## What’s going to come up on the exams?

Is not really what this post is about.

If you’d like to teach more than just what’s on a GCSE exam, then when asked “What will a question on this look like on the exam?” answer honestly “I don’t know.”

This post is about that question: “What’s going to come up on the exams?” as posed by pupils.

Not in the sense of ‘what topics,’ but rather ‘what would a question about this look like on the exams?’  This is, for me, often a very difficult question to answer.  I teach *a lot* around the typical exam content.  One straight forward example is function notation: not on the AQA spec, yet I’ve taught it anyway.  Less straight forward would be visual representations for quadratic expressions, which we’re working on now in Y10: rectangles, perfect squares, difference of two squares and completed squares.

I was taught none of this at school, and was forever baffled by why it was called ‘Completing the square.’  Made no sense.  The impetus then for me wanting to show these representations is that when I finally saw them five years ago, they cleared a frustrating haze that had existed for more than a decade prior.

But then you might be asked ‘what would a question about this look like on an exam?’ and that’s an understandable, but also sad and unfortunate question, because we’re not learning this because we fear it might come up on an exam, we’re learning this because it’s an integral part of mathematics.  So the answer to that question is perhaps ‘well it won’t be on the exam,’ which might be met with an exasperated ‘well why are we learning it then!’

Recently though, I realised something, and it’s allowed me to honestly shift my rhetoric for the better.  This new rhetoric might not be entirely satisfactory for the pupils, but it does avoid the opportunity to reject learning about content that doesn’t usually appear on exams.

When I was teaching in a school that went with the Edexcel exam (as most do) I felt I could confidently predict almost every type of question that was going to be on any exam.  They were same questions repeated again and again, it seemed, with only minor variation.  As I now come to look through past papers from the AQA exam board, however, especially in the most recent 3-4 years, I’ve realised that there really could be a question on the content we’re covering, and I honestly don’t know what that question might look like, if it arises!

AQA have been slipping in what I would consider ‘unseen questions,’ questions that are completely unlike anything that’s gone before, and that we could never predict.

I made the decision to teach my Year 9s (now Y10) about the identity symbol, including what an identity is, and when we can use its symbol.  I did it for reasons that had everything to do with learning maths, never expecting to see one on the exam paper (I’d never seen one on the Edexcel papers.)  Yet, in 2014 question 1 on the non-calc paper asked pupils to ‘circle the identity.’  It’s also been used in questions about proof.

I made the point of teaching what perfect squares are… only so that my pupils would know what perfect squares were, and their properties.  Mostly, I did it because if you want to understand how Completing the Square works, you need to understand what a Perfect Square is.  I never expected it to come up on an exam.  Then, in an AQA paper from 2011 I found the question:

“Prove that the sum of two consecutive triangular numbers is always a square number.”

The algebraic version of the proof results in a perfect square.  If you haven’t been taught what a perfect square is, you might get stuck at this point, since you wouldn’t recognise that trinomial expression as a square number.  You *might* yet get lucky, factorise it and figure it out… but you’re less likely to do so.

So, it turns out, increasingly things I am teaching only because I think they’re worth knowing are in fact making their way into the AQA exam papers, and doing so in ways I can’t predict.

As a result, when asked ‘What would a question about this look like on the exam?’ – if it *is* a fairly standard question type, then I explain what I know from experience.  If it’s something that I’ve never seen on the exam then rather than saying:

“It probably won’t be on the exam…”

I say, honestly:

“I don’t know.”

If asked whether it’s likely to be on the exam, I answer:

“I don’t know.”

If asked whether it’s been in past exam papers I might answer:

“I’ve never seen a question on it yet, but it could certainly still come up in a new form we haven’t seen before.”

“Yes, but I can’t predict what the question would look like.”

Really, that’s exactly how exams should be.  It’s almost liberating to feel that, to some extent, this is the case – you can’t drill for what you can’t predict.

Most importantly, it means we can get on with the job of learning mathematics without worrying quite so much about whether or not what we are learning will appear on the exam.

If you’d like to teach more than just what’s on a GCSE exam, then when asked “What will a question on this look like on the exam?” answer honestly “I don’t know.”