Wednesday, May 23, 2018


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.


  1. This is beautiful. I was definitely a student like Wilfred, up to college. I don't want to tell that whole story right now, but I'll point to it -- I was very anxious about my ability to hang intellectually in college, coming from a weird academic background that really emphasized innate talent.

    I want to think out loud about what you said to Wilfred. It was incredibly kind and generous. He's lucky to know you.

    "NOBODY is born just knowing the answer in math. Do you hear me?""

    This is your point, and it's a good one. I wonder (thinking back to the kid I was circa-the early 2000s) if this is what Wilfred is worried about. I wasn't worried about that -- I didn't think that people were just born knowing math or the answer. I knew that quickness or smartness came from experience and learning. I had two other concerns: (1) that I was too far behind and irrevocably behind my classmates in math and everything, and (2) that I needed so much more experience and practice than others that I could never excel intellectually.

    OK, and here's a wild thing to say now, but these are both sort of correct in a way.

    I've been wistful lately, thinking about the opportunities I left behind in my 20s as I dove head-first into a teaching life and a family. And I think it's roughly true that, right now, I've left some opportunities behind. I was daydreaming today about being a sort of cutting-edge mathematics researcher, but I don't realistically think that's where I am. I'm too far behind, and it takes me a lot of time to understand mathematical ideas. I could be wrong, but I don't think I am.

    Here's the thing, though, and I want kids like Wilfred to know this too: learning is fun and valuable even when you're not at the top. I feel like in our desire to emphasize growth and effort we sometimes put achievement on a pedestal, but who says achievement is so great?

    (Also on my mind:

    So that's what I'd want to tell Wilfred too, which is that who cares if someone gets the answer right away? Those kids aren't you. You're special, and you don't know the ways in which you're special. You just learn stuff because it's fun and cool, and you never know how you'll need to use it. You don't know what you're going to do or who you'll impact, but you do know that you're the only one who can do it.

    We need to help kids move away from the idea that *achievement* is even a goal, I think. Our moral vision can be more open-hearted than that.

    1. Yes, I love this. And this part gets to me: "I had two other concerns: (1) that I was too far behind and irrevocably behind my classmates in math and everything, and (2) that I needed so much more experience and practice than others that I could never excel intellectually."

      Beacuse there's all this stuff about access and opportunity going on here. Why have some kids had more practice? Because their parents have time / know-how, etc to give it to them, and his don't (I don't think). And that is going to continue to create an unlevel playing field for him. But I had no idea how to talk about all that at that moment, or even if I should.

  2. Yes to everything Michael said. I also loved Ilana Horn's speech at her daughter's NHS induction ceremony that he references. This is so important, the idea that achievement, that being FIRST, is not everything. It's hard for little kids to see that, is the thing. It often takes a lot of life experience to really believe that, even if you have parents and teachers giving you that message regularly, I think.

    I'm thinking too about a whole-class conversation I had about 4 years ago with my 4th grade class. I raised some questions them about growth mindset vs. fixed mindset type stuff, and I remember that almost all of the kids said vehemently that anyone could grow and change and become good at whatever they put their effort towards, and one kid very vehemently told them all that it was just not true. That there were certain doors that were just already closed for them. I think he might have used some professional sports examples for himself (ha), but what he was saying was kind of like what Michael's saying here about leaving some opportunities behind in his 20s. And I remember that while I admired all of the kids' growth mindsets and their self-belief, I also secretly felt like the naysayer was sort of right. The doors aren't always all open if you just work hard enough.

    I feel so nervous to say this out loud, like people will interpret it as me not believing in kids who face challenges (life, mathematical, other). But it's not that at all. I want to encourage kids, all kids and especially those kids, so much. But I also see things through kids' eyes a lot, and they are so honest. I want to acknowledge what they see ... that they want something (speed, the appearance of "ease") that they currently don't have and feel like they can't get.

    1. Whenever I talk about how some kids are behind or need SO MUCH practice of things like that, my husband gives me this terrible look and says, "But are you saying all kids can't LEARN?!" Because we are so not allowed to say that stuff. But I am 100% with you, especially because of the fact that the playing field is so not level. (Not to mention that yes, everyone has things that come easier to them than others, which is another conversation I've had with my classes, but it wasn't something I wanted to say to Wilfred because I think he has a pretty good math mind.)

  3. Michael and Kim's comments make me think of a recent podcast I heard with Chris Hayes and Brittney Cooper. I really recommend it.

    There is a section where Cooper talks about the source of so much parenting anxiety, which is that "you want your kid to be a have, vs. a have not. You want your child to be in the middle class when you know resources are shrinking."

    I think so much of the focus on achievement comes from a fear of what our society does to anyone who isn't a high achiever.

    1. Yes. Her speech is wonderful. Another thing I've learned from my husband (via his work with Rick Weissbourd is this idea that instead of wanting our kids to be happy or to achieve (which is what most parents identify as their top goals for this kids), the thing to stress is that they are good to other people. And that includes fighting for justice in the world. I love that she addresses all three of these goals (achievement, happiness, and goodness).

    2. Sorry, just realized I was commenting on Ilana's speech (from Kim's comment), not this podcast. But now I have this podcast cued up to listen to. Thanks!