alien counts in base 12. Here’s the actual narration:
Now if man had been born with 6 fingers on each hand, he'd also have 12 toes or so the theory goes. Well, with twelve digits, I mean fingers, he probably would have invented two more digits when he Invented his number system. Then, if he saved the zero for the end, he could count and multiply by twelve just as easily as you and I do by ten.
Now if man had been born with 6 fingers on each hand, he'd probably count: one, two, three, four, five, six, seven, eight, nine, dek, el, doh. "Dek" and "el" being two entirely new signs meaning ten and eleven. Single digits! And his twelve, "doh", would be written 1-0.
Get it? That'd be swell, for multiplying by 12.
For those of us who were really into this stuff, that concept was pretty cool. But for the average elementary school student struggling to learn his regular base-10 multiplication tables, introducing another base and number system doesn’t seem like the best teaching technique. To be fair, Dorough was just following the lead of the ill-fated “New Math” movement of the time, which I have mentioned in earlier episodes of this podcast. A group of professors decided that kids would learn arithmetic better if teachers concentrated on the theoretical foundations of counting systems, rather than traditional drilling of arithmetic problems. Thankfully, their mistake was eventually realized, though later educational fads haven’t been much better.
On top of pushing this already-confusing concept, the song introduced those strange new digits “dek and “el”, and a new word “doh” for 12. While it’s true that we do need more digits when using a base above 10, real-life engineers who use higher bases, most often base-16 in computer-related fields, just use letters for the digits after 9: A, B, C, etc. That way we have familiar symbols in an easy-to-remember order. I guess it’s fun to imagine new alien squiggles for the extra digits instead… but I think that just makes the song even more confusing to a young child. And why not just say “twelve” instead of a new word “doh” when we get to the base? (Note, however, that this song predated Homer Simpson.)
But the part of the song I find truly hilarious is the refrain, which implies that having this alien around would help us to do arithmetic when multiplying by the number 12. It goes, “If you help me with my twelves, I'll help you with your tens. And we could all be friends.” But think about this a minute. It’s true that the alien who writes in base 12 could easily multiply by 12 by adding a ‘0’ to a number, just like we could do when multiplying by 10. So suppose you ask Little Twelvetoes to multiply 9 times 12. He would write down “9 0”. Exactly how would this be helpful? You would now have to convert the number written as 90 in base 12 to a base 10 number for you to be able to understand it, an operation at least as difficult as multiplying 9 times 12 would be in the first place! So although this alien’s faster way of writing down answers to times-12 multiplication would be interesting, it would be of absolutely no help to a human doing math problems. You could be friends with the alien, but your math results would just confuse each other.
Anyway, I should point out that despite these various absurdities, the part of the song that lays out the times-12 multiplication table is pretty catchy. So if the kids could get past the rest of the confusing lyrics, it probably did still achieve its goal of helping them to learn multiplication. And of course, despite the fact that I enjoy making fun of it, I and millions of kids like me did truly love this song— and still remember it over 40 years later. Besides, this is just one of many brilliantly memorable tunes in the Schoolhouse Rock series. I think Bob Dorough’s music and lyrics will continue to play in my iPhone rotation for many years to come.
And this has been your Math Mutation for today.