“and”

How many dalmatians were in that movie again?

It was one-hundred-and-one, right?

Have I angered you yet? If you teach math, I probably have.

See, we math teachers are precise people. We like things to be just right. Part of being just right is using language correctly. In English number language, and is reserved for separating the whole number part of a number from the fractional part.

One and one-half

One and seven tenths

That sort of thing.

So when we hear one hundred and one, we freak out.

But separating the whole number part from the fractional part? That’s just one perspective. Sure, it’s the grammatically correct one.

But here’s the thing about grammar rules…they are arbitrary. Totally and completely arbitrary. Name a grammar rule and there’s a language somewhere that violates it completely.

Yet we English-speaking math teachers act as though the use of and were a signifier of mathematical understanding or competence. Which it is not.

Here’s another interpretation of and in English number language. Maybe and signifies a change of unit. In one and seven tenths, one is counting the original unit, seven is counting tenths. The and helps the listener to follow along; it signifies this shift.

In that case, one hundred and one is the same way. The first one counts a unit-hundreds. The second one (following the and) counts a different unit (which, awkwardly, we call either ones or units).

If I’m right about this, then you will have heard native speakers of English say something such as,

Three hundred and four thousand and twelve.

Three hundred and four counts thousands. Twelve counts ones. Then within the three hundred and four part, there are two different units also. Hence the and.

If I’m right, then you will probably not have heard native speakers of English say something such as,

Thirty and four.

Both of those words count the same units.

So I say let’s give up on this little obsession we have about and. Let’s not let it get in the way of effective, efficient communication in mathematics classrooms.

Let’s save our wrath for this:

Three point twelve.

10 responses to ““and””

1. barryrsmith

When I worked out three hundred and four thousand and twelve, I got 4312, not 304012. Or did you say, (three hundred and four) thousand and twelve and I heard it wrong…

2. barryrsmith

BTW, I think Abe Lincoln would like your interpretation of “and”

3. Christopher

Awesome, barry! I’ll give you your parentheses if you’ll give me my ands.

4. Michael Paul Goldenberg

There’s a least one person reading your blog who earned secondary certification in English and mathematics (granted, from the State of Vermont, where people say things like “Jeesum Crow” – often shortened to “Jeesums!”). And that fella is feeling a little conflicted over your “ands.” Thought in the movie, I take the “and” to signify and extra-special final dalmatian. Probably I’m wrong: too much water under that particular bridge since I saw the original, and I think I slept through the live-action remake.

5. Michael Paul Goldenberg

“though,” not “thought”

6. I think you mean “AMERICAN English-speaking math teachers.” Teachers in other English-speaking countries use “and” in the way that is proscribed in America. Their meaning gets across just fine.

7. I didn’t catch the 101 because I’m guilty of saying it with “and” if I don’t stop to think about it. I have my excuses. :)

8. I’m inconsistent with my use of ‘and.’ Sometimes I say it, sometimes I don’t. However, I announced the winner of an estimation jar at a school assembly one year. I revealed the total number of items in the jar and included ‘and.’ A fourth grade teacher, who’s now a good friend, immediately came up to me and corrected me after assembly. Classic. He did emphasize the fact that he had just informed his class the other day about the correct usage of ‘and.’ As for ‘three point twelve,’ I’m also inconsistent. Did you hear me on the 3 Act presentation to my staff say something like six point twelve instead of 6 point one-two or 6 and twelve hundredths? I’m intrigued to know where you stand?

9. Only elementary school teachers use “and” to mean “point”. For everyone else it means “plus” and “one hundred and one” is perfectly good standard English with no ambiguity to it. This is one of those myths that gets propagated from math teacher to math teacher without ever going through a reality check.

10. I agree with gasstationwithoutpumps – the “and” for me is the +. This is clear when you think of the 1 and 1/2 (1 + 1/2).

Then you think about 1 1/2 is really the juxtaposition of 1 with 1/2 – which usually means multiplication, not addition. As in the case of 2x (2 times x)

Which makes me argue that we mathematicians are not so precise after all.