Why `Hannah's sweets' question left a sour taste

12th June 2015 at 01:00
Row is a result of teaching to the test, academics assert

It was the GCSE maths question that sparked an internet storm, driving perplexed teenagers to express outrage on social media about a task they judged to be "the hardest thing ever to hit the human race".

But expert mathematicians have told TES that the now infamous "Hannah's sweets" question reveals more about shortcomings in the way the subject is taught than it does about how exams are set. They have suggested that maths teachers rethink their approach in the light of last week's controversy.

The Edexcel question that prompted students' ire asked them to prove an algebraic equation on the probability of Hannah picking two orange sweets from a bag.

"The question isn't actually that difficult if you know what you're doing," said Sue Pope, academic division lead for Stem (science, technology, engineering and maths) education at Manchester Metropolitan University. "The surprise, and what makes it look difficult, is that it links a quadratic equation with probability.

"The most important thing is to teach so that children really understand and see how things are connected, so that when they see things like this they say, `That's not a problem.' That's not being done very much at the moment, I'm afraid. Most textbooks teach one skill, then another, and it's rare that things are joined up."

Dr Pope, also chair of the Association of Teachers of Mathematics' general council, said that maths teachers should be given extra training to help them teach in a "connective" way. This would be even more important when the new, tougher, GCSEs were rolled out from September, she added.

Helen Drury, director of the maths teaching programme Mathematics Mastery, takes a similar view. "Because maths is such a high-stakes subject, teachers are under enormous pressure to teach to the test," she said.

"For a long period of time it has been rare that [exam] questions have required that kind of connective thinking.

"Teachers have been teaching in silos and focusing on rote-learning specific methods because they feel that's the best way to prepare students for success in the exam.

"A transition to less predictable questions will be painful and will come as a shock, but in the medium to long term will liberate teachers to teach students to think logically and focus on problem-solving."

Probable cause

Pupils took to Twitter to complain about the question. "Hannah eats some sweets. Calculate the circumference of Jupiter using your tracing paper and a rusty spoon," one said. Another tweeted: "The probability of me getting a good grade in this exam is 11,000. How many sweets does this mean I have?"

Rod Bristow, president of Pearson UK, which owns Edexcel, defends the question in an online article for TES today (find it at news.tes.co.uk).

"Don't get me wrong," he writes. "I have a lot of sympathy with students for whom the burden of exams has become excessive, and it's a burden whose weight needs debating."

The question is "aimed at students aspiring to an AA* grade" he explains, and tests "not just arithmetic computation but mathematical literacy".

"In any exam worth its salt, some questions will be more challenging than others," Mr Bristow adds. "Papers are set at the appropriate level to test the full range of students' abilities. In the event that any one paper turns out to be more or less challenging than usual, our marking and grading process ensures that students are awarded the grades they deserve."

Mary Bousted, general secretary of the ATL teaching union, said the controversy was a symptom of "a strange transition period [before GCSE reforms] where no one knows what the right level is".

"It's not good enough to have a question that pupils just don't attempt. You need to give students a fighting chance," Dr Bousted said, adding that she was pleased that social media had given pupils a "greater voice".

Food for thought

The question

There are n sweets in a bag: 6 are orange, the rest are yellow. Hannah takes at random a 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 13. Show that n - n - 90 = 0

The answer

When Hannah takes the first sweet, there is a 6n chance that it will be orange. When she takes the second, there is a 5(n - 1) chance that it will be orange. To work out the probability of getting two orange sweets, multiply the first probability by the second one:

6n x 5(n - 1)

We know that the probability of getting two orange sweets is 13.

So 6n x 5(n - 1) = 13

The next stage involves rearranging the equation.

(6x5)n(n - 1) = 30(n - n) = 13

Or 90(n - n) = 1

So n - n = 90

And n - n - 90 = 0

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