The problem with problem solving

Consensus is clear, but clarity matters. Everyone agrees that problem solving should sit at the heart of maths education. Despite this consensus, teachers still face a familiar issue: what makes a problem a problem in maths?

Strengthening problem solving shouldn’t be seen as a purely academic endeavour - it’s central to improving attainment, narrowing disadvantage gaps, and preparing young people for a world that demands flexible, critical thinkers. This isn’t an optional stretch activity for high attainers. Problem solving is essential to enhance mathematical learning for everyone – mathematicians at every age, and every stage. The challenge, and the opportunity, lies in turning it into something that makes a difference in every classroom.

To make progress, we need a shared map of the meaningful characteristics that give problem solving its value.

Why problem solving matters

Our consultation across the maths education community with teachers, academics, employers and young people highlighted the many ways in which problem solving can support young people. 

Problem solving: 

• improves attainment and deepens conceptual understanding

• boosts confidence and enjoyment

• builds the capacity to apply maths flexibly and critically 

• develops habits of explanation, structure-spotting, and systematic thinking 

• supports essential life skills including financial reasoning, media literacy, and decision-making. 

As the Curriculum and Assessment Review highlighted, pupils currently have “limited opportunity to engage deeply with foundational mathematical concepts” and too little time for the kinds of problems that foster mathematical thinking. At the same time, it’s important to be clear that none of this diminishes the crucial role of fluency, automaticity, and deep understanding of mathematical structures. The success of teaching for mastery has shown what is possible when pupils secure strong number knowledge and grasp the underlying relationships that make maths coherent.  

Our aim is to build on that success - not move away from it - by strengthening the problem solving opportunities that sit alongside conceptual understanding and fluent recall. In other words, we don’t just want pupils to know the maths but also to be able to think with it. But this is not simply a case of adding more problem solving. We need clarity about what constitutes valuable problem solving activities. Without this, teachers are left to interpret it for themselves, and assessment remains narrow. 

This is where previous approaches have struggled: high-level definitions can inspire, but they do not tell a teacher what kind of questions support pupils’ deeper mathematical thinking. To make real progress, we need to describe what valuable problem solving looks like in terms of mathematical questions themselves. 

Building on what works

Teachers are already doing this work, every day. 

When pupils share methods at the board, when a teacher presses for a reason instead of an answer, when classes discuss their approach to a story problem – problem solving is alive and well. But small, deliberate shifts could make a big difference.  

Together, we will explore how we can make problem solving and reasoning more visible, more deliberate, and more equitable across the system. None of this means more content or less coverage. Rather, it means making the thinking visible within the maths we already teach. 

What's next

That’s where Maths Horizons is focusing now: turning shared ambition into practical action.  

Through our collaboration with teachers, curriculum designers, and researchers, we’re building a national map of the kinds of tasks and questions that develop different forms of problem solving, and showing how they can be taught, learned, and assessed. In this way we will identify meaningful characteristics of problems, and how these can be woven through the curriculum to support deep understanding for every learner. Because problem solving isn’t an extra thing to add to the curriculum. It’s the thread that holds maths together.  

By clarifying the different forms problem solving and reasoning can take, we can design tasks, assessments, and professional development that support every learner at all stages to think mathematically. 

Maths Horizons is an independent programme informing the development of maths curriculum and assessment in England.