I feel as though every time I have a conversation about maths with a teacher or school leader, problem-solving is identified as something we want to work on.
Pupils find it difficult. They don’t know where to start. They can’t apply learned strategies to a new context and can often resort to guesswork when their way ahead seems unclear. Sometimes, they even just freeze, like rabbits in the headlights, unable to take a step or move their learning forward without significant support from a peer or adult.
To make matters worse, there appears to be some evidence that this issue may be more pressing now than ever before. Partial school closures, and the need for remote learning due to the Covid pandemic, may have resulted in fewer opportunities for pupils to engage in mathematical talk, metacognitive activities, or to receive formative feedback. Consequently, many teachers seem to be finding that children may be less independent, and are experiencing even greater challenges in applying their learning to problem-solving contexts.
Early research commissioned by the EEF indicated that mathematics learning was disproportionately affected by the impact of the pandemic – with a negative impact of –3months. Not only that, the impact appears to be more marked for pupils from disadvantaged backgrounds. More recently, some positive evidence, has shown that Year 1 children were only 1 month behind expectations in mathematics.
Is the problem specific to problem solving?
Part of the issue could well lie in the very nature of problem-solving. For example, ‘What Works Clearinghouse’ defines problem-solving as ‘the movement from a given state to a goal state with no obvious way or method for getting from one to the other’ (IES, 2018, p. 7).
I think this is useful because it emphasises the potential unpredictability of problem-solving. And because problems have no set routine or fixed and known procedure which can be used to solve them, this makes our job as teachers inherently difficult.
If problems have no fixed routine or problem-solving strategy and can consist of a potentially limitless combination of smaller steps, drawn from across multiple mathematical concepts, how can we possibly teach children how to solve them?
Recommendation 3 of the EEF ‘Improving Mathematics and Key Stages 2 and 3’ guidance report suggests some key actions that can help pupils to improve their skills in problem-solving. We need to:
- teach pupils to use and compare different approaches to problem-solving;
- show them how to interrogate and use their existing knowledge to solve problems;
- use worked examples to enable them to analyse the use of different strategies;
- encourage pupils to monitor, reflect on, and communicate their problem solving.
To me, this means that we need to spend more time talking about what we are doing and why.
For instance, rather than spending an hour’s lesson in completing a sequence of multiple different problems, with pupils working independently to correctly (or incorrectly) work through a series of tasks, we need to look at fewer problems, but in significantly greater detail. This would allow us to invest time in really drilling down into which strategies pupils use to solve specific elements of problems, and why, comparing these and reflecting upon which approaches are most effective.
By talking more – and perhaps ‘doing’ less – we can provide the kinds of models that pupils need to think about the rationale behind some of the choices that they make. They can see how other learners approach problems, learn to critique them, and also gain insider knowledge into a broad range of ways in which peers, and adults, think about problems.
Working in this way could enable pupils to really move beyond learning how to solve a single, unique problem, and towards a more comprehensive – and ultimately useful – understanding of how problem-solving works, so that they can learn how to learn and to best utilise strategies for problem-solving. We can also begin to make those invisible processes of thinking and learning visible, demystifying these so that pupils can see first-hand what successful problem-solving looks like.
School teachers and leaders are agreed that we want to work on problem solving, so let’s concentrate on the ‘what’ and the ‘why’.
Guidance Reports
Improving Mathematics in the Early Years and Key Stage 1
Guidance Reports