There’s a familiar divide between practice and policy. When it comes to grading, devices, equity, choice, student behavior, and much else, the views from inside and outside the schoolhouse are very different. That’s a big part of why educators and policy types tend to talk past one another. To delve into this disconnect, I reached out to Alex Baron, the director of academic strategy at a District of Columbia charter school, an Oxford Ph.D., and a former early-childhood and high school math teacher. Together, we’ll try to bridge a bit of the practice-policy chasm.
—Rick
Rick: Earlier this year, we got some brutal results on the National Assessment of Educational Progress. The math results were disheartening, showing we’re still mired in over a decade of slumping student achievement. I’m inclined to look at an issue like this through a policy lens. But that’s not always the most useful approach, especially when discussing this with a longtime math teacher like you. In fact, you’ve just published a new book on math, Counting On Yourself, that offers some useful ideas. Before I weigh in, do you want to say a bit about the book and how you think about our challenges in math?
Alex: Math often makes smart people feel dumb. Since math has objectively right answers, it also has objectively wrong answers; when we get a wrong answer, it can feel like there’s something wrong with us. I’ve taught math at the primary, secondary, and college levels; I’ve seen how math can torpedo academic confidence, which curdles into general intellectual insecurity that can last into adulthood. We get adults who say, “I’m not a math person,” who then pass math-phobia to young people, and the cycle continues.
This cycle has created a dire reality regarding mathematics. According to the 2024 NAEP scores, only 27 percent of 8th graders are “proficient” in math. On the 2022 PISA, the most recent iteration, American 15-year-olds placed 31st out of 36 tested OECD countries. These grim outcomes have real economic implications. A 2017 AIR study found that only 21 percent of students who never passed Algebra 1 graduate from high school in four years. Additionally, improving math scores has been shown to have a positive impact on earnings later in life. Two-thirds of community college kids and 40 percent of undergraduates take remedial-math classes, decreasing the likelihood of graduating and increasing college debt.
Rick, we know math is foundational for academic and professional success, but we haven’t found a way to explain it in a sensible, relevant manner. To help math make sense rather than create stress, I recently published Counting On Yourself: An Adult-ish Guide to Math and Money. The book offers a guided tour of math from preschool up through high school. It’s not just meant for students—but for a general audience, including adults, college students, and anyone who feels like math passed them by or steamrolled them.
I wrote Counting On Yourself with three key qualities that differentiate it from other math books. First, the book connects all math concepts back to addition. If you can add, you’ll see that “advanced math” isn’t as inscrutable as it seems. Here’s a sample about logarithms. Second, the book connects all math concepts to personal finance. People want to learn money management and also don’t see how math applies to their lives—Counting On Yourself addresses both. Finally, the book uses math to bolster self-confidence rather than undermine it. When you read Counting On Yourself, you’ll find math less miserable—and yourself more intelligent—than you’d thought. If you can learn math—something that you may be convinced you can’t do—what does that mean about your other self-beliefs? Maybe you can do a lot more than you think.
Rick: I find some of this really compelling. I’d like to give you a chance to get me on board with the rest. First, I get it when you talk about how bringing it all back to addition can make “advanced math” seem more intuitive and less intimidating. I’m always struck by the power of a compelling analogy. Second, I’m also mostly with you on the value of making math feel practical by linking it to finance, though I worry that making something “relevant” often means either eviscerating the substance or embracing a pretty tortured notion of “relevance.” Third, I guess I’m most skeptical of the notion that everyone can be a “math person.” I mean, a lot of students struggle with poetry, world languages, chemistry, or music. I don’t usually imagine that everyone can be a “poetry person” or a “music person.” I’d love to hear your thoughts about how self-confidence works in math relative to other subjects.
Alex: Kids know that poetry, chemistry, and music have lower stakes for them, which decreases how much their self-confidence hinges on those subjects. Kids also know that math comprises half of their SAT score, that annual high-stakes tests occur in math but not science or social studies, and that people who get math are automatically seen as smart in some ineffable way. In short, 100 percent of kids get the message that math matters, even though only 27 percent of 8th graders get the math itself. That discrepancy is a recipe to damage self-confidence.
To be clear, I’m not asking everybody to “love math.” I just don’t want math to stop kids from making it through high school, or for ambitious twenty-somethings to miss out on graduate school because of the GMAT math section, or for parents to viscerally fear supporting their kids with math homework. When people don’t get math, it makes them feel dumb in a way that struggling in poetry and dance does not. Maybe we don’t all have to be math people, though I imagine we’d be highly concerned if our child approached us and said, “I’m just not a literacy person.” But if our society maintains its twin proclivity to both prioritize math and yet tacitly sanction innumeracy as we plunge into the technological age, then I think we’re risking a lot more than kids’ self-confidence.
Rick: Fair points. Now, before we close this out, I want to bring up the issue of where practice and policy intersect when it comes to improving math instruction. In reading, there’s widespread agreement that good early reading requires a significant dose of phonics—and that it’s taken legislation and state leadership when it comes to instructional materials, professional practice, and teacher preparation to set things right. Left to their own devices, many teachers lack the skill, resources, or training to get this right. Are there analogous examples in math? Do you see places where policymakers or system leaders can provide a crucial boost in the right direction?
Alex: It’s a good question, Rick. As far as I can see, no “science of math” consensus has emerged à la the “science of reading.” But upon deeper reflection, even the science of reading is better framed as the “science of decoding” and mostly applies to—as you indicated—early reading; that is, the phonics breakthroughs do not address how we teach higher-order skills like comprehension and analysis. Reading is a complex family of skills that don’t have an instructional silver bullet; the same is true in math. As Zearn founder Shalinee Sharma said in your recent column, conceptual understanding and procedural fluency matter in math. That is, one needs both the procedural ability to solve 2x - 3 = 12 and the conceptual knowledge about why inverse operations help us isolate an unknown. That dual approach may sound like the math equivalent of “balanced literacy,” but to me, a balanced approach seems right in math.
Yes, math nerds bitterly disagree on how to weigh procedural versus conceptual instruction, and some popular curricular materials likely overindex on the conceptual side. But most serious stakeholders agree that we need some balance of both. Ultimately, being an educator is all about exploding false dichotomies: Procedural vs. conceptual. Social-emotional learning vs. core academics. Restorative vs. punitive justice. Nonfiction vs. fiction. Direct instruction vs. inquiry-based learning. In these debates, good educators exercise a lot more both/ands than either/ors. This is because practitioners understand that kids learn differently and that the skills we teach are complex. Like most things in schools, it’s as simple, and as complicated, as that.
