You finish the explanation. You ask whether that makes sense. They nod. You move on, and the same error comes back three weeks later as though the lesson never happened.
The nod was real. It just was not an answer to the question you thought you asked.
What “does that make sense?” actually asks
Put yourself on the other side of it. A fourteen-year-old, an hour into a subject they find hard, is asked by a friendly adult whether something makes sense. Saying no means admitting they were lost while you were talking, asking you to go back over it, and extending a lesson they would like to end.
Saying yes costs nothing right now. So the question reliably produces a yes, whatever is true, and the yes tells you nothing. It is a politeness test, not a comprehension check, and it is the most-asked question in tutoring.
Its cousins are no better: “any questions?”, “are you happy with that?”, “got it?” All of them ask the student to assess and then report on their own understanding, which is the very thing they are not yet able to do. A student who has misunderstood something usually feels fine. That is what misunderstanding feels like from the inside.
Ask for the thing, not the feeling
The fix is to stop asking about understanding and start asking for output. Four that work, roughly in order of how much time they cost:
Make them do the next one cold. Not with you narrating. Put a similar question in front of them and be quiet. Whatever happens in the next ninety seconds is the real state of things, and it is often not what the nod suggested.
Ask them to explain it to you badly. “Talk me through what you’d do, you don’t have to get it right.” Removing the requirement to be correct removes the reason to bluff. You will hear the actual model they are using, including the bit they invented to fill a gap.
Ask what would change if you altered one number. “Same question, but the coefficient is negative — what happens?” This separates the student who followed a procedure from the one who understood why the procedure works. They look identical until you move something.
Ask them to spot the error. Give them a worked solution with one deliberate mistake. A student who can find it has a working model; one who cannot will accept the whole thing, because it looks like what you did on the board.
The uncomfortable part
All four of these are slower than a nod, and all four regularly reveal that the last twenty minutes did not land. That is the point, and it is also why they get skipped — finding out costs you the comfortable feeling that the lesson went well.
It is worth it anyway, because that information has to arrive eventually. The only question is whether it arrives now, when you have the student in front of you and forty minutes left, or in March, in an exam.
And what to tell the parent
This is also where honest parent updates come from. “We found today that she could follow the method but could not say why it works, so we spent the second half on that” is a far more convincing thing to receive than “great progress today” — and you can only write it if you asked a question that could have produced a no.