“Often with a psychological brutality that nothing can attenuate, the school institution lays down its final judgements and its verdicts, from which there is no appeal, ranking all students in a unique hierarchy of all forms of excellence, nowadays dominated by a single discipline, maths.”

Pierre Bourdieu was not, as you might guess from this quote, a fan of ability grouping. But the practice of setting students by attainment is currently commonplace in maths classrooms in England, both primary and secondary.

One of the catalysts for this was a 1997 government White Paper that encouraged “setting pupils according to ability” as a way of “modernising the comprehensive principle”; this followed a Department for Education report in 1993 that also encouraged schools to increase standards by setting pupils by attainment. But the preference for setting has been reinforced since then countless times. For example, there were even reports that setting would be suggested as a compulsory measure for an Ofsted outstanding rating in the 2015 Conservative manifesto, although this never came to pass.

Setting by ability is most commonly reported in maths. In 2009, a survey of about 800 randomly selected primary, junior and infant schools in England and Wales found grouping by ability within maths classes to be taking place in approximately 56 per cent of Reception classes, rising to 72 per cent by Year 2. By Year 6, setting across the age range was much more common and only about 4 per cent of pupils were taught in mixed-ability groups (Hallam et al, 2009). Other research suggests that the prevalence is even higher at secondary and much more so in maths than in other subjects.

In the course of my job, I meet hundreds of maths teachers. Almost all of them use setting as standard practice in their schools (both primary and secondary). We are not alone internationally, either: the Organisation for Economic Co-operation and Development (OECD) last year reported that, at age 15, “ability grouping is relatively widespread across OECD countries, with more than 70 per cent of students…grouped by ability for maths classes”.

Benefits hard to find

So why is it so difficult to find research to support this? More importantly, what does the research that does exist actually say? I recently reviewed the effects of setting in maths and found - to my surprise - that the evidence from meta-analysis, Programme for International Student Assessment and decades of research just don’t support setting in maths, or indeed any other subject.

Francis et al (2015) found that “research has consistently failed to find significant benefits of ‘ability’ grouping and indeed has identified disadvantages for some (low-attaining) pupil groups. However, this research evidence has apparently failed to impact on practice in England.”

At best, the evidence is described as “unclear” (OECD, 2016) on effectiveness in student outcomes, while several other important - and negative - effects of setting showed clearly in the literature. Setting in maths “seems to reinforce socioeconomic inequalities” (OECD, 2016) and perpetuates a view that mathematical ability is measurable, stable and deterministic - a view “so dominant that it is often taken for granted as obviously true” (Boylan and Povey, 2003). Both of these ideas warrant further attention.

Firstly, the strength of current maths-setting practices on inequality is not fully known, but the OECD suggests that the relationship is significant - and that, in part due to this, “maths education often reinforces, rather than moderates, inequalities in education”.

Becky Francis, director of the UCL Institute of Education, who is currently undertaking a study of mixed-attainment versus attainment-grouping classrooms, suggests that we need to have a harder think about the purposes of grouping pupils and the potential effects. “The underpinning assumptions of setting are that there are natural and inevitable differences between students, which maps on to ideas of social class, ideas of entitlement, tradition and distinction,” she says. In other words, all the elements of education that are likely to preserve inequality.

Secondly, how often have we described a pupil - an actual person - as “bottom set” or “low ability”, and what effects might that have on their self-perception and our expectations as teachers? Boaler, Wiliam and Brown (2000) describe how students in all sets for maths report feeling demotivated and disaffected because setting places both expectations and limits upon them.

Fostering a negative self-image

As maths is the subject that a student is most likely to be set in, maths pupils are most likely to suffer from the negative effects mentioned above. Nardi and Steward (2001) found that “Most students expressed a view of mathematics as a difficult, elitist subject that exposes the weaknesses of the intelligence of any individual who engages with it (therefore puts confidence in their intellectual capacity at risk). In our data the students’ self-images of mathematical ability are overwhelmingly negative and likely to deteriorate further in a highly stratified environment of setting and testing (which also isolates the more able and accentuates a stereotypical image of mathematical ability as unusual and threatening). The lower their mathematical confidence is, the less willing the students seem to be to engage with maths as a hierarchical game.”

So maths leads in primary schools and maths teachers in secondary schools face some difficult questions: why do you set? Have you really stopped to consider why we might feel so strongly about setting in maths compared with, say, art, which is almost never set? What effect does setting have - what are the benefits and downsides? Which research are you using to back up what you do?

The answers to these questions should determine whether or not you set in maths; it should not be determined by whim, habit nor gut feeling.

For more information on grouping in maths, see the UCL Institute of Education study Best practice in grouping students and visit mixedattainmentmaths.com

Lucy Rycroft-Smith works in research and communications at Cambridge Mathematics and is a former maths teacher