“What Would a Mathematician Do?” — Developing Problem-Solving Behaviours
Part 1 of 2
After a fascinating lesson with a Year 6 class, I had planned to write a blog about the problem I presented to them and their response to it… and then, just a few hours later, the headlines for the new national curriculum were released.
I saw a post on LinkedIn from Helen Drury celebrating that there will be a greater focus on problem-solving in KS1–3 within the English National Curriculum reform and I immediately smiled, reflecting on that very classroom experience just hours previously.
What Would a Mathematician Do?
I’d been invited into an “outstanding” four-form entry primary school in Dubai to collaborate with teachers: planning a lesson, delivering it and reflecting on how it went. The Year 6 team had just completed a unit on arithmetic with fractions and wanted to challenge pupils with problems that would encourage them to think like mathematicians.
The teachers mentioned that most pupils were performing well (around 70% were secure on the content) but that they didn’t always behave like mathematicians. They tended to dive straight into work without pausing to reflect, predict, or plan. As one teacher put it, “They can do the maths… but they don’t always think mathematically and struggle to explain why something happens ”
That became our question for the day: “What would a mathematician do?”
Influences on Problem-Solving
Three sources have heavily influenced my thinking on this topic.
The first is a brilliant podcast — BAGS to Learn by Ben Gordon — where he interviewed Colin Foster. One particular line from that conversation has always stuck with me:
“When the problem-solving element is high, the content level should be low.”
That really resonates. If we want pupils to focus on developing new strategies — adding new tools to their mathematical toolkit — we must avoid cognitive overload. Don’t make them solve complex problems on content they aren’t fully secure with.
The second source is the EEF guidance on Improving Mathematics in Key Stages 2 and 3, which reinforces the importance of explicitly teaching problem-solving strategies — those tools for their toolkit.
And finally, the king of problem-solving himself, George Pólya, who gave us the classic four steps in his book “How to Solve it”:
1. Understand the problem
2. Devise a plan
3. Carry out the plan
4. Check the results
Polya’s steps encourage the behaviours of a mathematician when encountering a problem which are wonderful to explore with pupils (more on this in the next blog)
Framing the Lesson
With these influences in mind, the Year 6 team and I decided to focus on developing the mathematician rather than testing content knowledge. We wanted to give pupils a problem they could all access, one that would push their thinking and introduce them to problem-solving strategies as per the EEF guidance, not their arithmetic.
But before we get into what happened in that lesson, it’s worth pausing to consider what we mean by “behaving like a mathematician.” For me, it’s not about performing algorithms flawlessly. It’s about being curious, reflective, resilient and being willing to make mistakes and learn from them.
That’s exactly what this lesson revealed!
To Be Continued…
As the curriculum evolves to place a greater emphasis on problem-solving, we must remember that developing young mathematicians is about more than knowledge of methods. It’s about nurturing curiosity, persistence, and reflection — the very habits that define mathematical thinking.
In my next blog, I’ll share what happened when that Year 6 class took on the problem-solving challenge and how two pupils, in particular, taught us powerful lessons about what it means to think like a mathematician.