Ambition and achievement for all

Problem solving is fundamental to thinking mathematically and making sense of mathematics. It equips us to use mathematics in employment and everyday life. Therefore, everyone should have the opportunity to engage in problem solving.

But problem-solving experience alone is not enough. To benefit from the value problem solving offers, all pupils need to experience genuine success.

What, then, does it mean to say that everyone can achieve? And how should we respond to evidence that some children may have cognitive capacities that may give them a head start.

Variability in cognitive capacities

There is now a substantial body of evidence showing that children’s cognitive capacities are associated with learning and academic outcomes, particularly in maths. These include a range of cognitive processes such as executive function, metacognition, and verbal and spatial skills.

Working memory provides a useful example. There is now considerable attention paid by schools, teachers and the wider education sector to its role in learning, particularly the finding that we have a limited capacity to hold and process information. This has important implications for how tasks and activities are designed.

One of the most striking, yet less widely discussed, findings from this research is the extent of variability across children. While working memory capacity increases with age, the variability within a year group can be far greater than the change from year to year. For example, a typical group of 7-year-old children might include some children whose working memory capacity is below that of an average 4-year-old and others whose working memory capacity exceeds that of an average 11-year-old.

We do a disservice to children by ignoring this variability. Yet there is sometimes a reluctance to consider how it shapes achievement, perhaps driven by a well-placed desire to avoid two problematic misinterpretations.

Misinterpretation 1: Children’s cognitive capacities are fixed 

The false belief that children’s cognitive capacities are fixed can result in lowered expectations. In reality, these skills develop over time, and at different rates. For example, just because a child has lower than average working memory capacity at one point in time doesn’t mean that this will always be the case. Even at the same point in time, working memory capacity can vary depending on context and content, leading to patterns of relative strength and difficulty.

Misinterpretation 2: Cognitive capacities are determined by background

The false belief that some children may be better equipped to learn based on other characteristics or backgrounds can result in inappropriate assumptions being made and a lack of opportunities provided. When we look at outcomes for large numbers of children we do find evidence of attainment gaps, linked to social disadvantage, demographics or geography. But the factors that contribute to this are many and varied and this type of evidence tells us nothing about the potential of any individual.

Even if we reject these two misinterpretations, the reality remains that children differ in their cognitive capacities. Given this, what does it mean for everyone to achieve?

Ambition for all

Ambition doesn’t need to look the same for everyone for it to be equally meaningful and beneficial. The value of mathematical problem solving – for children’s experiences, attainment and future opportunities – is well established. So all children should have access to genuine problem solving.

This means resisting the tendency to reserve such opportunities for a select group. Too often, problem solving has been treated as a stretch activity only for high prior attainers, those perceived to have strong mathematical foundations and, likely, strong cognitive capacities. These assumptions limit both access and expectation.

Instead, we must ensure that all children can engage with problem solving in ways that preserve its essential value. Tasks should not be simplified to the point where that value is lost. Success should not come from trivialisation, but from grappling with meaningful problems where the challenge is real and attainable.

Achieving this requires a clear understanding of the different forms of value that problem solving offers, and how tasks can be adapted without diluting that value. In doing so, we can maintain opportunities to develop strategies, practise skills, deepen understanding, and experience success, while widening accessibility and sustaining high expectations for all.