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Mathematical Thinking for GCSE

by Julie Jacques (November 2020)

This week saw the first session of the Cambridge Maths Hub work group on Mathematical Thinking for GCSE. Because this is one of the Five Big Ideas in Teaching for Mastery I signed up. The work group is led by the Deputy Lead of the Cambridge Maths Hub. There were only three participants – me, a head of department and someone else who I didn’t get to meet because their microphone and video were not working. It meant I got to spend 90 minutes deeply unpicking maths questions with three other teachers – wow, what an amazing CPD opportunity! Being online makes accessing this workgroup really easy too. If you would like to come and join in the fun, email They have said that they will re-run session one for anyone else who wants to take part.

Two of my colleagues attended this work group four years ago and back then, as a department, we began to deeply unpick problem solving, focusing initially on year 9. My colleagues first presented NRICH’s 5-step progression in reasoning and I remember it taking a lot of thought to see how we could move students from one step to the next. The same occurred in the mathematical thinking workgroup this week! It is not a straightforward thing to understand and, as with everything in teaching, it takes time in lesson design and delivery to improve both our skilled questioning and the students’ reasoning skills.

If you are interested in looking further at what NRICH has to say then the five-step progression and Reasoning: Identifying Opportunities are both worth following up. These articles also give links to tasks which support with the developing of reasoning skills; you might like to try them out with your classes.

In the work group session we tried out a couple of teaching techniques for developing reasoning skills. I really like the idea of ‘hide and reveal’ because it is a visual technique that enables all students to access the mathematical ideas.

‘Questions for calculations’ was a reasoning technique which felt like we were moving further through the NRICH steps of reasoning. I had seen this task before, when my colleagues shared it with our department, but this time instead of just looking at the image and being asked “what questions could you ask?”, we were given the image and calculations and were asked “what could the questions be?” We spent a long time discussing this task. It wasn’t easy working backwards from the calculations to the image!

There is a third reasoning technique called ‘different approaches’, which we didn’t cover, but I’ll leave it here for you to look at.


The three generic structures of reasoning described here are:

  1. Hide and reveal

  2. Different approaches

  3. Questions for calculations

What is the potential use for each of these techniques in the classroom?

As you design lessons, can you include any tasks that support students with the development of their reasoning skills and their mathematical thinking? Could you use it in the hook, starters or the exit ticket?

Do come and join us for future sessions, or sign up to participate next year!




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