"Some kids are just dumb" is not good education policy

Yes, Freddie, I think UCSD students can do basic algebra

This student may or may not be able to learn advanced math. But she’s got no chance if we don’t bother teaching her. (Photo by Ariel Skelley/Getty Images)

When I write about the failure of our schools to teach kids basic math, education writer Freddie deBoer complains that I am ignoring the obvious fact that some children are simply not that smart and will never master advanced math. “Big-time proponents of quantitative assessment like Kelsey Piper here also can’t accept that academic ability is normally distributed and that there will always be a bottom 50%/25%/10% … [people like Piper] act like it’s a matter of crisis when that testing reveals the inevitable reality that some people just aren’t good at school,” he wrote in a recent comment in response to my UC San Diego innumeracy article.

When I write about the failure of our schools to teach our kids how to read, deBoer complains that I am ignoring the obvious fact that some children are simply not that smart and can never be expected to read.

If I say we should adopt high-quality curricula and train teachers on them, deBoer complains that I am “big mad that we haven’t just waved the magic wand and saved the kids, which she insists (again and again) is something we could just do, if only we had the will.” Never fear, deBoer knows better: “Not all students are equally talented, and this can never change.”

Now, “not all students are equally talented” is true. Some kids are smarter than others. Some kids will pick up a new mathematical concept from one example and some will require ten, or a hundred. Some kids, no matter how hardworking or diligent, simply will never with any reasonable amount of study be prepared for college-level calculus or reading James Joyce.

I myself found college-level real analysis harder than all my other classes combined and decided to study some other subject instead, and I think the main difference between me and my classmates who kept taking math was that they were smarter. So yeah, some people have more of a head for math than others, and, ultimately, many of us will eventually run into math that’s too hard for us and then we’ll quit.

But while deBoer and I seem to agree on these pretty obvious facts about the world, we disagree on what these facts imply about education policy. His observations about the variation of innate talent aren’t clever, they’re lazy curiosity-stoppers that end conversations when they should just be getting started, another way to excuse bad performance by our schools.

The fact that ability is not equally distributed doesn’t actually tell us how much effort we can and should put into teaching kids with lower capacities for learning. If someone is in the 25th percentile for innate mathematics ability, that doesn’t answer the question of whether they should be expected to pass ninth-grade Algebra!

But I’ll indulge deBoer. Let’s talk about innate intelligence.

Some kids are very bright. Some aren’t. Some kids generalize easily across lots of related concepts. Some don’t. Some retain things they learned in earlier grades easily. Some forget everything that isn’t in constant use.

If you’re teaching a math prodigy, you can often give one or two examples and they’re all set; they don’t need any more practice, they already drew all the connections between this and prior material. If you showed them how to do it with positive numbers, they figured out how to do it with negative numbers.

This is not how most kids learn math. Most kids need an example for each slight variant on the problem; they then need lots and lots of practice to reinforce the concept. They forgot a bunch of last year’s material and need review.

But most kids can master algebra with consistent high-quality support and instruction. Many kids who struggle to master algebra would master it with an adequate instructional program.

Pretty much all kids, including kids with significant intellectual disabilities, can learn to read if adequately instructed. And in specific cases where I have some insight into the actual situation on the ground, we are using “maybe the kids aren’t that bright” to ignore glaring, obvious instructional failures that we could instead just solve.

Frequently, deBoer complains that we’re expecting too much of students: “If you insist that every child can get to the Stanford-to-Google success track if we just want it bad enough, you’re inevitably going to generate pressure that forces students through the system that have no business advancing in it,” he wrote in a Substack Note.

But this complaint only makes sense if you lie about what I am actually proposing. I’m not saying that every kid can get into Stanford and then work at Google.

I’m saying that top students at California high schools can be expected to master algebra. I’m saying that most children can learn how to read. I’m saying that even students with poor innate capacity can benefit from access to a high-quality education that expects more from them than many of our schools do right now.

Let’s talk about a specific example. Recently, I was helping a student learn to factor quadratic equations. This is one of the algebra skills that students are most likely to struggle with; when kids fail algebra, this is often why.

If you’ve forgotten this, or never learned it, this is the skill of taking an expression like x^2 + 7x + 10 and rewriting it in the form (x + 5)(x + 2), which is a more useful format for some problems you might want to solve. To factor an expression like this, you look for numbers that multiply to the constant term (10) and add to the middle term (7).

