Seventy-four

Sometimes children know more than we give them credit for knowing. Sometimes, they don't know as much as we think they do. And sometimes, we're not even on the same planet.

I started my teaching career in a kindergarten classroom about a million years ago [ED: Check this figure]. That fall, some of the kids became very interested in bean estimates--that is, putting some dried kidney beans in a small glass container and then trying to guess how many there were. At first, we stuck with relatively small numbers--up to 20 or so. But before long, the children wanted to try their luck with larger numbers.

Well, why not? I remember thinking. I knew that most teachers would say it was pointless to go much above twenty with beginning-of-the-year kindergarteners. Conventional wisdom held (and still holds) that it's difficult for children that young to comprehend numbers such as 500, 200, or even 50. But these kids were interested. And maybe they were smarter than your average five-year-old where numbers were concerned. Or maybe the conventional wisdom was wrong.

So one day I let a child pile a few handfuls of beans into the container and then get estimates. [Actually, in this context, "guesses" is a better term--most children gave the first large number that popped into their heads.] To check the guesses, we poured the beans onto the floor at meeting time, and I modeled separating them into groups of ten, with ones left over. They seemed to understand this just fine. "Let's count by tens," I said, pointing to the piles in turn, and they chorused along with me, ten, twenty, thirty, all the way up to seventy. "Now we have to switch and go by ones," I instructed them, and touched the ones in turn, counting aloud: seventy-one, seventy-two, seventy-three, seventy-four.

"There," I said, sitting back. "Seven tens is seventy, and four more ones makes seventy-four. That's a lot of beans!" The children nodded soberly. It was a lot of beans. "Seventy-four beans," I repeated. "We should write that number down so we don't forget. I wonder if anybody knows how to write it. "

Several hands waved. What a capable class, I remember thinking. Understanding the decimal system so well at such a tender age! I chose the child who had filled the container, and she stepped up to the board and picked up the chalk. "Seventy-four, right?" she asked.

"Seventy-four," I confirmed.

So she wrote, and stepped away to admire her handiwork, and with a sinking heart I saw what she had written--

7D4.