Memory is the residue of thought.
Lots of students struggle in math class. I would conjecture that, of the many students who I have been unsuccessful teaching, the principle reason they didn’t learn is that they spent much of their time in my class thinking about things besides mathematics. Here are some profiles of students who I’ve seen struggle.
Identity & Belonging
Some students come to my class each day feeling like they don’t belong. Maybe it’s because they perceive my actions as racist or sexist, maybe it’s because of societal messages about whether their identity is one that is supposed to be good at math. If students perceive that they don’t belong in my math class because of who they are, they are likely to quit thinking when things get hard, or otherwise find something else to think about because math isn’t for them.
Anxiety presents itself in a range of ways. I’ve seen students who physically shake, or put their head on their desk and shut down, or start crying. Others keep it inside. What they have in common is that, while they are in math class, their mind is consumed with fear and worry, and there’s no room for mathematical learning.
Students spend lots of hours in school during their lives. They are likely to learn some things during that time. For some students, they have learned that if they copy things from the board, write down answers figured out by others in their group, and generally stay hunched over a piece of paper looking studious, they are unlikely to be bothered by the teacher. They are doing some thinking during class, but that thinking is about how to look like a student, not how to reason about mathematics.
Some students have an intense dislike of mathematics; they would rather be anywhere in the world than my math class. Even if those feelings don’t trigger anxiety, they lead to avoidance mechanisms like doodling, refusing to answer questions, writing fake answers on the page, hiding misconceptions, and more. These students aren’t thinking about math; they’re thinking about how unhappy they are in that moment and everything else they’d rather be doing.
This is not an exhaustive list, but these are different behaviors I have seen with some frequency that prevent students from learning. I have one big takeaway here.
Never Blame Students
These issues may not be my fault. They may be rooted in years of experience. They may be enormously challenging to work against. It might be really easy to just say “hey, Jimmy never paid attention, so he’s gonna fail this class”. That doesn’t matter. It’s my job to send anti-racist messages about how my classroom works. It’s my job to work with anxious students to create familiar routines, support systems, and a safe space for them to learn. It’s my job to teach students what effective effort and learning look like. It’s my job to create opportunities for engagement that teach students what it’s like to enjoy doing math.
I wrote last year about math ability, and made an argument that I didn’t see any evidence that math ability exists. It created quite a bit of argument on Twitter; many folks disagreed pretty strongly, for a variety of reasons.
I think my statement then was too strong. I’m mostly agnostic on math ability. I don’t know whether or not it exists. But I do know that the four phenomena above exist. And in every student I have taught who might be categorized as low ability, at least one, and often several, of the above issues are at play. In most cases they’ve been at play for years. I don’t know whether ability exists, but I know that these four issues are ones I can do something about. Talking about math ability seems unproductive in that context; I believe in teaching kids, I believe that every kid can learn, and I believe it’s my job to figure out what obstacles are in a student’s way and do something about them.
I don’t mean to stir up the math ability fight again. I don’t mind whether or not folks believe it. I do think that, when I’m confronted with a challenging student, I have lots and lots of tools that I can use to start moving them forward, and talking about ability is a dead end. There are no easy solutions to any of these problems, but they’re all problems I can do something about.