I once taught a Form 2 boy who was, in lessons, easy to teach.
I would explain something and he would follow it. I would set a question and he would do it. His small test marks were respectable.
Then his first final exam came back at just over 50 out of 100.
Based on what I saw every week I had expected around 80. A thirty-mark gap is not explained by having a bad morning.
After the exam we sat down with the paper. I did not ask him why he had failed to do it. That question has no answer a thirteen-year-old can give. I went through it question by question and asked the simplest thing I could.
「呢條你會點樣做啊？」
He did it. Right in front of me, with no clock running, and correctly. Then the next one.
I looked at him. He was braced. Shoulders drawn in, eyes not quite meeting mine. He had assumed that what came next was being told off.
I told him what I actually wanted was to find out what he didn't understand, not what he'd done badly. That I was trying to understand him, not blame him.
He didn't say anything for a while. Then his shoulders came down, and he smiled.
After that we got through the paper properly.
Four terms, two ways to split them
One of the questions he got wrong was on factorisation.
In Form 2 factorisation there are questions with four terms. You can split them two and two, take the common factor out of each pair, then factorise again. Or you can take three of them together, recognise that they form a perfect square, and deal with the remaining term after that.
Only one of them will actually finish the factorisation. The question does not tell you which.
I asked him: 「兩個一組、兩個一組，你做唔做到？」
He could do the first step. He got the common factor out of each pair, and then he stopped. The first step had looked right, which is exactly what makes the wrong route so easy to take.
「咁如果三個一組呢，你會留意到啲咩？」
He was quiet for a long time. Then something seemed to occur to him.
He could factorise perfectly well. He had simply done so many two-and-two questions that the other way did not readily occur to him. In an exam, nobody is going to drop a hint.
That is the difference between a small test and a final exam. A small test is like being told in advance that today you only need the screwdriver. A final exam is the whole toolbox tipped out on the table, and you choose.
DSE, IB or IGCSE, the logic is the same. A method learned by rote performs beautifully when somebody points to which one to use. But without having really joined it all up, a student who meets a complicated question under exam pressure simply comes apart.
I should admit this fooled me for years. A student who follows along well in a lesson feels like a student who understands. It shows attention, cooperation, a decent memory. But it does not necessarily mean he has really grasped it, and plenty of teachers, me included, have mistaken the one for the other. Which is why a good teacher has to know how to ask the right questions. It is the only way to find out what a student is actually struggling with.
"Careless" is a surface symptom, not a real cause
The easiest explanation for a wrong answer is carelessness. Be more careful next time.
But when the same kind of error repeats term after term, "careless" has stopped explaining anything and become a label. Something is causing those errors.
So I did not immediately put him on more practice. We went back to the ways of splitting, and on every question he had to tell me how he intended to group it, and why, before he was allowed to write anything down. Name the split before you write.
It was slow at first. Then it got faster, and better.
A year later his final exam results were in the eighties.
Building the foundation early matters. What is left unsettled in Form 2 does not sit still and wait. It becomes the premise of the next topic, which assumes you already understand it, and then the next. By Form 5 the same gap has two years of material stacked on top of it. It can still be fixed. It is just a much bigger job.
One thing to try this week
Pick a question they got wrong. Don't ask for the answer. Ask why they chose that method.
If the answer is "I don't know, it just looked like that kind of question", that is the problem you need to face.