# Hannah’s Sweets

Seems everyone has something to say about this so I’ll add my thoughts. Quick disclaimer, I haven’t seen the whole paper yet although I don’t think that’ll make any difference to what I’ll write here. I’m also not going to go through a solution here. If your reading my blog, I’m confident you’ve already worked it out.

There was a question on Edexcel’s GCSE maths paper 1 on Thursday which has caused many complaints (19 pages worth of comments with 20 comments per page on Student Room as I write this). It goes like this:

And

(b) Solve n² – n – 90 = 0 to find the value of n.

So, what’s the problem? Well, as far as I can tell, the main problems are:

- It’s difficult,
- It’s in an unusual format (based on previous questions about probability),
- The context.

I honestly can’t say that there’s any significant problem with this question. Calls for a lower grade boundary are optimistic and let’s bear in mind that this is only one question (I’m not actually sure how many marks yet) however, all of the skills required are comfortably within the realms of GCSE maths:

- Conditional probability
- Forming and solving equations
- Algebraic fractions
- Rearranging equations
- Proof
- Solving quadratics (part b)

So, let’s be clear, there’s no reason why the exam board can’t ask this question based on what the syllabus covers. Exam boards are being asked to include more problem solving questions and for me, this falls into this camp.

It is still very difficult though. I have seen numerous comments along the lines of “It’s not that hard, what’s wrong with students?” type claims. That’s harsh and, frankly, it **is** difficult. I’ve taught enough maths students to know that this a question that will challenge all but the most competent. I’ve also seen this being referred to as “a simple probability” question and I can’t agree that conditional probability mixed with algebra counts as simple. As I’ve said above, it’s not an unreasonable question but I won’t accept any claims that this isn’t *that* hard. I am sure that some students will get this question right but they’ll obviously be very much in the minority. Also, for people reading the question on twitter, facebook or on a newspaper website, you should recognise that that is a very different scenario to you being sat in an exam hall taking a test that you’ve been being told for years is one of the most important exams of your life. You’d be under a little more pressure.

In terms of the formatting, I think it is fair to assume that examiners will always be trying to look for new ways to test understanding of the syllabus. There would be complaints if all the questions are predictable and too similar so, given that we don’t want that to happen, you have to expect questions in formats you’re unfamiliar with. In many ways, this is exactly the examiners’ job. So again, here, I don’t think we have too much to complain about. I have seen some comments saying that teacher’s should make sure that students see questions like this so that they aren’t unfamiliar. This is probably true but I certainly can’t invent questions *all* the time and even if I did, I couldn’t guarantee that I’d come up with one like that. As it happens, I do try to invent questions, many other teachers do too and there are a number of creative teachers on twitter sharing ideas as and when they can. Perhaps there’s an argument here for textbooks to be trying to include more questions along these lines. One thing that might have helped would have been to say “Hannah takes two sweets out of the bag. The probability that they are both orange is 1/3”

*Edit: some helpful people on twitter have shown me two similar exam questions from Edexcel’s 2002 and 2004 papers. There are also similar questions in a GCSE textbook. Perhaps it’s not that unfamiliar then. *

This leads us into the context. Now, here I do have a bit of an issue. It’s so transparently fictitious that it’s annoying. No one would buy a bag of sweets which only contains yellow and orange ones. They’re the ones people hate. Joking aside, who is telling us this story? It doesn’t feel like it’s Hannah unless she likes talking about herself in the third person. That means it’s someone else who is giving us this information and they appear to be the smug kind of person who thinks this is an interesting question which they know the answer to. I’m not convinced it is that interesting and the answer isn’t particularly satisfying. Anyway, the context adds nothing to the question other than making it feel a little bit like a question you may have seen before. (As I typed that, I realised that that may be enough of a justification in itself for the context.)

*Edit: after conversations on twitter, the context does allow for the concept of ‘without replacement’ to be involved without using those actual words. This does actually make the question easier. Also, as commented below, the context means part b only has one solution which is a useful skill to check *

A post on the Independent’s website makes this point:

But most importantly, why do examiners think students won’t be able to handle questions unless they’re put into a “real-life” situation?

