Trying to learn a little bit about how people learn math has been one of the most interesting pieces of my apprenticeship here in Haiti. I’ve written before about my frustrations at the way bright and serious Haitian children work with numbers. (See: Needing Permission, Boul Does Math). Many of the children I know are, I think, held back by an approach to teaching math that has them memorizing processes rather than puzzling with quantities. They don’t use their good sense. They use fixed procedures – often poorly remembered – instead.
One teacher who has been for me a pleasant exception to the rule is Millienne Angervil. She teaches second grade at the Matènwa Community Learning Center. (www.matenwa.org.) I’ve written before about her teaching style, which I very much enjoy watching. (See: Starting Where They Are.) When I returned from the States with new teaching materials for math to try out, it was only natural for me to ask Millienne whether she would be interested in experimenting with them.
The materials I brought were created by a company called Friendly Math. (www.friendlymath.com.) The program helps kids develop basic quantitative skills. That means learning to do the four basic operations, but also gaining a sense of shape and size and an ability to estimate. Generally, it helps them towards a sense of quantity and form. Part of its premise is that such work can be done most effectively through play. Ruth Champagne, whose husband is interim president of Shimer College, developed the program. I found out about it through him, and he gave me several of their books to try out.
The particular activity Millienne and I set out to try with her students involved shape puzzles. The kids would get a certain number of brightly colored shapes – triangles, squares, diamonds, trapezoids, and hexagons – and then would get a larger shape that they’d have to somehow fit them into. The activity has two main goals: to help the kids practice reasoning with one another and to sharpen their sense of space. The Friendly Math book also talks of measurement, but since all the game pieces are measured in inches, a unit that the Matènwa second-graders don’t know yet, Millienne and I decided to leave that piece out for now.
Just to make the activity work, Millienne and I had a lot to prepare. Part of what’s so good about the Friendly Math books is that they come with all the materials that you’d usually need. There were three pages of small geometrical forms to be cut out, and lots of puzzles to solve with them. But the books are not really designed for a school that would have one book in a classroom of 22 kids. To make them work, Millienne and I would have to keep track of how many puzzle pieces we’d need, and create extra copies of the puzzles we wanted to use.
I’m left-handed, and as bad with scissors as many lefties are. So cutting out the little pieces was for Millienne. I traced multiple copies of the various figures that the kids would have to cover by figuring out how to deploy their little game pieces.
I also made a giant puzzle for the blackboard. I made a couple of eight-inch squares and four similarly sized triangles out of plain paper. On the board, I traced one possible way to assemble them. Millienne and I both felt that the easiest way to help the kids understand the task at hand would be to lead them through one puzzle together, and doing one big enough for everyone to see seemed as though it might be the key.
The kids took some time getting the puzzle on the blackboard right, partly because of the way I had them work at it. I asked volunteers to come to the board one at a time to tape one puzzle piece into position. By the time four of them had positioned their pieces, they had left two pieces that couldn’t be combined to cover the last bit of space. But after a couple of tries, they got it right, and, more importantly, they got clear about how the game was supposed to work.
Millienne organizes her classroom in several different ways, depending on the activity she’s leading the children through. But it’s furnished with five tables with benches. The kids sat around the tables and, so, were organized into obvious teams of four-five. We chose three of the puzzles from the Friendly Math book, and gave one to each table. We told the kids that the first table to finish would win.
The class that followed was a funny mixture of periods of loud, seemingly chaotic chatter and surprisingly quiet intervals. The kids really worked at the puzzles. And though the different tables worked at different speeds, and though some of the puzzles were distinctly more challenging than others, they were consistently able to finish them in a reasonable amount of time.
It turned out that, not too surprisingly, the kids ranged pretty significantly in their initial ability to work the puzzles out. But what was most important was how willing they were to play with them. Rather than stand back and wait for the answer to appear, most of them became very hands on. They would simply start placing pieces, and see where they got. Generally speaking, one of the kids at each table would dominate, at least until he or she got stuck. That is: until they got to a point at which the pieces that remained could not be fit into the remaining space. Then another child would take over, often with a different idea about how to get started.
Millienne and I were pretty hands-off-ish. We wanted, at least this first time, to see how things would play out. And several points became clear:
First, most of the kids really liked the work. They were engaged and showed that they felt distinctly rewarded each time they got a puzzle right. This was true, whether their table was first or last. None seemed to mind being the fifth of five groups to win.
Second, groups of five children were too large. Two, or at most three, in a group would work much better. Five made it too easy for kids to hide if they were inclined to doubt their own ability to figure things out. I saw one little boy, sitting at his table, with his back turned to the other kids who were at work. When I asked him why he wasn’t participating, he insisted repeatedly that he couldn’t do it.
Third, and in the same line, Millienne thinks that what she might need to do is work individually with several of the weaker kids on days when she can assign the rest of the children something to do on their own. It might be hard, given how much the kids like the puzzles. Those to whom she assigns something else will be drawn to the puzzles and her. But she manages her classroom well, so should be able to overcome the challenge.
What will be interesting to try to gauge is how this and other Friendly Math games – Millienne has already assigned me to return to Matènwa with more – affect her students as learners as math. For now, her optimism is enough for me, with or without further evidence. That optimism was linked mainly to the enthusiasm and the beginnings of teamwork that she saw in her kids, two very promising signs.