A year or so ago, our math department met with one of the feeder middle schools to engage in a required exercise. The course-alike teachers had to put together a list of “needed skills” for each subject, to inform the teachers of the feeder course of the subjects they should cover.

One of the pre-algebra teachers looked at the algebra “needed skills” list and said, “Integer operations and fractions! Damn. Why didn’t I think of that?” and we all cracked up. End of Potemkin drill.

All teachers working in low-ability populations go through a discovery process.

Stage One: I will describe this stage for algebra I teachers, but plug in reading, geometry, writing, science, any subject you choose, with the relevant details. This stage begins when teachers realize that easily half the class adds the numerators and denominators when adding fractions, doesn’t see the difference between 3-5 and 5-3, counts on fingers to add 8 and 6, and looks blank when asked what 7 times 3 is.

Ah, they think. The kids weren’t ever taught fractions and basic math facts! What the hell are these other teachers doing, then, taking a salary for showing the kids movies and playing Math Bingo? Insanity on the public penny. But hey, helping these kids, teaching them properly, is the reason they became teachers in the first place. So they push their schedule back, what, two weeks? Three? And go through fraction operations, reciprocals, negative numbers, the meaning of subtraction, a few properties of equality, and just wallow in the glories of basic arithmetic. Some use manipulatives, others use drills and games to increase engagement, but whatever the method, they’re basking in the glow of knowledge that they are Closing the Gap, that their kids are finally getting the attention that privileged suburban students get by virtue of their summer enrichment and more expensive teachers.

At first, it seems to work. The kids beam and say, “You explain it so much better than my last teacher did!” and the quizzes seem to show real progress. Phew! Now it’s possible to get on to teaching algebra, rather than the material the kids just hadn’t been taught.

But then, a few weeks later, the kids go back to ignoring the difference between 3-5 and 5-3. Furthermore, despite hours of explanation and practice, half the class seems to do no better than toss a coin to make the call on positive or negative slopes. Many students who demonstrated mastery of distributing multiplication over addition are now making a complete hash of the process in multi-step equations. And many students are still counting on their fingers.

It’s as if they weren’t taught at all.

But teachers are resilient. They redouble their efforts. They spend additional time on “warm-up” questions, they “activate prior knowledge” to reteach even the simple subjects that have apparently been forgotten, and they pull down all the kaleidoscopic, mathy posters and psychology-boosting epigrams they’d hung up in their optimistic naivete and paper the walls with colorful images formulas and algorithms.

They see progress in the areas they review—until they realize that the kids now have lost knowledge in the areas that weren’t being taught for the first time or in review, much as if the new activity caused them to overwrite the original files with the new information.

At some point, all teachers realize they are playing Whack-a-Mole in reverse, that the moles are never all up. Any new learning seems to overwrite or at best confuse the old learning, like an insufficient hard drive.

That’s when they get it: the kids were taught. They just forgot it all, just as they’re going to forget what they were taught this year.

All over America, teachers reach this moment of epiphany. Think of a double mirror shot, an look of shocked comprehension on an infinity of teachers who come to the awful truth.

End Stage One and the algebra specificity.

Stage Two: At this point, some teachers quit. But for the rest, their reaction to Stage One takes one of two paths.

Blame the students: The transformation from “these poor kids have just never been taught anything” to “These kids just don’t value education” is on display throughout the idealistic Teach for America blogs. It’s pretty funny to watch, since on many sites you have the naive newbies excoriating their kids’ previous teachers for taking money and doing nothing, while on other sites the cynical second-years are simultaneously posting about how they hadn’t understood the degree to which kids could sabotage their own destinies, or some such nonsense. Indeed, I once had a conversation with a TFAer at my school, and she said this to a word: “I’ve realized I’m a great teacher, but my students are terrible.”

Not that this reaction is unique to TFAers. Many experienced teachers who began their careers in a homogenous, high-achieving district that transformed over time into a Title I area with a majority of low income blacks or Hispanics have this response as well.

It’s easy to denounce this attitude, but teaching has taught me that easy is never a good way to go. These teachers are best served at a place like KIPP, where the kids who don’t work are booted. It’s not that the kids learn more, but at least the ones that stay work hard, and that allows the blamers to reward virtue. At comprehensive schools, the teachers who saw their student body population change over time respond by failing half or more of their classes.

These teachers please both progressives and eduformers, because they have high expectations. Their low-achiever test scores, however, are often (but not always) terrible.

Acceptance: Here, I do not refer to teachers who show movies all day, but teachers who realize that Whack-a-Mole is what it’s going to be. They adjust. Many, but not all, accept that cognitive ability is the root cause of this learning and forgetting (some blame poverty, still others can’t figure it out and don’t try). They try to find a path from the kids’ current knowledge to the demands of the course at hand, and the best ones try to find a way to craft the teaching so that the kids remember a few core ideas.

On the other hand, these teachers are clearly “lowering expectations” for their students.

Which is the best approach? Well, I’m an accepter. Not that I was ever particularly naive, but despite my realism, I was caught off-guard by just how much low ability students can forget. But as I’ve said before, that’s the challenge I see in teaching.

I could go into more on this, but this post is long enough. Besides, I don’t want to lose sight of the opening story and the pre-algebra teacher’s mockery of the entire point of the exercise. Of course they were teaching integer operations and fractions. Of course they were doing their best to impart an understanding of exponents and negatives. They didn’t need the list. They knew their job.

Teachers know something that educational policy folk of all stripes seem incapable of recognizing: it’s the students, not the teachers. They have been taught. And why they don’t remember is an issue we really should start to treat as a key piece of the puzzle.