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Make Math Make Sense · Mar 16, 2026

The Power of Expectations

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Abby Gordon · Make Math Make Sense

I’ve been coaching at a school this year in a midsize city that, like most cities in the U.S., suffers from a high degree of economic segregation. There are two public middle schools in this city, one in the wealthier part of town, one in the poorer part of town. The one I coach at, in the poorer part of town, is majority hispanic, with about 76% economically disadvantaged students. The other school is more racially mixed and about 40% disadvantaged students.

One day after work, walking through the retail center of town that divides the disparate sides of the city, I stumbled into a consignment shop barely bigger than a suburban closet. When the single other person in there and I made eye contact, I took the opportunity to say how impressed I was by how many great finds were packed into that tiny space. It turns out this person was the owner of the shop, and we started chatting. She asked what brought me to her shop, and we got to talking about my work. When I mentioned at which school I was coaching, her eyes widened and she said, “Oof, good luck with THAT.”

Her words sat with me for hours – days, even (full disclosure: this happened two months ago, so I guess months). Why had she responded that way? I was too taken aback to say anything other than a muttered “thanks,” but her comment shifted our conversation. She wasn’t on my side. She wasn’t on the side of the hardworking kids and even harder-working teachers in this school. She was someone who would write them all off because of her beliefs about what the school in “that part of town” was like.

If I were quicker with comebacks, I could have – should have – said: I don’t need luck. Less than an hour ago, I witnessed some of the strongest algebraic thinking I’ve seen in years, from a class of 8th graders no less (Algebra 1 is typically taken in 9th grade). I don’t need luck, because the teachers at this school believe in their students. They care about their students, probably more than you can imagine. That day, I saw two teachers commiserate over one of their students moving to another district. I saw a teacher glow over a homemade meal that a student’s mom had dropped off for her. I saw a principal and a math coordinator using high-level research to guide their leadership. I saw teachers hold every student to high expectations, not letting a single one slide by unnoticed. These teachers’ belief in their students holds more power than luck ever could.

One of the ways the department coordinator has made her expectations clear is by continually pushing the teachers to ask high-level questions during math classes. In the 8th grade algebra class I had just been in, students were learning to find solutions of systems of equations. Rather than ask “what are the coordinates of this point?,” the teacher asked the students to explain what a solution to a system of equations means. The first question calls for a simple and direct answer. A student could say “(3, 5)” and be correct, but the teacher would have no idea if he understood the concept or had simply copied an answer from his neighbor’s paper. The student’s answer also wouldn’t help anybody else understand anything better. This teacher demanded more. He wanted to make sure his students knew what the solution to a system meant and how to apply that understanding to a novel problem.

Most students (and probably adults who have gone through algebra) would say “it’s where the two lines cross” or “the point where they meet.” And many teachers would be content with that answer. But this teacher expected more. The student he called on explained that the solution is “the coordinate pair that makes both equations true.” Several others chimed in, adding to that explanation to help the class build understanding.

In another school I’ve been working with for several years, the Algebra teacher also holds all of her students to high expectations. In her large classes of twenty-five or thirty students, she notices the minute someone puts their head down or attempts to get away with not doing their work. You can do this, she reminds them, and I’m here to help you. She doesn’t let anyone hide or get off the hook – and high schoolers are pros at both of these. If they don’t know something when she calls on them, she’ll come back to them in a few minutes after they’ve had the chance to listen to their peers, expecting them to show their understanding then.

There’s a lot of research out there showing that teacher expectations have a profound influence on student achievement (see John Hattie’s meta-analysis here, for example). If teachers think their students can’t do it, guess what? The kids live up to the expectations. If teachers think their kids can do it – and convey this message, along with the support the students need to be successful – then, once again, the kids will live up to the expectations. As the poet Anais Nin said, “We don’t see things as they are; we see them as we are.”

Part of living up to expectations is structural: if teachers don’t think students can tackle a harder challenge, they won’t give them a harder challenge. Students learning is then limited by what the teacher has let them learn. As much as we think we know our students, they always surprise us. Someone who struggled to learn one topic may excel in the next (Geometry, for example, is a famous equalizer). The other problem is that students can tell what the teacher thinks of them and will act accordingly. This is related to, though not entirely the same as, stereotype threat, which Claude Steele described beautifully in Whistling Vivaldi. If I’m a high-school student who knows that my teacher thinks I can’t do the math – and I may also be facing familial and social difficulties, as well as all the other stresses teenagers in the U.S. face – I’m probably not going to spend a whole lot of energy trying to prove that teacher wrong.

In much of my professional development work, one of my norms for teachers has been to avoid labeling students. When we refer to the “low” students or the “high” students, we’re revealing that we have fixed mindsets about how those students are going to achieve. We’re putting them in a box before even giving them the task. Many teachers try to work around this norm by referring instead to their “strugglers” and their “ones who get it fast.” Just changing the wording doesn’t change the mindset that the wording reveals. Any language that groups students like this has the same effect: it reveals that the teacher is already expecting certain students to struggle. And students can certainly feel those expectations, no matter what language teachers use.

What we need to do instead of labeling students is think of them as individuals who may need different supports in order to succeed with that particular math task. Maybe some students need a visual aid; others would benefit from manipulatives; and others could use a refresher of a certain skill. Rather than assuming they can’t do something, what if we asked ourselves: how can I ensure that they can? What scaffolds can I put in place to ensure that all of my students can do this math? And how can I make that belief clear to them?

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