Familiar

In recent months, I have occasionally seen one second grader, Wilfred, engaged in passionate mathematical discovery. At other times, I have seen him head down during math, tears dripping. In fact, he's cried during math a handful of times that I can think of. It rips me up inside each time.

This week, we've been working on two-part problems that involve adding two quantities, then figuring out how much more you need to get to 100. He has been dejected, overwhelmed, and tearful.

Today, though, he worked with his teacher and had more success. I walked in and could hear his teacher saying, "See, Wilfred, you CAN do it! Do you see that you can do it?"

I walked him to the bus this afternoon.

"I heard you worked really hard and figured out some hard problems today!" I said as we made our way down the stairs.

"Yeah," he replied with a small smile.

"You know," I said carefully. "That's how math usually is. Usually, you can't just look at a problem and know the answer. You have to think about it and work hard to figure it out, maybe try some different ways, before you know the answer."

"Yeah," he said.

Then, after a pause: "But not for all kids. Some kids just know the answer right away."

There it was. The thought I'd been fearing.

"Only if what they're doing is familiar," I said, reaching for a word we've used often this year instead of saying something is "easy" (thanks to Tracy Zager for that suggestion). "If they've practiced that kind of math a bunch before, they might know the answer right away. But only if they've had a lot of practice."

"No," he said dejectedly, refusing to give in to my arguments because of what he had seen with his own eyes. "Some of the kids in our class haven't had practice. But they still know the answer right away."

I stopped, crouched down on the hot blacktop, and looked him right in the face.

"The only reason kids know the answer right away is if they have had a lot of practice," I insisted. "They might not have had practice in school. Some kids have had more practice with math before they got to school, or when they're not at school. But NOBODY knows the answer right away unless it's familiar to them because they've practiced it. NOBODY is born just knowing the answer in math. Do you hear me?"

"Yeah," he answered, half resigned, half hopeful.

This is what some kids think, folks. They see other kids who know the answer right away, and they think: you're supposed to do that. If you can't do that, you can't do math. And now it's the end of May, and school is almost over, and that's what Wilfred thinks. He thinks he isn't good at math because he doesn't know the answer right away.

I go back in my memory to the mental image I have of Wilfred during one of our inclusion math lessons, when he was making arrays of cubes with 4 in each row. He was ecstatic when he told me that 72 was twelve groups of four and six more groups of four, and he was over the moon when I talked him through the multiplication equations that would show his discovery. There was no quick "knowing the answer" -- it was an hour of completely student-led exploration and discovery, driven by his own questions. It was one of the highlights of my year, and, I hope, of his. I'm holding out hope for more of those mathematical moments for Wilfred.

Edited to add: 

There has been a great conversation, partly in the comments and partly on Twitter. 

My takeaway from the conversation is this: The way you handle a moment like this, as a teacher, depends so much on what you know about the student, your relationship with the student, and probably your own experiences as a learner. Read the comments and tweets below for more.