The Solution to Hannah’s Sweets

This isn’t really a blog post, it’s just a random rant. It started as a reply to a Facebook thread, but it got a bit out of hand, so I thought I’d put it here instead. It’s a short response to the current British GCSE maths exam question that has gone viral. Also I accidentally posted my last entry one day early, so this can fill the Saturday void! 🙂

There are n sweets in a bag. Six of the sweets are orange. The rest of the sweets are yellow. Hannah takes a random sweet from the bag. She eats the sweet. Hannah then takes at random another sweet from the bag. She eats the sweet. The probability that Hannah eats two orange sweets is 1/3. Show that n²-n-90=0.

Teenagers in a GCSE maths exam think this problem is unfair. I agree.

To students raised on a maths philosophy that eschews understanding in favour of knowledge and a syllabus that turns all of maths into procedure, this is a bizarre non-sequitur of a question. The sudden appearance of a wild quadratic equation sends them into a panic and they don’t know how to proceed, even if they can do all of the maths involved. This is because they aren’t taught that maths is exploration. They have no confidence to start writing a solution without seeing how it will link to the end. They don’t know how to trek through the forest of maths, except to follow a pre-existing and well-worn path. This is not their fault, nor even the fault of their teachers. It is the abject failure of a pedantic, narrowing curriculum that reduces our pupils to calculators, the result of a dangerous philosophy that treats maths as a mechanical instrument instead of a language of creative and logical thought.

Here’s the other problem. Like almost all maths exam questions, it’s breathtakingly anodyne, offering nothing beyond limp lip-service to the gods of probability and algebra. It serves no purpose except to compound an already entrenched opinion that maths is just irrelevant magic. There is nothing of interest or substance here. Nothing to connect maths meaningfully to a practical reality or suggest to students that it is is important and useful. It asks teenagers to take a pointless scenario and abstract it out of the real world and into the world of maths. The demarcation seems all too clear, obscuring forever the most beautiful and critical truth: the real world is the world of maths!

People think they know the solution to this question about Hannah’s sweets, but they’re wrong. The actual solution is this: re-write the problem, re-write the exam, re-write the entire primary and secondary maths syllabus, and re-write the way we think about maths.

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