Hannah’s Sweets – a great time to be a maths teacher!

Lots of ink has been spilled about this question elsewhere.  I just want to respond to a couple of things that I have seen written, either on tweets or on blogs.

“A question shouldn’t have material from different areas of maths.”  I think this is absolutely wrong.  The idea of ‘using and applying mathematics’ was that you can, um, apply the mathematics you know.  There is no requirement that it must all come from one topic area. 

I think one of the big problems with modular mathematics specifications was the expectation that only the content of that module would be tested.  This meant that questions that involved ideas from two particular parts of the syllabus just couldn’t be set. 

“Kids haven’t been taught to use algebra with probabilities.”  I would think it reasonable for pupils to see unfamiliar contexts on an exam paper, given how many different contexts there could possibly be.  Let’s take a fairly typical sort of exam-style question:

Neo’s doctor tells him to take a blue pill every 10 hours and a red pill every 12 hours.   He takes the first red pill and the first blue pill at the same time.  After how many hours will he next take both at the same time?

The underlying mathematics here is LCM.  Do questions of this type say “use the lowest common multiple to work out …”?  No.  Is it an unfair question if pupils haven’t covered questions about pills?  What if Neo is waiting for Trinity next to the bus stop and notes that buses leave to go on route A every 10 minutes and route B every 12 minutes (always dead on time)?  He sees buses A and B leave at the same time.  How many minutes will he have to wait until he again sees buses A and B depart together?.  Is that unfair if pupils have covered questions about buses? 

“Grade boundaries should be adjusted downwards.”  Gosh – this one has cropped up a lot.  I assume that people saying this don’t realise that grade boundaries do change anyway.  Every time.  Here, from the Edexcel website, are the boundaries for linear maths from the last two exam sittings.  The grade boundaries are different.  (This raises a host of other issues and questions, but those are not relevant here).

“The question involved some irrelevant information.”  Again – it is perfectly reasonable to have to scythe through irrelevant stuff when solving problems. 

“The context for the question was rubbish.”  Well – yes it was, but it’s quite hard to create exam questions that build up to a genuine and sensible context in the space of a couple of marks.  The context of this question is no worse than those about people taking pills or waiting for buses.  I think you could attack almost any exam question on these grounds.

So why did this question make so many people so cross?

I think the big thing is that people who have learned their maths solely by being shown identikit questions will have found this difficult. 

There were several memes that cropped up after that paper.  One was a very positive response to the stem and leaf diagram question.  Why was that?  Because it was an easy question about an easy topic and was very similar to questions that have appeared in previous years. 

Revision nowadays seems to focus very largely on past papers, to a much greater degree than it used to.  (I wonder whether that is because everything is now so readily available on the internet.)  I helped out with some AS-level Psychology revision a few weeks ago.  I know no Psychology, so my role was to read out the question and then, later, to read out the markscheme.  After three or four papers I was familiar with the main texts and ideas and felt that _I_ could mount a reasonable answer to some of the questions.  If pupils get used to seeing very similar questions in past papers, then when an unusual one crops up perhaps it is not surprising they feel it is unfair. 

The most recent Edexcel probability-with-quadratics question I could find was from June 2004, so perhaps those pupils didn’t go back that far in their past paper practice?

Here is that question (and it happens to be question 19, the same as Hannah's):

This question is arguably harder than the Hannah question, and I was surprised to see it was worth 13 marks!  Was it a good job that twitter didn't exist when this question was published?  Perhaps. 

(Steve Wren (@Yorkshire_Steve) pointed out that the modal score for part c of this question was zero, so candidates certainly found it difficult!)

Finally, why is it a “great time to be a maths teacher”?  It has been lovely to see how many people have been interested in how to answer the question, and wanting to talk about maths.  But most of all, it has prompted a debate about the nature of maths and how it should be taught, and that has been potentially rather valuable.