For the last few days my morning has begun at 6:00 on the dot. That’s when my son swings open the door to our bedroom and asks for help with a math question. Fielding questions from a small child who wakes you up and demands help an inch away from your face seems like a good way to sharpen your classroom skills. It’s like some bizarre emergency preparedness drill. This is a million dollar teacher-training idea, but for you I give it away for free.
On the other hand, all that time in the classroom is decent prep for dealing with some of these parental duties. And it gives those of us with young children an N = 1 perspective on a perennial teaching question: what are kids looking for when they ask for help? And I think the answer is that in that moment what they want most of all is to understand. They aren’t primarily interested in having their own original thinking validated. And the implication is that telling kids they’re wrong is mostly trouble when the kids aren’t able to quickly grasp what was incorrect.
This is a bit of a story, but stick with me.
When my son barged into our room this morning, he told us he had two math questions he needed help with, 16 x 9 and 16 x 12. I told him that this was great, but to be quiet so that he didn’t wake up the baby.
Once I picked up the baby (baby woke up) I told my son than I thought 16 x 10 would be a good place to start, since it was so close to 16 x 9. I asked, do you know 16 x 10? He told me it was 160.
Fantastic, now we’re cooking. This is a conversation I’ve had approximately ten billion times in my life as a 3rd and 4th Grade math teacher. I took the next step. Would 16 x 9 be bigger or smaller than that, I asked? He thought and said, smaller. Yes!
I went in for the kill. (Uhh so to speak.) 16 x 9 is smaller than 16 x 10. I asked, how much smaller? This is the hard part, the part that puts a lot of pressure on one’s conceptual understanding of multiplication. If 16 x 10 is ten groups of 16, then we can take away a 16 from 160. If 16 x 10 is sixteen groups of 10, then we have to think about what happens when all those 10s turn to 9s. Without practice thinking this way, kids tend to shrug and guess.
That’s what my son did. He said that we should take ten away from 160. He had zero confidence at all in this. He asked if he was right, and I said it wasn’t.
Now what? I knew that the thing to do would be to draw a picture. Unfortunately, I was horizontal and undressed. I started talking about groups of sixteens … I was shut down by my son who, after all, is six years old and who I recently overheard telling his kindergarten teacher that he is inspired by “vehicles.”
The boy started complaining that he already knew the answer anyway. Cool, I said. So you know the answer is 144. But then he got really annoyed at me, telling me I had spoiled the problem for him. And then I tried to walk this back. I realized that his own fragile competence was on the line. Also he gets loud when he’s worked up and the clock now read 6:01.
Anyway, when he came in he had also said he wanted help with 16 x 12, and I casually changed the subject to that problem. I dragged my sorry butt out of bed and to the table. I poured him a bowl of Cheerios and grabbed a piece of paper and a marker. Then I drew a rectangle in green. I told my son I was going to draw a picture of 16 x 12, but start with 16 x 10. Then I asked him which was bigger, 16 x 12 or 16 x 10, and then how much I would have to add to the green rectangle to make up the difference. This all went much better.
Why did our talk about 16 x 12 go better than 16 x 9? Clearly things started going south when I told him that subtracting 10 wasn’t right. But I also corrected him on things while we were talking about 16 x 12. He told me the wrong dimensions of that green rectangle at first, for instance.
There were two differences when we talked about 16 x 12. First, he was loading up on breakfast cereal and riding a blood sugar high. Second, he understood what I was talking about when I corrected him. That’s thanks to the image. A wonderful thing about people is we turn correction into self-correction. You can’t help but take some credit for recognizing your own mistake, even when someone else points it out.
But when I corrected my son the first time he had no idea why he was wrong, and because of that he freaked out a bit. It’s OK to tell my kid that he’s wrong, but if he doesn’t understand why it’s not going to go well. And it’s the same with students. Don’t focus on whether you’re honoring their original thinking or not — they wouldn’t ask for help if they didn’t want access to your expertise. Focus instead on whether you’re connecting what they don’t yet understand to what they already do.
Is this all there is to it? No. The same boy I’ve written about above just asked for help building something with his toy magnets. He was trying to build a porch, but it kept collapsing. I had an idea and showed it to him. I have to say, my solution was pretty clever. I’m great at toys. The boy took a look at it and decided it was “stupid” and “bad” and that I was “dumb.” Only some of which is true! (It was a great porch.)
It’s not all about understanding, but a lot of it is.