Saturday, January 23, 2010

Richmond Math Salon and Base Three

I've been doing this for a year and a half now, and it's finally beginning to gel. There are some anchor families who come most of the time. There are new families coming. I'm starting to be able to describe how important it feels to me to work with parents and kids together.

Most of the folks coming to the math salon are homeschoolers. It's even more important for them than for others that the parents enjoy math. But, really, every kid, whatever sort of schooling they experience, will have a richer experience of math if their parents enjoy it.

But most parents don't. Most people over 6 or 7 or 8 don't. (You know, after they've had enough arithmetic lessons to think it's either boring or senseless.)

So if they can bring their kids to a math salon or a math festival or... and work on something together, then the parents can relearn how to have fun with math.

Today I had a sign up on my front door:
Enter at your own risk!
This doorway takes you

hrough a spacetime warp,
Onto the planet of Triplay.

Are you ready?!

When people come in, there are games like Blink!, Set, Rush Hour, and Quarto to help them settle in. And Lori, the mom in one of the families that has come often, was there to assist me, since I was expecting a larger than usual crowd, with younger kids. (Although I've had months where tons of people are going to come, and then half of them can't make it.) Lori's daughter Audrey helped me too, sharpening pencils and playing a game with her mom, so mom would be ready to explain it to other parents.

We did this for close on an hour, I'd guess. Then I gathered all 20 of us in my small living room (except the girl who was sleeping in a bedroom). I started us off by talking about the people on Triplay having only 3 fingers on a hand - we all held up our hands, either with two fingers folded down, or fingers grouped in the Star Trek (live long and prosper) way.

We began discussing how the people of Triplay (Triplatians?) count: one, two, hand, hand and one, hand and two, two hands. We were all holding up our hands while we counted and talked about it. When we got to three hands, we needed a new word. We voted on whether our word would be handhand or handred. We voted for handhand - the cuter one. But then we got to four hands, which is handhand and hand. Too confusing! So I talked about how our language evolved over time to handred.

We kept counting, decided that 3 handreds was a handsend. (We didn't write it down at first. When we were writing these down later, it was interesting to think about how they might be spelled. It felt like a linguistics exploration too.)

The kids started drawing people from this planet, and some of the adults drew too. After a while of that, we began to design the Triplatian monetary system, and came up with names for the coins. I had a bunch of plastic chips available to use as coins, but I'm not sure how much use they got. We came up with our own names for the 3 cent piece (trickel), the 9 cent piece (handrime) and the 27 cent piece (hansellar). I'm not sure what the 81 cent piece was named.

A few of the adults began working on how numbers are written on Triplay - 1, 2, 10, 11, 12, 20, 21, 22, 100, and 101 are the first ten numbers, if you use our place value system and their base (three). They did that with no suggestion from me, so I was all the more excited to see the work they were doing. Two of the people working on that had mentioned having traumatic childhood experiences at home with math, so you know that diving in like that took some courage. (Isn't it amazing sometimes how our efforts to parent well push us to grow in ways we never expected?)

As usual, the adult conversation eventually meandered from our activity over to what coop classes they've found, and questions about books. I pulled out at least a dozen books, and we talked about how they do things in China (read Liping Ma's book, Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States, for the good stuff, but we also talked about how pressured kids are there, as in many countries).

This was the best math salon I've done yet*. Other sessions there've lots of people, and things seemed to go well, but this time it felt like we really had a great balance of individual and group exploration, and I was tickled that I've gotten better at working with younger kids (drawing pictures, yeah!). Four people came later, so there were 24 people in all - the most that have ever come to the math salon.


*I've had lots of math salon sessions flop, mostly due to low attendance, but can't find the energy or courage after those to write. I'm so impressed by the math teachers who blog about what they're struggling with. I will try harder next fall, when I'm back to teaching, to tell you all about some of my bad days.


  1. If I had 3 fingers I think I'd count in base 4. My left hand would be the 1's place and my right hand the 4's place. Each multiple of would 4 bring all left hand fingers down and put one more right hand finger up. I could count to decimal 15 this way.

    (As a 5-finger-per-hand human I use my hands to count in base 6.)

  2. congratulations on your success
    with this event; very exciting
    (i hope someday to participate
    in suchlike events but...
    thanks for your forthrightness
    about the "flops"... i'm a long
    way from ready to *lead* one).

    i've got a special affection for
    base three. there are notes
    by me on file concerning
    *power*-of-three bases
    (specifically, 9 & 27 of course;
    since 27 = #{letters}+1,
    its convenient to use the
    ordinary sing-along
    "a,b,c"'s as "face values"
    and you can make up
    all kinds of puzzles with
    what for many beginners
    is the *right amount*
    of math. i used the
    "base conversion" process
    from 9 through 3 into 27
    (or back again of course)
    essentially as an excuse
    to re-present the concepts
    used in -- hi rick, love
    the "binary" blog -- doing
    conversions from "octal"
    to "hexadecimal" via
    "binary" (i.e., natch,
    base 8 to base 16 via
    base 2).

    rudy rucker has some of this
    in _mind_tools_ btw but my
    work was independent.

  3. To r.r. vlorbik: where can we see your work? I love base 3 too.

    To Sue: what a great salon!!! Thank you for sharing!

  4. starting at p. 21 here.
    thanks for your interest!

  5. I'm reading late, again. I would have liked to be here, too.

    I've actually never played with base 3... But I know, to check if a number is even, add the digits...



  6. Oh wow! That is cool! I see it, but had not come close to thinking about it. My next salon is today, so I'll mention that. Thanks!

  7. Looking forward to todays Math Salon I am So Excited:)

    Madeline MacCoun-

  8. I had so much fun today at your house and with all the kids and the trampoline it was AWESOME!!!!!!

    See u next time
    Madeline MaCoun-


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