Math in the alphabet

How is the alphabet like or unlike the counting sequence, and what comes after the letter Z?

The children attended a well-run chess day camp this summer. Good people running things; a warm and welcoming atmosphere. Lots of varied activities to keep kids’ bodies engaged as well as their minds.

Sadly, this takes place on the complete opposite end of the Metro area from where we live. We had to drive all the way across St Paul, Minneapolis and deep into St Louis Park during rush hour. Ugh.

This led, one day, to my trying to find a topic of conversation to keep at least one of the children occupied while we drove home. I recount for you this conversation below.

—

Me: Tabitha. Can I ask you a question?

Tabitha (7 years old): Sure.

Me: What letter comes before I in the alphabet?

T: H. That was kind of an easy question.

I love that she has turned into a critic. If I am not challenging her, she calls me on it.

What she has not seemed to notice yet is that these questions she deems easy are just my openers for the good stuff.

Me: Yeah. Here’s a harder one. What letter comes two letters before S?

There is a fairly long pause here. This is a harder question because of how most of us know the alphabet—forwards. If we want to know what is 2 less than 71, it is not so hard to count backwards. We have lots of experience counting backwards. But we don’t have so much experience saying the alphabet backwards, so we need to make up a strategy.

T: Q and R.

Me: Q is two letters before S, yes. Now you ask me one.

T: What letter comes after Z?

Brilliant. What a great question. I wish I had thought of it myself.

Me: Oooooo. Good one. I say A. I say it starts over.

T: Nope.

Griffin has been listening in but not participating. He sees his chance to get in on the action.

Griffin (9 years old): Negative A.

Me: Wouldn’t that be what comes before A?

G: No. It comes after Z. It’s negative A.

T: Nope. Not that either.

Me: OK, then. I am stumped.

T: Nothing.

Me: Huh?

T: Nothing. No letter comes after Z.

So what do we learn?

This is a more sophisticated version of another mathy letters conversation I had with Tabitha a while back. Back then, we were trying to figure out which of two letters comes first in the alphabet. Here, we are more paying careful attention to precise placement (two letters before, not just before).

The other interesting thing going on is our three different ideas about what comes after the end.

My idea: After the end, we go back to the beginning, like the days of the week.

Tabitha’s idea: There is nothing after the end. It just ends.

Griffin’s idea: The end is like zero. When you get to the end, you repeat what you already had, only using negatives.

It is OK that we didn’t resolve who is right.

Starting the conversation

About a year ago, I started making a habit of having the kids ask me the next question. I highly recommend it.

You know how your children are always testing the limits of rules in everyday life? Like you say, “Do not touch” and they see how close they can get their finger to the forbidden object without actually touching it? That is normal and necessary behavior on the part of children.

They will do it in the world of ideas, too. Tabitha did not choose “What letter comes after Z” at random. She chose it because she knew it would be interesting to talk about. It probably would not have occurred to me to ask it. Our conversation was richer because she did.

15 thoughts on “Math in the alphabet”

  3. Hi Christopher,,
    I think every parent of young children should follow your blog; what an excellent resource- and even though I am a math teacher and am passionate about helping children learn to discover its beauty- your discussions offer a lot more than just math…. parenting skills, communicating with children, playing with children, the beauty of just being together. Thanks for sharing; I have become an avid follower!

  4. According to Mental Floss:
    By the early nineteenth century, & was the 27th letter in the alphabet, coming right after Z. Without a title yet, it was still read as just “and,” which made reciting the end of the alphabet a little confusing—”X, Y, Z and and.”

    1. Brilliant, Denise! I remember reading somewhere that the ampersand used to be an English letter. I had never thought to ask where it came in the alphabet, though. Now I will be seeking original documents on that matter. Also, I will pass this information along to Tabitha and Griffin.

  5. It’s no credit to me, just serendipity. That link happened to show up in my Twitter feed just after I read your post. With so little time to spend on Twitter and all the stuff I miss, I love it when things come together 🙂

  7. Hi – at first I beg your pardon for my “english” – I have been learned 28years ago. Second – I asked this questicon to my son (10year auti – has some problems, but is “very good” at simple logic). What letter comes two letters before S – and he said P .. and its right. Thats way : two letters before – is P. So – I must modify – what is the second letter before S 🙂

    1. Thanks for the note, jolana88!

      I wonder if your question turns out to be a language question. In English, some phrases having to with sequencing are ambiguous. I don’t know if it is the same in Czech.

      The standard English construction is that yesterday is one day before today, and that R is one letter before S. What you and your son are counting are letters between the letters in question.

      Tabitha has recently insisted on counting the days between today and the one she is waiting for. So on Monday, she will say that there is “one day until Wednesday”. The standard English construction would say that there are “two days until Wednesday”.

      Around our house, we notice these differences and play with them. “How many days until tomorrow, then?” (Zero, counting Tabitha’s way; One counting my way). “How many days until today?” (Zero, counting my way; I suppose negative one, counting Tabitha’s way).

      One more note on these matters—when I was in graduate school, I had a friend who had recently come from Hong Kong. He was teaching an undergraduate math class and had told his students on a Monday that their homework was due “next Wednesday”. Two days later, he was ready to collect the homework, and every student in class was surprised. “You said next Wednesday!” they cried. “Right,” he responded, “and this is the next Wednesday!” He and I had a lovely talk about the meaning of next in discussing days of the week in American English, and he decided it would be safer to put dates on homework assignments—less ambiguity.

  8. Pingback: Math Teachers at Play #79 | Let's Play Math!

  9. I mean – yes, it´s just a language disparity. In Czech ( I am not expert, just love my mother tongue) is – f.e. – yesterday only “day which was” – no one day before today. That´s why one letter before S is R, second Q – so two letters before – is the P (as third). Any way – I mean, that the language distinction is interesting 🙂

    1. Wow! “Day which was” is a delightful turn of phrase. Thanks for sharing that. Tabitha used to say “last day” for “yesterday”. This seems very similar to (if slightly less poetic than) “day which was”.

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