When the school year starts, and I meet my new class, I immediately see a room full of students with an incredible capacity to think about math and a ton of prior knowledge – but I know some of them don’t see themselves that way. I see a room full of mathematicians, but I know that some start the year wondering if they could ever belong or succeed in any math class, much less mine.

This is the most important thing I’ve learned about teaching children: Our students learn whether they’re good or bad at math from us. 

That’s why, as educators, our values form the bedrock of our instructional practice. Our students come bearing untapped intellectual gifts, but we have to teach math in a way that demonstrates how much we believe in them.

Based on how math is often taught, however, math can feel like something that belongs to the teacher, not the student, much less the community. When students experience math as a disconnected and impersonal set of learnings, it becomes that much harder for them to believe that they can truly understand a math concept, even after they’ve memorized it superficially. Then, when students need to draw on their knowledge during assessments, they don’t feel confident because they don’t feel like they have the power to use math. Our students’ capacity for math is deep and definitive – because that’s how they’ll come to see themselves as mathematicians. The goal is for students to thrive in all of our math classrooms, not just mine. Every time I teach math in a way that’s accessible and real for my students, I’m teaching them: “The math is yours.”

For example, not long ago, I noticed my students were feeling frustrated about figuring out the concept of slope. I decided to come up with a new activity that would make my students feel empowered about the challenge – not as kids struggling with a hard topic in class, but as mathematicians grappling with an exciting idea. As soon as I shared this activity, my students took a huge leap forward in their learning and confidence! That’s why I want to recommend my three steps:

1. Connect the learning goal to the world students know. 

As I started brainstorming ways to teach slope, I kept thinking, “My students already understand how this works. They just don’t know that they know. How can I activate knowledge they don’t believe they have?” I realized that for my students, slope was an abstract idea. The first time I tried to teach slope, the students came to class and I asked them to tap back into their knowledge of slope, but they didn’t feel like they had any concrete knowledge to tap back into. I realized that I hadn’t connected it to their lived experiences. I needed to make slope feel real and familiar. It occurred to me that there was a hill, a couple blocks away from our school, that the kids had to walk up every day to get to the subway. So I decided to bring that hill into our classroom. It worked better than I expected and I used the metaphor from then on. Teaching slope using that hill made all the difference for my students and gave that math relevance and belonging in their own lives.

2. Model stepping out of your comfort zone to encourage students.

In our next class, I tacked up a big piece of paper. I drew my students’ walk from the school to the subway station, and I drew four kids on skateboards. One was at the top of the hill, one was halfway up, one was near the bottom, skating on flat ground, and one was on a cliff. I’m not very skilled at drawing, and I realized that gave me a chance to model risk-taking. I said, “Which of these figures will go faster and why?” That got the kids laughing because, of course, my stick figures weren’t going to hang in the MoMA, and I hadn’t considered how students would interpret the stick figures, either! (Also, as a big guy, they might not have had a lot of confidence that I knew how to skateboard). By being silly and showing my class I felt safe stepping out of my comfort zone, and letting them attempt to make drawings in their notebooks, I set the stage for them to start stepping out of their comfort zones and sharing ideas about how slope might work – even if they didn’t know whether their ideas were right or wrong.

3. Cultivate passionate debate among students.

Next, I wanted to get my students tapping into their existing math capacity as they thought about the drawings, building towards a more concrete understanding of slope. So, I got a debate going. I love encouraging students to debate passionately about math, and I highly recommend it. A good debate encourages kids to take ownership of their math knowledge because explaining what you know, what you think, and why you think it builds good argumentation, a foundational mathematical skill. What’s more, it encourages students to embrace their mathematical identity because, as I tell them, mathematicians argue about what they know, what they think, and why they think it all the time! So I invited students to get up, study the drawing, and take a stand on this question: “Which skateboarder is going the fastest?” I asked them to choose: The one at the bottom skating uphill? The one in the middle skating downhill? Or the one at the top? Or the one near the cliff?

Right away, everyone had an opinion, and they weren’t afraid to share. They picked up pens, drew arrows to illustrate their thinking, and speculated on every aspect. One student asks “Doesn’t it depend on whether the skater is kicking or not?” to which I reply “Well, assume they’re just standing on their board.” One student said, “The one going uphill is slow now, but after they get to the top and skate down the hill, they’ll be going the fastest.” I thought that might be a winning argument, but another student came up with a whole new angle: “No, that’s wrong: The one on flat ground already skated down the hill, so they’re already going the fastest.” Their conversations were richer and more knowledgeable than I could have imagined. 

Practically everyone agrees that the skater on the cliff shouldn’t try that at all.

I do that activity with all my classes, including a group of students who had struggled with math in the past and were not yet at grade level, as well as a group of multilingual learners who were working towards English fluency. Every time, the students generated passionate, knowledge-rich debates. It would have felt intimidating if I had asked one of my students to make an argument defending how slope worked, but it wasn’t intimidating for them to make an argument defending how fast a skateboarder could go down that hill. Instead, they were excited. They were arguing about momentum, velocity, wind resistance – all concepts I knew they understood, but they didn’t believe they understood. That drawing gave them a way to tap into their knowledge, articulate it, and take ownership of it. 

I’m a math educator, but I always say I don’t teach math – I teach students math. This idea means I have to make lessons that respond to how students learn math as opposed to a set of lessons disconnected from their own concepts. It can be easy for students to see math as something they try to figure out for class but not something they have a deep, personal capacity to learn, connect with, and use. It’s not unusual for students to walk into our classrooms thinking that math belongs to people who are smarter, who are older, or who aren’t in their immediate circle. But here’s what we know: math belongs to all of our students. That’s why it matters so much for us to show every one of our students, “I believe you can do this math. It’s already yours. How can I get you there?”

When we attend to student belonging and teacher expectation, we can do wonders for our classrooms and communities.