I once taught a Form 2 boy who was, in lessons, a pleasure to teach.
I would explain something and he would follow it. I would set him a question and he would work through it, correctly, without much fuss. His 小測驗 marks were respectable. Nothing about the way he worked in front of me suggested any difficulty at all.
Then his first big exam came back at just over 50 out of 100.
Based on what I saw every week, I had expected around 80. Any student can have a bad morning. Any student can misread a question or run short of time. But a thirty-mark gap is not a bad morning. Something else was happening, and I did not yet know what.
A quiz and a big exam are not the same task
Parents often tell me their child does fine on the small tests and only falls apart in the real ones. It sounds like a nerves problem. Usually it is not, or at least not only.
A quiz runs twenty or thirty minutes and covers one topic, normally the one just taught. The marks barely touch the report card. And crucially, the question does not require the student to work out what kind of question it is — the whole paper is on one topic, so the method is chosen for them before they read a word.
A big exam is a different job entirely. It covers months of material. The marks matter, and the student knows it. And every question now begins with a decision: of everything I have learned, which idea does this one want?
That decision is the part nobody practises. A student who has memorised a method can execute it beautifully when told which one to use. Ask them to choose, under time pressure, from six months of material, and there is nothing underneath to choose with.
So the small tests were not evidence that he understood. They were a task that a shallow grasp could survive.
I should admit that this fooled me for years. A student who follows fluently in a lesson feels like a student who understands. It is evidence of something — attention, cooperation, a decent memory. It is not evidence of understanding, and I used to treat it as though it were.
The most useful thing he gave me was a wrong answer
After the exam, we sat down with the paper. I did not ask him why he had failed to do it, because that question has no answer a thirteen-year-old can give.
Instead I went through it question by question and asked him the simplest thing I could:
「呢條你會點樣做啊？」
He did it. Correctly, there at the table, with no clock running.
We moved to the next one. He did that too.
So the real question was not why he couldn’t do them. It was this:
「點解你上堂嘅時候識做，但考試嘅時候你又唔識呢？」
And then, on a question where he had written something he plainly knew was wrong:
「點解你會寫一啲明明你知道唔啱嘅答案落去呢？」
That was the conversation that told me what was actually going on, and it produced two answers rather than one.
The first was that several ideas underneath the topic had never been properly settled. In lessons this had stayed invisible, because a method taught ten minutes ago can be reproduced without being understood. He was not pretending. He genuinely could do it. He simply could not do it from anything solid.
The second was that under real exam pressure he became disordered — not merely nervous, but unable to think in sequence. Things he knew perfectly well did not arrive when he needed them.
Neither of those would have surfaced if I had only watched him work in front of me. The wrong answers were the useful part. A correct answer tells you the student got there; it does not tell you how, or whether they could do it again on a bad day. A wrong answer, gone through properly afterwards, tells you exactly where the floor gives way.
“Careless” is a description, not an explanation
The easy reading of his exam paper was carelessness. Silly errors. Be more careful next time.
I think most of us reach for that too quickly, because it is comfortable — it implies nothing is really wrong and next time will simply be better.
But when the same kind of error repeats, term after term, “careless” has stopped being an explanation and become a label. Something is producing those errors. It might be an idea that was never secured. It might be what pressure does to a particular child. Until you know which, “be more careful” is advice with nowhere to land.
That distinction mattered more to him than any correction I made. He had been told to work harder and be more careful for a long time, and neither instruction told him what to actually do differently. What changed things was that someone sat down and tried to find out where the problem actually was — and let him see that it was findable.
A year later, his big exam results were in the eighties.
I do not think that happened because he became more careful. It happened because we stopped treating a gap in understanding as a personality flaw, and went back to the ideas underneath the topic until they held.
There is one piece of timing worth knowing. Gaps like his do not stay the same size. An idea left unsettled in Form 2 does not sit quietly and wait; it becomes the assumed foundation of the next thing, and the next. By Form 5 the same gap is buried under two years of material built on top of it. It is entirely fixable at that point. It is simply a much larger job than it was.
You can read more about how the mathematics programme works.
One question to ask your child this week
Pick a question they got wrong in a recent test, and ask them to talk you through it — not to correct it, just to say what they were thinking at the time.
If they can do it now, at the kitchen table with no clock running, then the problem was never that they didn’t know it. That is a far more hopeful place to start than it sounds.