Five Little Goldfish

The set up for this game I play with the 4-5 year olds is simple. I say, "We're playing a game at the red table. There are Goldfish and you get to eat them."

The kids who chose to join me are asked to sit around the table on chairs. I hold up the large container of Goldfish and say, "I'm going to pour out a big pile in the middle of the table. You will get to eat some, but only if you listen to me. If you don't want to listen to me, you can go do something else." And there are always a lot of things to do that don't require listening to me or any adult.

I pour out a pile of crackers in the center of the table.

"Okay, I want everyone to take five gold fish."

"My fish are all kissing each other."

Most of the kids count aloud. It takes a lot of concentration to keep your own count while others are also counting. And the kids figure that out, which I think is why when I ask, "How many does everyone have?" so many of them say, "I have five," then go back and recount, more quietly this time. In other words, they're checking their math. It's one of the basic tenants of committing mathematics -- always go back and prove it. In this case, most kids go for the recount. I've not taught any of them this: this is just what most kids do when they play this game.

"My fish are in a pattern. They fit like a puzzle."

Naturally, I'm also checking each kid's stash. There are always one or two who attempt to simply snatch gold fish. These children are good naturedly busted, permitted to eat their crackers, then sent on their way. Others simply mis-count. I take note of the kids who struggle with one-to-one correspondence as they count, then role model the habit of pointing at each object as I help them with their recount, "One, 2, 3, 4, 5."

When I'm sure it's a true statement, I say, "Okay, everyone has five. I've arranged mine in a row . . . one, 2, 3, 4, 5."

"My fish are all hugging their mommy."

This typically inspires kids to make their own arrangements.

"I made mine in a row too," expressing a proof of my mathematical assertion that 5 = 5.

"I have two on top and three on the bottom," stating both a design and mathematical truth, 2 + 3 = 5.

"I made mine in a circle," expressing a basic artistic and geometric concept.

"My fish are a school of fish."

I say, "Five little gold fish swimming in the ocean. Along comes a great big whale and eats two of them!" I always play along and pointedly eat two of my fish. "How many do you have left?"

There are always some who just know the answer, "Three!" but most have to count be be sure. Both are valid ways to arrive at the answer. Then, "Three little gold fish swimming in the ocean. Along comes a great big whale and eats one of them . . ." As the game goes on, we work with schools of up to 10 fish, sometimes subtracting through eating, and sometimes adding when I invite everyone to, for instance, "Take three more fish. Now how many fish do you have?"

"My fish make a flower."

Sometimes they help each other. It's not considered cheating. It's not frowned upon. It's a game that is most fun, that makes the most sense, that most satisfies us when everyone is getting the same answers, further and finally proving the universality of the math we are doing. Collaboration, not competition, is the essence of education.

This is math, of course, but it's not math. It's a game. I keep it a game by not belaboring mathematical ideas or concepts. Yes, I use terms like "addition" and "subtraction" and "equals," when I can as part of the natural flow of things, because it's always good to introduce vocabulary words "in context." I support the kids in any way necessary to help them figure out how many fish they have. Most grasp these basic math concepts with relish, because what we are doing is built into most humans, while others get there because they're motivated by the camaraderie of the game or the story of gold fish and whales or simply because they really like those crackers. That's built into us too.

It doesn't matter how you get there: it's about playing the game. It's all we care about. The math part just happens because that's what young children do when they play together.

And the children who have no interest in our game? They're over there playing something else, equally driven to make sense of the things that interest them. They will ultimately learn what we've been learning when they need it to satisfy themselves, not when I want them to know it, and not even necessarily when they're "ready" (although that's part of it), but when they need to know it in order to play the game they want to play.

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