Education Endowment Foundation:EEF blog: How can we improve children’s problem solving in maths?

EEF blog: How can we improve children’s problem solving in maths?

The EEF’s Maths Specialist Kirstin Mulholland explains how to improve pupils’ problem-solving using metacognition.
Kirstin Mulholland
Kirstin Mulholland
Associate for school engagement and evidence use

The EEF’s Maths Specialist Kirstin Mulholland explains how to improve pupils’ problem-solving using metacognition. 

Blog •4 minutes •

Let’s be honest: we all know that maths is different this year.

Research conducted by the Education Policy Institute for the Department for Education, reported that average learning loss stood at 3.5 months in maths for primary school pupils by Spring 2021. It’s also likely that disadvantaged pupils have been impacted even worse than their classmates.

Some elements of the curriculum are likely to have been more severely affected than others. Perhaps remote teaching contexts have meant that mathematical talk has been limited, or opportunities for meaningful feedback have been truncated? We may find that some children are less independent and resilient as a result, which presents challenges around applying their learning to problem-solving contexts.

In our day-to-day practice, we can consider how best to support children to become more independent and motivated, encouraging them to take greater ownership of their learning in maths.

Recommendation 5 of the EEF’s Improving Mathematics in Key Stages Two and Three’ guidance report suggests that helping pupils to develop metacognitively can be effective: the ability to independently plan, monitor and evaluate their thinking and learning. But what does this look like in the classroom?

Below are three key potential strategies which just might provide a place to start.

1. Modelling metacognition: Think Aloud’

The EEF guidance report suggests that, Initially, teachers may have to model metacognition by describing their own thinking’. This can be achieved using a Think Aloud’ strategy, where teachers narrate their thought processes to provide a model of how an expert’ learner approaches a problem.

Whilst Thinking Aloud’, it can be helpful to ask yourself some key questions as you model your approach to understanding the problem. These can be remembered using the acronym REEL:

R = Read.

What do I know about the problem so far? What information is given to me?

E = Explore.

What is the problem asking? Which information is relevant? How can this help me?

E = Exemplify.

Can I use a visual to represent this or can I restate this in my own words?

L = Link to prior learning.

Can I think of any similar problems I’ve solved before which could help me here?

As teachers, we can also model the metacognitive cycle of plan, monitor and evaluate, to show exactly how we check that our work remains on track, and how to adjust our approach when we experience difficulties. This can help pupils to understand that even expert learners experience difficulties, and that flexibility and resilience are vital for successful learning.

2. The debrief’

The debrief provides an opportunity for pupils to reflect upon and evaluate the effectiveness of their chosen problem-solving strategies. At this time, the teacher uses questioning to draw out and make explicit the various strategies pupils have used to approach the tasks undertaken.

Once we’ve done this, we can then support pupils to reflect on how successful they have been, to consider whether a different approach might have been more effective, and to identify other scenarios in which these approaches could be useful. Key questions include:

- What exactly did you do?
- Why did this help you?
- What was challenging? Why?
- Is there a better way to…?
- What changes would you make? Why?

Questions such as these prompt pupils to unpick and examine their learning strategies. This provides a model for other pupils in the class, developing their understanding of the range of approaches available. Additionally, it also allows us, as teachers, to make those invisible thought processes visible, helping pupils to better-understand them and develop more efficient strategies where needed.

3. Using worked example

Worked examples provide step-by-step demonstrations of how to solve a particular problem. This reduces the cognitive load experienced by pupils so that they can focus on developing deeper conceptual understanding.

For example, pupils could explore the different steps used to understand why particular choices were made, or compare different strategies for solving specific problems to consider efficiency. This develops children’s metacognition through supporting them to understand the learning process, making specific steps and actions explicit. This allows pupils to thoroughly consider and critique approaches to specific problems.

Worked examples can be complete, or can contain deliberate gaps or errors to be addressed. They’re used after the teacher’s initial input for the lesson, and provide clear models which help guide pupils through the problem-solving process by scaffolding practice. Gradually, the scaffold provided by the worked example is removed, preparing pupils to complete problems independently. In this way, worked examples can be seen to provide an intermediary step between the teacher’s focused input and the pupils’ independent practice.

There’s no doubt that many pupils find problem-solving in mathematics challenging. However, by helping them to understand not just how to solve individual problems, but how to learn more effectively in the face of these, we can ultimately make a real difference to children’s independence, motivation and resilience.

If you are interested in learning more about promoting children’s independence and resilience through supporting children to develop metacognition, please do contact her via kirstin.​mulholland@​eefoundation.​org.​uk.