I kind of agree with this point. One of the beautiful things about maths is that it develops the ability to think abstractly. Of course, maths can also be applied so I do like questions to be in context where appropriate. Having said that, I do detest pseudo-context and would rather leave context out when it really isn’t there. So how might this question look without Hannah and her sweets?

*A set contains n objects where n is a positive integer.*

*6 of these objects have property A and the remainder have property B. *

*In an experiment, one object from the set is to be selected at random with each object having an equal chance of being selected. *

*The experiment is carried out and it is noted that the first object has property A. This object is removed from the set.*

*The experiment is carried out again on the modified set.*

*You are given that P(both object removed in this way have property A) = 1/3*

*Show that n² – n – 90 = 0*

Apologies if that’s bit clumsy but you get the idea. Is that better than Hannah? People would have complained about that too.

So, on balance, do I think this question should have been on a GCSE paper? Yes.

Am I surprised that students are complaining about it? Not really. Are you honestly saying you’ve never complained about something that didn’t go as well as you’d hoped? I know I have.

Great post Dave, incidentally 3 marks for part a and 3 more for part b.

Ok. Thanks.

The thing that surprised me was where this question was in the paper. I have seen “standard” probability tree questions at the very end implying they are the hardest question on the paper yet this was question 19 of 24. Question 22 asked for the value of 2^-3. I do think if this question had been the last on the paper it would have created less hype as pupils would be expecting the end questions to be the hardest. On a side note, last year was Kevin with his pigs, this year Hannah with her sweets, I wonder what it will be next year?

Hi Kerry. You’re probably right about if it was at the end there’d be less fuss.

I think I’d prefer question difficulty to be mixed up a bit more so students don’t “work to the staples” or give up about half way through.

(Kevin, pigs) (Hannah, sweets) (Simon, monkeys) <- my prediction

n = –9

Yes. I accept that the context does matter a little for part b.

I impress on the kids I tutor in school maths that they actually have to briefly explain why 10 and not –9 is the only acceptable answer.

Yes. I expect the 3rd mark is for that point.

Some people on twitter have pointed out that there’s a pretty similar Q from 2002 paper and another not too dissimilar from 2004

i think it’s a great question if for no other reason than it brings the subject of questioning into the national spotlight. I’m sure the examining are secretly delighted.

More so, I think it is indicative of the type of question we want to see more of in the new GCSE. Less rote learning of method and more credit and emphasis put on interpreting and using the syllabus content. At A Level I want more students who have been exposed to this type of question.

I sometimes think it’s not about getting the exact answer. It’s about your though process and attempt at the question. I think that getting 100% should be realistic anyway. Good read.

I hadn’t thought about that point but yes exposure is good.

I’d personally like to see more open ended question but as you say, fewer ‘obvious what to do’ questions is desirable.

Reblogged this on The Echo Chamber.

Hi Dave

As you allude, I think there would be a lot less furore over this if the pseudo-context was dropped from the question.

The virus is spreading to A-level exams – as @srcav pointed out on his blog recently.

The problem is that a lot of students fixate on the – often bizarre – context and this automatically throws up a barrier in terms of a student’s confidence in solving the problem. Sometimes the abstract posing of a problem removes anxiety!

Also alluded to in a previous comment was the position of the question. It is clearly designed for A* students to attempt, so it should have been the last question in the paper.

I know what you mean but I do think the abstract version of this question would create anxiety for many too.

As things stand, yes it should probably have ben later on in the paper but I’d like that to be something that changes with the question difficulty intentionally mixed.

The context seems quite childish to me. Questions about eating sweets are usually associated with the early elementary grades. For that reason, the sudden appearance of a quadratic equation is jarring and absurd. I think that many people are responding to this incongruity.

Hi. Possibly true.

It is hard to find convincing probability scenarios that are within the realm of GCSE maths though.