Mathematics

When a Child Understands but Cannot Do the Questions

They are not lying. Following a worked example is recognition; doing a question is recall. Two questions at the kitchen table tell you which one you have.

Short answer

Why does my child say they understand but cannot do the questions?

Because understanding while watching is recognition, and doing a question needs recall. Cover the worked example and ask for one similar question with different numbers — that is the whole test.

The short answer
Because following an explanation and producing a solution are different tasks. Watching a worked example removes the hardest part of a maths question — deciding which method applies — so it feels smooth and produces a genuine but misleading sense of understanding. Cover the example and set a similar question to find out which you have.

What changes the answer

If the child can redo the exact example from memory but not a version with different numbers, they have learnt the example rather than the method — the commonest state and the one that collapses in an exam.
If they cannot even redo the example with it covered, nothing was retained at all and the session was watching rather than working.
Two days changes the result, because recognition decays within hours; a test run immediately after the lesson flatters everybody.
Where the algebra is right and only the numbers are wrong, this is not a recognition problem at all and needs arithmetic fluency instead.

Three things 'I understand' can mean

The first is 'I followed that'. True, and worth nothing — it is a passenger's understanding of a route. The second is 'I could do that one'. Half of what is needed. The third is 'I could do one I have not seen', and it is the only version that survives a test.

A child saying 'I understand' almost always means the first, and they are not being dishonest. The sensation is real, it is strong, and from the inside it is indistinguishable from the third.

The two-question test

It takes about eight minutes at the kitchen table and it settles the argument without anybody having to be right about the other person's state of mind.

Question one: the same question as the worked example, with the example covered. Nothing changed at all. Question two: the same type, different numbers, and one surface feature moved — fractions where there were whole numbers, the unknown on the right-hand side instead of the left, the diagram rotated, the units changed.

Both right means recall, and you can move on. First right and second wrong means they have learnt the example rather than the method. Neither means they were watching. The reason for moving a surface feature rather than only the numbers is that a child working from a memorised template will follow it perfectly as long as the question looks the same — and every exam question is written deliberately not to look the same.

Why a worked example manufactures exactly this illusion

The hard part of most maths questions is not the arithmetic. It is the choice: which method, which formula, which of two similar-looking rules applies here. A worked example arrives with every one of those decisions already made, and it never shows the moment of choosing, because there was nothing to choose.

So watching an example exercises comprehension thoroughly and never exercises selection at all. The student comes away completely accurate about what they experienced and completely wrong about what they can now do.

This is also why a video in which everything looks easy is often the least useful revision a student does. The feeling of clarity is the product being sold, and it is not the same product as being able to answer question 17.

The question that exposes it in ten seconds

'Why did you multiply there instead of dividing?' A child with recall gives a reason. A child with recognition says 'because that's what they did' or 'because that's the rule'. It costs nothing and can be asked in the middle of homework without turning anything into a test.

The second useful one is 'what kind of question is this?'. Naming the type is the selection step. A student who cannot name it cannot select it under pressure, however well they can execute it once told.

What to change

None of these takes extra time. They redistribute the time already being spent, away from watching and towards attempting.

Change the ratio: one example watched, three questions attempted, from the first day of a topic.
Cover the example before the practice starts, not after the first question has gone wrong.
Mix topics within a practice set, so the question has to be identified as well as solved.
Retest two days later rather than the same evening.
Ask for the method to be said out loud before anything is written.

Common questions

Is my child lying to me?

No. The sense of understanding while following an explanation is real and it is an accurate report — just a report about a different task from the one the test will set. Treating it as dishonesty makes the child defensive and does not change the outcome.

Does this happen in other subjects?

Yes, and it is worst wherever there is a model to follow: mathematics, physics, essay structure. It is least visible in subjects assessed by recall of facts, because there a student can tell for themselves whether they know something, and the illusion has nowhere to hide.

So should they stop watching worked examples?

No — examples are how a method is introduced and there is no substitute. The problem is stopping there. The rule that fixes it is that an example is followed immediately by attempts, with the example out of sight, on the same day.

How do I test this without turning it into a test?

Ask them to teach you the question. It is the same test — selection and sequence, spoken aloud — and children submit to it far more willingly than to being handed a worksheet by a parent who has just said they do not believe them.

Last updated August 21, 2026