I teach a Form 4 girl whose homework is very good. What she hands in is nearly all correct.
Her last final exam came back in the sixties.
She told me she had run out of time. That was true, but it was not the reason.
There had been a harder question in her homework and she had done it well. I asked her how she had worked it out. She said she had followed the worked example. Two or three days later I gave her the same question again. She said she had forgotten how to do it.
Homework gives you all the time you need, and a worked example to check against. An exam gives you neither.
An easy question she thought was a hard one
Later she brought me a question from a quiz that she had not been able to do.
It went like this. You are given the equation of a line, L1, and you are given a point. Find the equation of a second line, L2, which passes through that point and is perpendicular to L1.
I told her this was a very basic question.
She stopped short. It had not occurred to her that this was elementary, and she had not known it.
I should admit I found it strange too. A student who can handle the centroid and circumcentre of a triangle, stuck on this? When a student can do the difficult questions, a teacher naturally assumes she has got the topic.
So I did not show her how to do it. I asked her, one step at a time.
「要計一條直線嘅 equation，你需要咩資料呢？」
「要知其中一點嘅 coordinates 同 slope。」
「係。有時題目冇直接話你知 slope，都可以用其他方法計出嚟。咁呢條題目有咩資料幫到你？」
「已知其中一點。」
「咁 L2 同 L1 嘅關係呢？」
「啊，係喎。」
She laughed, a little embarrassed, and then asked herself: why couldn't I see that before?
More hard questions will not make the easy ones easy
Plenty of parents tell me they want their child doing harder questions. I understand the thinking. If she can manage the difficult ones, the simple ones will look after themselves.
It works the other way round.
In homework, a worked example is the finished picture on the lid of a jigsaw box. Copy it and the puzzle goes together quickly. In an exam there is no lid, only the pieces. A student who knows every piece can still build the picture. A student who has only ever looked at the lid is holding nothing.
She could do those complicated questions because she had seen how that kind of question was done. She could not do this one because nobody had done it in front of her.
Producing an answer by following an example, and working one out yourself, are two different things.
I did not tell her to stop doing hard questions. I changed the order. She now works through basic questions alongside them, until she can see what a question is asking without stopping to think, and only then goes back up.
Learn the pieces before you build the picture.
One thing to try this week
Next time they do their homework, notice whether they keep turning back to the worked example. Don't stop them. Just count how often.
The more often they turn back, the less settled that topic is.