No sooner do I mention Eric Walstein than Emily Messner’s long profile of him appears in the Washington Post. You get a vivid sense of this devoted and — um, what’s the opposite of soft-spoken? — educator, who’s been wrestling Montgomery kids through math since — well, I don’t know how long, but he was already an old hand when I met him. I was seven. He ran me through some arithmetic problems and bawled me out when I gave him an answer of “Two hundred and six.”
“There is NO SUCH NUMBER AS TWO HUNDRED AND SIX!” he told me. He wrote “206” on the board. “This number is called TWO HUNDRED SIX.”
OK, in restrospect, I don’t really understand why he needed to insist on this point. But I was tremendously impressed. I’d never met somebody who would have cared in the slightest how properly to pronounce “206.” Let alone somebody who would yell at a seven-year-old kid about it.
The article isn’t just about Walstein, but about the raging battle over how math is to be taught in Montgomery County, one of the fanciest public school systems in the country. Messner is to be commended for going a little deeper than “Are calculators good or bad? Are standardized tests good or bad? Are math education Ph.D.’s good or bad?” which is all one usually gets on this issue.
Also: more memories of Ted Widerski in the comments on Madison’s School Information System blog.
Quomodocumque 
“Two hundred six” is a completely bogus way to pronounce 206. Nobody outside the U.S. does it, and nobody at all did it before the 20th century. For centuries everyone said “two hundred and six” until some American educators decided they were going to single-handedly change the language, that the supposed ambiguity between “two hundred and fifty” and “two hundred and a half” was intolerable.
If you look at the Wikipedia article http://en.wikipedia.org/wiki/Names_of_numbers_in_Englishm , you’ll see that although the rest of the article talks about what people say, the relevant paragraph says “American students are taught (emphasis added) to say”, a very different matter.
Number names are part of the language (unlike, say, symbolic notation), and not subject to arbitrary alterations by tin-plated dictators with delusions of godhood. The whole thing was and is a silly business, and the people who propounded it were and are being ridiculous.
I’ve never heard before of anyone saying “two hundred six” for two hundred and six,
let alone insisting on it. (Or if I have, I’ve assumed that they were misspeaking, and
ignored it to the point of forgetting it later.)
What is the rationale? Is this really what is taught in American schools?
(I was taught in Australia before coming to the U.S. for grad school, roughly
14 years ago.)
“Is this really what is taught in American schools?”
Yes. I was raised in America and taught to say “two hundred six” instead of “two hundred and six.” To this day I still say the former and retain my conditioned disdain for the latter. On a more conscious level I certainly don’t care either way and would never correct anyone (in particular, since I have learned through experience that the rest of the anglophone uses the “and”).
“What is the rationale?”
Boy, Matt, you’re really not from around here, are you? You could get your mouth washed out for that kind of impertinence…
(The explanation given by John Cowan above makes, as is his point, little sense, but that’s more sense than I would have expected. No explanations whatsoever were given to us students.)
I like the charming style of introducing some character’s age, in 19th Century novels, as for instance, “…a heavy-looking young man of five-and-twenty” (this from Jane Austen). This order is still the one existing in German.
In French, a well-known difference of style exists for seventy and ninety, which are “soixante-dix” and “quatre-vingt-dix” in France, and “septante” and “nonante” in French-speaking Belgium and Switzerland. In fact, in the last case, “octante” is also used for “quatre-vingt” (eighty) — which of course makes sense…
The ‘and’ is reserved for the decimal point. Thus 206.75 is read ‘two hundred six and seventy-five hundredths. THe teacher recites the words, the students copy down the correct numeral or the reverse, they see the numeral and recite or write down the word name. Too many ‘ands’ confuse young minds! It’s usually only stressed in American elementary school when children are learning place value names for numerals with decimal fractions, and usually the ‘why’ is explained as well.
Actually most adults (American), non-math types would say “two O six point seven five.” But then, we’re not a very numerate society.
OK, OK, but I wasn’t trying to make Walstein sound like a crazed pedant! The point of the anecdote is that his big personality showed me, a somewhat meek little kid, that it was possible and even kind of charismatic to have strong opinions and feelings about mathematical objects. The value of that lesson was kind of independent of the opinions and feelings actually being expressed.
Dear Pete,
Thanks for the confirmation. I’m surprised not to have noticed this in all my time here.
It sounds very strange to my ear, but then again, thinking about it, in almost all
other contexts there is no “and”; e.g. constructions like twenty five; one thousand
one hundred (as opposed to one thousand and one hundred, which might actually imply
the number 100100); etc. On the other hand, I do say one thousand and ten (and all
Australians would). Presumably you say one thousand ten?
So it seems that the “and” is used only to link the last two digits to the rest of the
number, and so is a little anomalous. On the other hand, it seems relatively harmless,
so (assuming John’s claim is correct) it’s a little surprising that twentieth century school
teachers took it upon themselves to remove it from American English. After all, the
construction “two hundred and six and a half” is not so bad to my ears (although presumably
it grates on yours).
Dear Emmanuel,
The German style of construction also survives in the children’s rhyme “Sing a song
of sixpence, a pocket full of rye, four-and-twenty blackbirds baked in a pie”. I’m
not sure when this rhyme dates from. (It is presumably quite old.)
Shakespeare uses a few times the construction “X-and-twenty”, including twice in “The Winter’s Tale” (at least, according to the online versions I’ve seen; I don’t know if there’s an easily accessible facsimile of an original folio/quarto to look at for confirmation).
