Let me confess something all educators intuit, but a few say it: after more than a decade teaching university students, I have actually never seen the thing I'm actually paid to produce. I've seen answers to tests and quizzes, piles of them; I’ve read tons of essays, good and dreadful. But the thing those answers are supposed to stand for, the understanding underneath? I've never laid eyes on it.

Nobody has.

Saying this out loud (and thinking about it as a result) is important, especially these days, when AI is wrecking education and educators at all levels are scrambling to find ways to either accommodate or limit the impact of AI on student learning.

I’m aware that this might also sound like a riddle for philosophers, but it’s much more important than that because it strikes at the very core of what a grade is.

Hear me out.

A Grade Is a Thermometer

If you’re not an educator, you probably haven’t spent much time thinking philosophically about what a student grade, as an evaluative measure, essentially is. What is it, really?

The best way to understand anything is by analogy, so here’s one. Think about how a doctor uses the concept of a fever. Your temperature matters for your health, and a good physician monitors it closely, because it hints that something deeper is going on. But no doctor worth their salt would confuse the number on the thermometer with the disease. The fever is a trace; the illness is what she's actually treating.

A student grade works the same way. It’s not the most important thing in the world, although it can seem like it during midterm or final season. A grade is a useful signal about something you can't observe directly. It’s a surface to something deeper and more meaningful: the skill beneath it.

The problem with modern education, as many educators are aware, is that we've slid into treating the signal as the disease itself much too often in education. Grades have become, both for the educators and the educated, the only thing that seems to matter. And that’s a problem, because once the the number becomes the thing we chase, improving the numbers becomes the whole game.

Economists have a name for this phenomenon: Goodhart's Law. When a measure becomes the target, it stops being a good measure. Point an entire system at raising a number and you'll get a bigger number that means less and less. Teach to the test long enough and you'll manufacture superb test-takers, which is not the same thing as people who understand anything (and is sometimes the exact opposite).

Teaching Is Detective Work

So if understanding never shows its face, but is represented by the surface of a grade, how does anyone teach it without becoming a slave to the measure? How can educators approach any instructional task?

It’s not impossible, but it requires a different perspective about the nature of teaching.

Here’s another helpful analogy: we should see teaching as a scientific activity, and teachers no different than, say astronomers, who are trying to find planets they can't see. If you’ve read anything about astronomy, you’ll know that astronomers rarely spot the space objects they’re after directly. For example, they may notice a star wobbling a little, or an orbit bending where the math says it shouldn't, and they infer the invisible thing from the pull it exerts on the visible ones.

Thus, teaching is like detective work: a back-and-forth process of agency and inference. Teachers never observe a student's understanding directly; they observe its footprints: a correct solution, a careless mistake, a long pause before the answer, or a bluff of confidence with nothing underneath it. None of these reveals understanding, but each is a clue teachers use to build a hypothesis about a mind they can't pry open.

This turns the ordinary conception of teaching on its head. If the job were just exporting facts from the teacher head into student’s, then clear explanation would be the entire skill, and the best explainer would be the best teacher. But explanation is the easy half, and it only comes second to something more important: a question. What does this student already believe? What do they know?

As a teacher, if you skip asking the question about the student’s mind, even a flawless explanation of a simplest concept will sail right past their head. Everything good teachers do has to be calibrated against the hypothesis of what students already know. If the lesson is too demanding, it will land on blank stares, and nothing will stick. If it’s too simple, they’ll be bored, and there’s nothing more demoralizing that a classroom full or bored students.

In Praise of Wrong Answers

All of this points to the main value of dynamic and successful education: the value of a wrong answer. Yes, there is more value in these than, sometimes, in the correct ones.

To an outsider, this may sound like an overly stretched claim. Surely, knowledge is about knowing the right things, not the wrong ones. But, more often than not, the path to the right things goes straight through the wrong ones.

Consider this example. Take three students who write down the same wrong answer to the same math problem (say, one about proportions). To the grading software, or a teacher rushing to grade all the tests and run home, they're identical: they’re all simply wrong answers.

But if you open the hood to see what’s underneath it you’ll find that a single wrong answer can hide three completely different stories about why the answer was wrong in the first place. Perhaps the first student never understood proportions to begin with. Maybe the second understood the math fine but forgot to convert the units (he was careless). Or, maybe the third one spotted a surface resemblance to last week's problem and confidently ran a similar procedure that was inappropriate for this problem.

We could have the same destination, but three different roads to it. Each of these roads needs a different teaching tactic. Explaining proportions to the second kid wastes both your lives; drilling unit conversion with the first one misses his problem entirely. What do you do when the entire classroom is like this?

If you’re aware of this problem (or you’ve just become aware right now), you’ll immediately understand why parents (who can afford them) hire individual tutors. The real secret of one-on-one tutoring isn't that great tutors explain better (though they do). It's that they spend a huge amount of time asking questions to students that perhaps look beside the point but actually do the hard detective work inferring the student’s state of mind. Why'd you pick that method? What did you expect to happen before you ran the numbers? Can you solve it another way? Questions like these aren't unnecessary chit-chat but little experiments educators run all the time: each answer is another reading off an instrument, another clue about the model in the student's head.

Which is why, to a good teacher, a wrong answer is often worth more than a right one. A correct answer is strangely mute: the student might have reached it through genuine understanding, or memorization, or mimicry, or plain luck, and frequently you can't tell which. But, a wrong answer talks like a weak criminal caught by the FBI. It shows you the shape of the reasoning that produced it, and hands you a map of the misunderstanding, which happens to be the one thing you need to repair it.

The Answers are Always Underneath

The fun thing about this is that none of this is unique to schools. A doctor doesn't care about the fever for its own sake; she cares about the process producing it. An engineer doesn’t care about a metric for the metric’s sake. Across medicine, science, and engineering, the visible outcome is only an evidence about a hidden mechanism. Teaching is basically the same trade.

So maybe the model of education we have in our heads has things backwards. We pour our effort into answers, because answers are what institutions can see and count and file away. But the answer on the page is only the thermometer reading. The understanding beneath it, alive, shifting, half-formed, is the patient.

And you don't cure a patient by getting very, very good at reading thermometers.