Yesterday, I worked with a boy named Elijah. He was supposed to be doing a worksheet dealing with the values of various sets of coins, but it quickly became clear that he had very little understanding of what coins were worth. I asked his teacher whether I could work with him on that understanding, rather than try to pull him through the worksheet. She nodded knowingly. If teachers were perfect, they’d only give children appropriate challenges. And we do keep trying to zero in on perfection, but we’re not there yet.
I asked Elijah whether he knew what a quarter was worth. He started guessing. So instead, I told him that a quarter was worth twenty-five cents, and then I asked him what it was worth. He replied, “Twenty-five cents.” I asked him what two quarters were worth, and he replied, “Twenty-five cents.” I told him that if one was worth that much, two would have to be worth more. So he said, “Twenty-six cents.” Then, as I started to explain the error in his thinking, he said, “Twenty-seven cents…twenty-eight cents.”
At that point, I could have put more energy into backing up with him and dealing with the concept he needed to deal with. But he was tired of concentrating on this. He was quite distractible, and he’d already been concentrating on it for what seemed, to him, to be a long time (what seemed, to me, to be the better part of a minute). He liked to work quickly, and I did not have the energy to try to get him to slow down at that moment. Instead, I told him that two quarters equal fifty cents, then asked him what two quarters equal. He replied, “Fifty cents.”
Elijah doesn’t like to spend much time working on things he doesn’t understand. Neither do I. I’ll bet many of you don’t, either. I decided to try getting him to remember that one quarter is worth twenty-five cents, and two of them are worth fifty. He likes memorizing, and has had some success with it. Most of the other children in the class were working on learning math, but this did not feel like a good time to work with Elijah on math. So instead, I spent the time helping him memorize the value of one quarter, and the value of two quarters.
Memorizing is not math. A child can memorize the times tables and have no idea what multiplication is. In fact, Elijah has been memorizing the times tables, and in order to get him to agree to practice telling me the values of one quarter and two quarters, I had to intersperse four times five, three times four, and so
on. He’s a little more willing to practice what he doesn’t know if he’s also allowed to practice what he knows.
Elijah presents a challenge to me, and to the other teachers who work with him. I’m going to try to rise to the challenge – see whether I can find the right balance between allowing him to feel successful and helping him move closer to understanding what he’ll eventually need to understand. He wants to succeed, and for him, success has a lot to do with speed. When a child learns slowly, it’s tricky to incorporate speed into his educational plan. I’ll let you know how this works.