Jubilation and Triangulation

Sandra Dodd

Usually it looks like we're just playing around. When it doesn't look like we're playing, I work on it. Unschooling works best when we're playing around. Much of our play involves words, music and humor. It has to do with merrily connecting the dots, in a real world way, and in a mental-connection way.

Keith, my husband, loves Babylon 5, and the fourth season just came out on DVD.

At the end of one of the shows, the long-dark-haired Brit guy (I only know this show from passing through and staring for a bit and moving on, but someday I think I'll watch them all) is singing. And he's singing "Modern Major General" from Pirates of Penzance.

Our family knows Gilbert & Sullivan's Pirates of Penzance through the wonder of video, and because some people were cool enough to make a movie of it, which is great. Keith showed me that Babylon 5 scene, in which the character sings all through the credits, and at the end of the credits someone says "CUT!" and he interrupts his singing to say "what"? Layers and levels of past and present and imagined future; fantasy and reality.

It was fun to think of a futuristic character singing something from the 1880s. It's like Data playing baroque music on Star Trek TNG, or when there was a Patsy Cline revival on the short-lived Space: Above and Beyond series. In all those cases, the science fiction connections came from my husband, and the musical documentation could come from me, and my kids had access to both.

I went back into the other part of the house where Holly was, and right out of the blue she said, "What is a hypotenuse?" I didn't know I had been singing this to myself: "With many cheerful facts about the square of the hypotenuse."

I stood and looked at her and thought two things: "Was I singing?" and "Do I know what a hypotenuse is?"

The answers were "I must have been," and "I think so."

I said, "I can't tell you, because you don't want to know the names of triangles."

She asked why I'd say that, and I said, "You told me you didn't want to know the names of triangles."

"And you believed me?"


While that was going on I had picked up a paperback dictionary that at hand and checked to make sure I was correct, because I have an abiding math-fright. But I had remembered correctly. When math can be in English—even English that came from Greek, which math terms often are anyway—I can usually remember it.

I said, "If a triangle has the corner of a square, has a right angle (and I showed her with my thumb and forefinger), then this long line (showed with my other hand) is the hypotenuse."

She looked at me for a long moment and said "Oh! Okay." And she went back to playing Harvest Moon.

What it took to build up to that moment was Pirate of Penzance, Babylon 5, and some hours over a year or two of Holly and me playing a game called Math Arena.

Math Arena is a "buzz in when you know the answer" computer game. One of the contests is picking a match from an assortment of triangles, turned all kinds of directions, to the one they show. Holly can match or beat me at it, but when we first started I could beat her. Wanting to help her out, I had offered to tell her the names of the various shapes of triangles.

She said no, she didn't want to know their names; I should just let her do it her way.

I think in words. Keith likes a computer solitaire game done with mahjongg tiles. He likes to play it with national flags or Chinese symbols. I can only play it if I set the game to show letters of the alphabet. I can't play from just visual designs.

I play some other kinds of visual solitaire games but unless I can name the pictures, I can't play well. I can't hold an image in my head clearly enough to compare it against other things. Holly can. When the triangles come up on Math Arena, I have to think "isosceles" and then look for one (or "right" or "equilateral" or "obtuse" or whatever). Holly doesn't have to.

So my strewing plan was this: The next morning I would wake up early, make tea, and get out the geoboards. We have three. I would set up three basic triangles. When Holly got up and noticed these out, I would point at the hypotenuse on the right triangle. Either she would say "huh!" and "Would you make malt-o-meal?" and it would be over, or she might ask "And what are these other two?" Maybe it would be a couple of days of playing with triangles and maybe it will be one little "huh!"

That was my whole plan. I was going to be fine with however minor or glorious it was, because I knew she would have something to tie it to in her head, another dot to connect, and all that internal triangulation would be more valuable than any vocabulary study and formulaic recitation we could do.

But what happened was that I forgot to check back on my geo-board kid-trap. When I remembered in the early afternoon, Marty and Holly were working on fancy designs with colored rubber bands, and making "how many triangles?" puzzles for each other to count triangle within triangles. I came over and said, "That is a hypotenuse," and I pointed right at a green rubber hypotenuse. Holly said, "I know, I told him already." Not only had I missed my big chance to review it with her, she (at twelve) had already explained it to her brother (the fifteen year old).

We played a dictionary game one day that week with lots of people, about what languages various English words were originally from. One that was called out was "hypotenuse!" and I said without hesitation "Greek!" Holly was there, but neither of us said "Hey, they said 'hypotenuse'!"

The day after, we babysat some friends, and we were all playing Math Arena. The "game host's" name (which we had never had reason to note before) is "Felix Hypotenuse." "Felix" is from Latin, and is related to "felicity," another word they sing in Pirates of Penzance. It's fun for me that Holly enjoys that sort of trivia.

And so, after years of avoiding the term at Holly's direction, we had a week where "hypotenuse" came up repeatedly. It was fun, and it's a story worth telling, but it neither makes nor breaks any past or future learning. It's a small part of a big whole, one dot in countless millions. If Holly were to die soon, she wouldn't need to know any more about triangles than she knows today. If she lives a long life, she has all that time to learn more. She's playing, she's having fun, and she's learning.

© Sandra Dodd 2004
This essay appears in the book Moving a Puddle.