She had always been good at mathematics. Her teacher and her parents were confident she would get a 7 when the real exam came.
It was her final year of the IB Diploma, and she was taking Mathematics: Analysis and Approaches at SL. In the first-term exam her Paper 1 went very well. On Paper 2, in the same exam, she lost over 30 marks.
On Paper 2 alone, she would not have got a 7.
Her school would use the first-term results in setting her predicted grade, which goes on her university applications. When the results came home, her parents were worried. Mathematics had always been her strength. Was there something in the course she hadn't really understood?
A sudden drop: is it the content?
It is a natural thought. AA SL is not a light course, and losing over 30 marks on one paper makes it easy to assume some topics haven't been learned.
But one thing doesn't fit. Same exam, same course, and her Paper 1 went very well.
I asked her:
「你 Paper 1 做得咁好，點解 Paper 2 會失咁多分嘅？」
「因為今次 Paper 2 有好多題要 plot graph，又要 zoom in、zoom out。考試嗰陣緊張，一時之間又搵唔到點樣撳。跟住就越做越亂，仲影響埋其他嘅題目。」
In IB Mathematics AA, Paper 1 allows no calculator. Paper 2 requires a graphic display calculator, the GDC. Her answer pointed to the GDC, not the content.
But why would a student this good at mathematics be defeated by a calculator?
The problem was that she was too good at mathematics.
Many Paper 2 questions are written with the GDC in mind. Done by hand, some take a long time and some can't be done at all.
But she could do a lot of questions by hand, so by hand is how she did them. The more fluent she was by hand, the less she used the GDC, and the less she used it, the less she knew it.
Paper 1 played to her strength. That Paper 2 happened to have a lot of questions where the GDC had to draw a graph, zoom in and out, and adjust parameters, and everything she had never really practised showed at once.
Not all of those 30-odd marks were GDC questions, either. She didn't know the GDC well enough to find the right buttons, she grew tense, and questions she could normally do went wrong too. A big drop in marks does not always mean a big problem.
「咁你考試之前，知唔知自己 plot graph、zoom in、zoom out 嗰啲唔係太熟？」
「其實我平時都有用 GDC plot graph，我以為自己都識，冇諗到臨急臨忙時搵唔到點撳 zoom in、zoom out。」
It is like someone who cooks well buying a multi-function oven and only ever using it to reheat things. On the day guests are coming and a chicken needs roasting, she finds she doesn't know how to set the temperature or which button sets the timer. In the rush, even the dish she is best at gets burnt.
She had assumed she would catch up on the GDC quickly. I told her that using a GDC is a skill in itself, and a skill takes time.
Better to stumble in practice than in the real exam
「咁你覺得會唔會仲有其他 GDC 嘅 function 或者技巧，你可能都未必熟呢？」
「我諗都會有嘅。」
「所以我哋要做多啲唔同嘅練習，如果有乜嘢唔熟我哋都可以及早發現再做好準備。」
After that she worked through many different kinds of questions, and sure enough another one turned up: using the GDC for a definite integral, drawing the graph and then finding the area under the curve. She wasn't fluent with that either.
Without that practice, she would probably have found out in the real exam. That is why regular practice, of many different kinds, matters.
As an IB student, she hadn't done the kind of drilling found in many traditional DSE schools. But practice was never meant to be rote learning. Working through different questions lets the gaps show up early, instead of waiting for an exam to find them.
The big drop was worrying, but fortunately it was found early, while there was still time to fix it. We spent time practising with the GDC after that, and she got her 7 in the final exam.
One thing to try this week
If your child's results have dropped suddenly, don't rush to ask "Is there a topic you haven't revised?"
Ask instead: "Which questions lost you the most marks? Had you practised the method those questions needed?"