By Tom

I was teaching my third graders how to solve division problems the other day. Specifically, we were solving story problems which involved division, and the students had to figure out what to do with the remainders.

The first problem involved brownies. There were three people sharing sixteen brownies, and we figured out that each person received five whole brownies and one-third of the last one. Simple enough.

The next problem involved balloons. Again, three people had to share sixteen balloons. Balloons, of course, don’t lend themselves well to fractions; a third of a balloon is essentially worthless. For this problem, we decided the best answer was five balloons each, with one balloon left over, to be popped. For some reason, third graders always prefer to pop the leftover balloon, rather than let one of the five people have it. Maybe it’s greed; maybe it’s the thrill. Who knows.

We practiced several of each type of problem, until they got pretty good at deciding whether a problem was a brownie problem, where the remainder gets turned into a fraction, or a balloon problem, where the remainder is left alone.

Then I introduced a new problem. Sixteen people were going on a boat ride. They had to rent rowboats, and each boat held three people. How many boats would they need?

“Five and one-third!” said Ronald. He saw this as a brownie problem.

“So Ronald, you think they should rent five whole boats and then get one-third of another boat?”

“Of course!” He was adamant.

Let me explain about Ronald.

For the first six years of his life, Ronald lived with his mother in the streets and crack houses of Vancouver, B.C.  Ronald had to fight and argue for everything: food, clothing and attention. Now he lives with his grandparents, who are trying to undo the damage. They’ve given him a structured life, they have him in counseling and sleep therapy and they keep him away from his mom. He’s improving – gradually – but he still has a long ways to go before he’ll be able to do something as simple as have a pleasant conversation with another person. He’s bright enough, but has what are known as “high needs.”

Back in the classroom, I decided to explore Ronald’s solution. I drew sixteen people on the board, along with five boats. I put three of them into each boat, leaving one guy off by himself.

“So Ronald, this guy can’t fit into any of the boats, which only hold three people. Are you saying that they should get another boat, divide it into three pieces, and put the guy into one of those pieces?”

“Yeah, because sixteen divided by three is five and one-third.”

“But does that make sense for this problem?”

“Yes.” Ronald has learned not to back down from a fight, verbal or otherwise.

 I drew a boat and then drew lines on it, dividing it into three pieces. “Which part should we put him in?” I couldn’t resist.

”Right there,” Ronald said, pointing at the bow.

Kobe piped up, “But it would sink, Ronald. Plus it would ruin the boat, and the people are renting them. They’d get in trouble.”

Kobe was right, and it was time to step in. “Ronald, this isn’t a brownie problem. Nor is it a balloon problem. This is a boat problem. In boat problems, you have to add another whole when there’s a remainder. The people need six boats.”

Later, after the kids had gone out to recess, I glanced up and saw the picture with the remainder guy sitting in his own cut-up boat. I thought of Ronald, who at that very moment; was keeping the recess monitor busy with an escalating argument involving a kickball game. (Apparently Ronald didn’t think he was out at second.) Later, during lunch, Ronald commanded the attention of the lunchroom supervisor who was trying to get him to clean his mess. As Ronald moves through the school day, every adult with whom he comes into contact ends up helping him work through one problem after another. And he’s not the only one. He’s one of the two or three kids in every class whose behavior isn’t extreme enough to earn a place in a self-contained special education classroom, yet still demand a lot of attention.

One of the unsettling realities of education is how our resources are divided. Ronald, Kobe and every other student is worth about eight thousand dollars of state money. That’s how much our district gets to educate each child. The money flows from the state to the district, where it’s essentially transformed into time.

Teachers like me have to take that time – which comes equally on behalf of each student – and decide how to allocate it. We try to be as fair as possible, but kids like Ronald make that very difficult. For every minute I spend with Kobe, I easily spend ten with Ronald.

Is that fair?

I’d say yes, but it’s easy to see how someone from the outside would disagree. In the business world, for example, you only get what you pay for. If my wife and I go out for dinner and order the same meal, we each get the same amount of food, despite the fact that one of us might be hungrier than the other. Lawyers bill by the hour; if a case is complicated and takes more time, it costs more.

So why shouldn’t we divide our resources evenly in education? For me, it gets back to the idea of “high needs.” If we call a student – like Ronald – “high needs,” then we have to address those needs. Or at least try to. That’s what’s supposed to happen in a society when one member “needs” something.

The other option is to simply divide my time equally among my twenty-nine students and let the chips fall where they may. In fact, many teachers divide it that way. They’ll give kids like Ronald one warning, maybe two, and then send them to the office so they can give the rest of the students their share of instructional time. Like a brownie problem.

Only it’s not a brownie problem. Like it or not, Ronald needs his own boat. Otherwise, as Kobe pointed out, he’s going to sink. And then we’ll all be in trouble.