Everyone loves an 'impossible maths exam' story

[noblegiraffe]

The latest country to have an exam that has left students in tears is New Zealand. www.theguardian.com/world/2017/nov/22/impossible-new-zealand-maths-exam-even-flummoxes-teachers

Here's one of the questions if anyone fancies a go. I'm pretty sure there must be a more elegant solution than the one I came up with!

Think you're very right Rafa I asked a couple of Oxford science undergraduates last night - they made it very convoluted!

Seeline Imagine you have a compass, and you place its point at G. You draw your arc. You then take your compass away and draw 3 lines from G, to meet the arc.

You now have 3 lines, starting from G. Those 3 lines are GD, GB and GE.

You know they are all the same length (because your arc was the same distance from G all the way along).

Now you draw in your picture of the square, and the kite - and you rub out the GB line.

The distance from GB doesn't immediately look as though it's the same length as GD and GE but it is.

Does that make sense?

My dd drew that as a demonstration - which pushed towards the trig answer. We were really impressed by the equilateral triangle answer.

(And I was impressed by all of it. Dd found me pondering over a drawing and abandoned her Sociology homework to talk me through it. I have MN and noble to thank for a lovely half an hour of mother-daughter bonding. )

My DS apparently did it using the cos rule, sigh...

What? How? Cosine rule on the equilateral triangle??

Certainly hope not! I basically hid my head in my hands and didn't ask. He did get the right answer, and my guess is that whatever he did was probably correct but daft. He has form for that!

I've got post-grad maths. This is a terrible question for an exam.

It's not a difficult problem. It's at the level of a junior UKMT challenge. The problem is that nowadays children are not trained to think. They rather learn by heart formulae to calculate things which is good enough for the accountant-like jobs they will be doing later. Geometry is for true mathematicians. Many great mathematicians started to love maths when they discovered geometry. This story is a great illustration of the fact that our kids are not really learning maths at school. Their mind is rather being shaped to run a system defined by others.

As I said above, I think it is more straightforward than many of the geometry questions DS faced in practice 9-1 GCSE papers last year, because the underpinning knowledge it requires is quite limited and of the same type (angles within a triangle / on a straight line), rather than requiring e.g. circle theorems.

If they ONLY accepted the elegant non-trig solution, then I think it would be trickier, but if they accepted the one basic trigonometry step as part of a successful answer, then i think it's OK as a 'later question' in the papers.

I agree that the junior UKMT challenge papers normally contain something like this, too - so accessible to 'reasonably able within their cohort' young mathematicians.

I'm surprised that apparently in New Zealand they do a paper called geometric reasoning but weren't prepared for that type of question. Geometric reasoning isn't such a big focus of GCSE so I wouldn't be too surprised if English students were flummoxed, especially as the sorts of problems that English students face usually don't require the drawing in of extra lines.