What Against Algebra Actually Means
The phrase comes from a well-known piece by Jordan Ellenberg in The Atlantic where he argues that people don't actually fail at algebra because they're bad at math. They fail because of how it's taught — and more importantly, how it's used as a gatekeeping mechanism rather than a thinking tool. Algebra, in Ellenberg's framing, is fundamentally about generalization. It's the practice of taking something you can compute concretely and abstracting it into a form that lets you reason about entire families of problems at once. When students learn x + 3 = 7 as a puzzle to reverse-engineer the answer, they're doing arithmetic dressed up in new clothes. That's not algebra. That's a trick.Against Algebra The Atlantic
The article pushes back against the cultural narrative that algebra is inherently difficult and that struggling with it reflects a personal deficit. Ellenberg's point, essentially, is that traditional algebra instruction often strips the subject of its actual usefulness — which is teaching people to model situations, spot patterns, and reason about unknowns without needing to compute them immediately. I've seen this play out in practice, honestly. The problem isn't the content. It's the pacing and the testing culture around it. When you're told there's one right path to x, you stop thinking about why the equation exists in the first place.There's a specific issue that comes up constantly: students who can do arithmetic fluently will suddenly freeze when letters are introduced, not because they can't solve the problem, but because they've been trained to associate symbols with procedural manipulation rather than meaningful relationships. I ran into this repeatedly when helping people prepare for placement exams. The workaround wasn't drilling more equations. It was going backward — showing them what the equation was describing in plain language before touching any symbols. One edge case worth mentioning: standardized testing compounds this. Tests like the SAT or ACT algebra sections reward speed and pattern-matching. They don't test whether someone understands structure. So students optimize for the test format, which means they learn to recognize problem types and apply shortcuts. That works for the exam. It falls apart the moment the problem doesn't match a memorized template. I had a student once who could solve any linear equation on a timed basis but couldn't explain what 2x + 5 represented in a word problem about phone plans. We spent two weeks doing nothing but translating between words, tables, graphs, and equations before she could hold all four representations in her head simultaneously. That's the gap most instruction never addresses.
Why People Actually Struggle
The counter-intuitive part is that early success in arithmetic can become a liability. Students who breeze through computation develop habits of treating math as a series of operations to execute, not a language for describing situations. When algebra arrives, those habits don't just stop working — they actively interfere.Another thing most people miss: the distributive property isn't just a rule you apply. It's the single most important structural idea in all of algebra. Understanding why a(b + c) = ab + ac is necessary to understanding factoring, quadratic equations, polynomial multiplication, and eventually calculus. But in most classrooms it's presented as a procedure, not a principle. Students memorize the steps and forget the why within a month. The most useful takeaway is probably the shift in framing: treat algebra as a tool for organizing thought rather than a hurdle to clear. This changes everything about how you approach problems, tests, and even your own relationship with the subject. But it also means you have to be intentional about it. There's no auto-generated version of this. You either find resources that emphasize conceptual understanding — such as tasks from the Mathematics Assessment Project at UC Berkeley or the Illustrative Mathematics curriculum — or you build your own. The hard truth is that Against Algebra The Atlantic describes an ideal that most current systems aren't designed to deliver. The testing infrastructure, the pacing guides, the textbook sequences — they're optimized for coverage, not comprehension. Knowing this matters because it changes how you should approach learning the material yourself. Don't wait for the system to teach you algebra properly. Seek out the explanations and problems that force you to think about structure, and skip the drill-and-kill worksheets unless you're specifically preparing for a timed exam.