This task does not require mathematical genius. It does require a firm grasp of your multiplication tables. If you are excruciatingly slow in running through all the possible factors of 10 in your head, then this task will be agonizing. And when kids struggle on this task, in my experience, a weak grasp of multiplication is usually why.

Nearly all students can memorize their multiplication tables if drilled on them extensively. Some will pick them up much faster than others, to be sure, but nearly all of them will learn them.

However, many schools these days don’t drill multiplication tables. In a school that doesn’t drill multiplication tables, only two types of kids will wind up with a firm-enough grasp of their multiplication tables to do the above factoring problem: kids whose parents make them drill at home and kids who learn really fast and picked up their multiplication tables without requiring much drill.

So, let’s say we didn’t bother teaching kids their multiplication tables and now they’re struggling to factor quadratics. What can we conclude?

One thing we could say is “they’re probably innately not that bright.” It’s true that they’re probably not innately so good at math that they could route around missing the prerequisites, nor so good at math that they picked up multiplication tables despite going to a school that refused to drill them.

But mostly, I think that “they’re not that smart” is not the right diagnosis of why they are struggling. They are struggling because we didn’t teach them a prerequisite skill!

Now, even in a classroom where we did drill multiplication tables, some kids are going to struggle to factor quadratic expressions. For some of them, algebra requires a level of abstraction that doesn’t come naturally, and even though they can memorize the procedure to solve the problem, they don’t understand why we use that procedure. As a result, when they stop having it memorized, they have no way to rederive it.

Those kids would probably benefit from a teacher who understood this concept firmly enough to explain it from a number of different angles. But many teachers don’t, so those kids are going to stay confused.

For some other students, they don’t care about this or see any relevance to their life, and they simply aren’t going to put in the work to master it. And for some kids, the number of repetitions they would need to master this particular skill is extremely high — because they have very weak innate ability — and it’s not worth spending a year of their lives trying to master it.

If a class has all the prerequisites and the material is taught effectively, some kids still won’t learn it. Those kids probably shouldn’t be pushed to take higher-level math — unless they later return to the subject with new motivation; they might well be capable of it if they actually care.

In a world where you are effectively teaching all the prerequisites, motivating students, and introducing the skill, then innate ability and motivation are the remaining factors in how well kids learn. And so then you can say that probably it’s not worth trying to force the kids who aren’t picking it up to keep trying until they hate math and you.

But that is not the world we are in. We are not providing mathematics instruction that is so effective that the only reason kids fail to learn is lack of innate ability and motivation.

We are providing frankly quite bad mathematics instruction. As a consequence, lots of children are failing, despite having adequate ability and motivation, for reasons like “they had a bad teacher in a key year” or “their school district doesn’t drill multiplication tables.”

In the real world, many student struggles are explained by what a terrible job we are doing of teaching, not by lack of innate ability. This is obvious once you actually look at what tasks these kids are failing at.

And yet, if a student fails, the innate-ability people will immediately loudly chirp “You know, some kids are just dumb!” Now, maybe this is a useful thing to inject into a conversation where someone is optimistically asserting that if we just spend enough money, all children can learn calculus or get perfect SATs or do some other thing where innate knack is genuinely often the limiting factor. I wouldn’t know, because I haven’t been in such conversations.

The present environment is one in which we are instead delaying and diminishing math education because of bad pedagogy, dumb education fads, overwhelming incentives for grade inflation, and a shortage of highly effective math teachers. It’s where most kids are performing way short of their potential. And in the present environment, when you see a hardworking, motivated kid who can’t do algebra, your first assumption should be that we did not teach them algebra.

I think Freddie deBoer means well, in some sense. I think he’s angry on behalf of kids who are set unrealistic expectations by people who just want to pretend that all kids are the same, and I think it is indeed unfair to pretend all kids are the same.

But what he’s doing is treating kids’ current performance — under fairly atrocious instructional conditions — as what they are truly innately capable of, and then accusing anyone who thinks we can achieve better instructional conditions of pretending all kids are the same.

Not all kids are the same. But most of them can learn algebra if they’re willing to work hard. And when they fail to factor quadratic equations, it’s usually because they had a lousy teacher or were never drilled on their multiplication tables.

Sometimes, you have to actually look at the details before you draw broad, sweeping conclusions — and I think you have a particular obligation to do this if your broad, sweeping conclusion is that all children who are currently failing math are simply too dumb to merit instruction.