*The limits of my language mean the limits of my world.*

*Ludwig Wittgenstein*

As we progress towards the first GCSE sitting of the new specification in Mathematics, it has become clear to me that as Mathematics teachers we now face two challenges:

- Ensuring students are confident with as many of the 250+ concepts as possible.
- Ensuring that they can interpret questions properly to choose the correct methods to answer the questions in the paper.

The latter is incredibly important now. It has struck me in recent months that in many of the questions, the Maths required is not that hard, particularly in the case of the ‘common’ Foundation and Higher tier questions. No, it’s knowing exactly where to start in tackling a question that’s the greater challenge.

With this in mind, on Friday as a department we looked at supporting students in developing close reading strategies to understand how to tackle a problem. We chose a 5 mark ‘classic’ functional problem, shown below.

We then followed these steps:

- The teacher reading the question aloud, fully.
- The teacher instructing the students to highlight any key words, statements and values as they read the question aloud.
- The ‘students’ (i.e. the rest of the department) then annotating the question with any things that they think they needed to do to tackle the problem – but not answering it.
- The teacher then leading the class through reading the question again, but highlighting key words, adding further annotations to the question text, diagram, etc, and establishing all the decisions that need to take place to successfully answer the question,
*but still not answering it.* - The ‘students’ then working out a solution to the question, taking into account all the required decisions in order to tackle the problem.
- As a group, going through the solution, linking the solution steps to the decision made.
- We then switched back into ‘teacher’ mode as a group, to see if there was anything we’d missed.

How many decisions do you think were made in tackling that problem? 5? 8? 10? I reckon it was more like 15-20 decisions, depending on a student’s fluency in timetables, estimation, use of formulae, choosing trapezia or rectangles and triangles in order to break down the floor area.

Here’s my annotations – it’s not a complete set, but you get the idea:

My (amazing) AHoD, Mohammed Usman, made some great points. Don’t assume that what is obvious to you is obvious to the student – do they know if the fact that it’s a conservatory is important or not? Are they estimating to see if their answer is sensible? Do they recognise that if 4.5 packs are needed, that they need to buy 5 packs? Jenny Thompson rightly asked if you’d expect students to calculate the percentage discount on the pack price first, or as a discount on the whole cost – if the former, does that make the calculation more difficult? If the latter, will students forget to apply the discount, and make an incorrect judgement?

Carolyn Bate and I had a discussion about the final part of the question. Carolyn gets students to write a full summative sentence at the end of the method; I said that a simple ‘yes’ or ‘no’ would suffice with a clear method, but then could see Carolyn’s point given that students are being asked to give judgements based on assumptions in the new specification, and need practice in this regard. I also made clear that ultimately area is the multiplication of two dimensions – which the m^{2} in the question should trigger. All too often as an examiner I’ve seen students confuse the concepts of area and perimeter, and using the ‘m^{2}‘ trigger should address that.

**Conclusion**

Some would say that students therefore need to improve their mathematical literacy, but I think it’s more important than that. I think we as teachers need to ensure we are clear on the number of decisions made in what might be a very simple question, and make sure we’re giving students the tools in order to make those them successfully – hence why as a department we’re placing real emphasis on close reading as part of our support for Y11 over the next few months, alongside our day-to-day teaching.

I’d like to thank Emma Steele and Carolyn Bate for leading the session, Head of School Jenny Thompson for bringing her English expertise and the rest of the Dixons Trinity Academy Maths Department for a) being brilliant as always and b) making the session really productive.