[From a class last year at Berkeley Arts Magnet.]
I’d like to describe our classes by telling you about Wednesday’s class. We began The Seven Ravens, Grimm’s fairy tale number 25. In my retelling, the hero, now a girl, faces three challenges before she can turn her brothers and sisters from ravens back into human form. The first challenge is to count the stars. I threw out over a hundred small plastic balls for them to catch. Then their challenge was to count them all. At first they looked like the chase scene of a Buster Keaton film, with everyone walking by themselves, not working together, maniacally counting “One, two, three …” but they were inadvertently kicking the balls around so their counting wasn’t getting anywhere. I waited them out for a couple of minutes and someone saw that it was all madness, and commented, “We’ll never be able to count the stars. They keep moving around!” Next another student got the idea of grouping the balls by color — which makes sense enough, they are skilled at grouping. But when we counted one pile (27) and then the next (16), they realized that since they don’t know how to add, and so that wasn’t going to work.
I then decided to help them out by suggesting groups of ten, and showed them that a triangle formation of 4 + 3 + 2 + 1 (like bowling pins) yields 10. So they set about arranging the balls into triangles, but since the rug and floor made for a hard surface, in order to not have the balls roll around, the students needed to place them very carefully and to work together to get all balls into triangles of ten.
Finally it was time to count. But even with our neat triangles of ten, most of the students still didn’t “believe in ten”. They started counting individually within each triangle: “One, two, three … “ I let them do this for several minutes. But at one point [a student] looked at the orange balls and at a glance proclaimed, “There are 41.” I stopped the class. She had understood the four groups of ten + one extra. I pointed this out to the children, and now they counted all the balls by tens: “Ten, twenty, thirty, …” There were 121 in all.
That is a lot of adventure to count the stars, and the hero of The Seven Ravens still has two more challenges to go before she can change her brothers and sisters back into human form. The next challenge involves a pesky old dwarf who only talks in negatives:
It’s not the tallest, not the smallest,
It’s not the round one, have you found one?
The final challenge will involve a path with steps numbered 1, 2, 3, … 30. They children will have to figure out a hidden step by guessing:for example someone guesses “12” and my thumb indicates that the hidden step is “higher” than 12; perhaps the next clue indicates that the next step is “lower than 25.” They have to keep these clues straight as we hone in on the number.
We have done five fairy tales so far, and like The Seven Ravens, they turn into puzzles that challenge them to think creatively, to work cooperatively, and to use their bodies, either in small motor movements or full-out games on the playground. We may also use drama by having them act out the story.
The story: your children scared me last week, every one of them, by how attentive they were in listening to the introduction to The Seven Ravens. We had been doing games from the previous stories for three full weeks, and that was my mistake, that was too long without a new story. So they prodded me, “Can you tell us a story?” and when I said yes, they immediately assumed their positions on the rug, on the couch, crowding around me. And they waited with such a sense of anticipation. Teachers always want students to “listen better”, but I had better be careful what I ask for. Right before I began, I had an odd memory. My high school calculus teacher was fond of saying that “mathematics is the language of science.”. But your children have taught me that fairy tales and stories are the language of mathematics.