Interestingly, it’s in the speech just following the famous stage direction “Exit, pursued by a bear”…
Here’s what I remember being taught. It’s mandatory to say “and” in “one hundred and three fourths”, where it means “plus”. (If you leave it out, you end up with 103/4 instead of 100+3/4.) It’s standard to say it every time you have a fraction, even if it isn’t as necessary as in that case. It’s acceptable but non-standard to say it in “two hundred and six”, since that is indeed 200+6. However, you shouldn’t say it there because if you get in the habit, then you might end up saying it in ambiguous situations. For example, “two hundred and six thousand” is not allowed, on the grounds that it could be interpreted as 200+6000.
Of course, this is totally unnecessary, since there’s no real danger of ambiguity in “two hundred and six thousand” (in practice, everybody inserts mental parentheses). I also don’t know whether these considerations are the original motivation, or just an explanation invented by my teacher. For example, I was also told that the reason people calculated so many digits of pi was to see whether they ever started to repeat. It’s too bad that’s not true, since it certainly sounded compelling back when I didn’t know pi was known to be irrational.
P.S. I don’t remember it being taught with this sort of example, but I guess “one hundred and three fourths” is also ambiguous (100+3/4 vs. 103/4), if you say “one hundred and three” for 103. That’s actually a more serious ambiguity, if you ever want to talk about 103/4. Even if you don’t want to talk about improper fractions, how would you interpret “one hundred and three two hundredths”? It doesn’t seem good for 100+3/200 and 103/200 to have exactly the same standard English name.
Dear Henry,
Although I’d not thought about before now, I would say “one hundred and three quarters” both for 100 + 3/4 and 103/4. (And “one hundred and three two hundredths” for both 100 + 3/200 and 103/200.) Somehow, this ambiguity never seems to have arisen in serious fashion in practice. I think what I do (and I would imagine all non-US anglophones would do) is to change the intonation depending on the situation, so the first would be “one hundred (… pause …) and three quarters” and the second “one hundred and three (… slight pause …) quarters”. If necessary, I would then explain further (e.g. “one hundred and three all over four” in the second case).
Since I seem to know what I would do to resolve the ambiguity, perhaps this actually has arisen in practice. This is quite possible, I guess — it never would have occured to me that there was any alternative approach to naming these numbers before participating in this thread, and so I can easily imagine that I’ve dealt with this ambiguity in the past and not thought twice about it.
Dear Jordan,
I realize this whole conversation is a little off-topic, but as you can tell, I for one am enjoying it, and am learning something novel and surprising about my adopted home. (Whatever problems concerning the human condition that it hasn’t yet managed to solve, it has solved the problem
of unambiguously naming numbers in English.) So I hope that you are not too put out.
Also, I agree that it is good to see people being passionate and opinionated about mathematics and mathematical objects, and I can see how Eric Walstein would have made a strong impression on you. It makes one wonder what can be done to spread this passion more broadly. (Similar thoughts were prompted by your post on expository math books.) If you have more ideas to share on this point, I would certainly like to hear them.
Note: as always for the posters on this blog (as far as I can tell), the smiley faces are unintentional — they were merely supposed to be closing brackets. On the other hand, in the future, a smile may indeed cross my face during the pause, as I savour the newly revealed (to me, at least) ambiguity that is inherent in the way that I name these numbers.
Note: for future readers of this discussion, Matt’s last comment has motivated me to figure out how to turn off the automatic smiley-conversion feature which is, for whatever reason, a WordPress.com default setting. It appears to have worked retroactively, so don’t go looking for “the smiley faces” referred to above.
The comments on that article are kind of vicious. I think you were indoctrinated into the Walstein cult at an impressionable age, and honestly if someone like him had taught me calculus in second grade, I’d see them through rose-colored glasses as well. I was pretty jealous of the attention and training you got so young, where I’d scrounged up books in the public library. I had to beg to go to his Sat morning camp, the hassle of having someone take me was a luxury for my family. I recall a fairly similar blowup about “and”, directed at me or another newbie my first day, and from my older perspective (14 or 15), it seemed juvenile. I don’t think he’s a pedant, I think it was a (sub)conscious form of psychology, a way to assert his authority over kids who are used to being the smartest person in most rooms. The accusations of his being sexist fit my experience of him. When I think back to the stream of people who recognized an unusually driven and intelligent woman – college profs (UMD when I was taking calc in high school and MIT as an undergrad) showed me more guidance than he did.
I think the arguments about calculators are similar; having an intuition or understanding of math is fairly independent from how quickly you can crunch numbers. The art of math is being removed from schools? Welcome to the information age, facebook and twitter. It seems like part of a societal cultural shift away from deep, intelligent discourse and towards the 30-second sound bite. The thing is, people are already intimidated by math; they don’t need to be told “you’re doing it all wrong”, they need to be shown the beauty and the joy. He’s outspoken but in a deeply arrogant and pedantic way that exacerbates the problem. It’s like the discussion of classical music, the generation around Leonard Bernstein gained a widespread appreciation for it within the middle class; sometime in the last 50 years it’s gone from being beautiful to the equivalent of broccoli. Which, Walstein would counter by telling people to practice their scales.
And, I know working mathematicians who would agree with the idea that we never understand math, we just get used to it. Ultimately a lot of life acts like a black box; I can read a good book without having a deep understanding of how the book works its magic or fails to.