I believe any student can learn from the right teacher.
I have had many, many conversations with students whose biggest struggle came down to a disconnect between them and their instructor. Not ability, not effort — a mismatch in how the two of them were carving up the world.
The relationship often reminds me of Plato’s cave. The teacher is trying to bring the student into the teacher’s world, but the student can only see that world through the lens of their own. Every step forward is a small breach in how the student already understands things, and the wrong guide will struggle to help them through it.
What my own teaching has taught me is that the arrow runs both directions. The teacher is also only capable of interpreting the world from inside their own perspective, and the student is also, constantly, trying to pull the teacher into theirs. Perhaps that is just an analogy for communication in general. But it strikes me as an apt description of the specific difficulty of being both the teacher and the student at once. Both are captives of their own viewpoint.
That framing changes what the job is. If the gap is a translation problem, then the work is not repeating the explanation louder — it is finding out which language the student already speaks and building the explanation out of that. A student who understands how a bank account works already understands conservation laws. A student who has argued with an autocorrect already understands most of what makes a compiler frustrating. The material is rarely the obstacle. The route in is.
What that looks like in practice
I ask what you already know before I tell you anything. Not to grade it — to find the bridge.
I make the reasoning visible, including the dead ends. Textbooks show the path that worked, which quietly implies that the author saw it immediately. They didn’t. Showing the false starts is more honest and more useful.
I refuse to call anything trivial. “Obviously” and “simply” are words that tell a struggling student the problem is them.
I let the student be wrong out loud. A misconception you can see is one I can work with. One you are hiding because you are embarrassed will follow you into the next course.
The limits
We cannot meet the needs of every student, and we cannot make every student care. I have stopped treating that as a personal failure. But it does not change the math on the ones we can reach, and there are more of those than most people assume.
We can make a difference. That is enough reason to keep doing it carefully.