KS1 and KS2 Maths – ability grouping

The best way to deal with the wide range of maths ability in your class is rarely to place children in groups of high, middle and low attainers, says Mike Askew. A more subtle approach is required...

When running professional development sessions I’m often asked, “Do you believe in ability grouping for mathematics?” The sentiment doesn’t surprise me, but couching it in terms of ‘belief’ does. Saying one believes (or not) in ability grouping leaves the door open for a response of, ‘Well, I believe otherwise,’ and neither the answer nor the response does much to change practices.

However, I do know there is sufficient evidence clearly demonstrating the benefits and drawbacks of different types of grouping to show that grouping practices should not be left to beliefs.

Between class grouping

Some primary schools choose to organise children into ‘sets’ for mathematics teaching, often organised around three levels of mathematical attainment. You can see the logic to this. The National Numeracy Strategy advocated dividing classes into three or four attainment groups; so if a school is large enough, why not put together all the high attainers, all the middle attainers and all the low attainers?

Well, the research evidence is clear: setting pupils does not lead to higher attainment for all. At best, the children who gain from such an arrangement are the higher attainers, but even then the gains for that group are not that impressive. And study after study has shown the gap between higher and lower attaining groups gets wider when children are put into sets (and there are detrimental effects on the attitudes of lower attaining children).

One study, for example, tracked 1,000 KS2 pupils who were taught using the same teaching materials. In test results, the pupils in mixed ability classes significantly outperformed those taught in sets. Another study of 12 primary schools found the KS2 results of pupils grouped by ability were rarely higher than the average for the local authority, or England overall.

Within-class groupings

If children are in heterogeneous classrooms, then what is the best way of grouping them to deal with the diversity of mathematical attainment? In contrast to research into between-class grouping, the research into within-class grouping is more positive: it can raise attainment.

But the picture of what makes for effective withinclass grouping is complex. There is no one-size-fits-all model of grouping and it is certainly not as simple as organising children into high, medium or low attainment groups. Research findings indicate the importance of grouping students in particular ways for particular purposes; the type of grouping depends on the type of learning outcomes being worked on and the learning tasks set. For mathematics, it is helpful to think about groupings for fluency, problem solving and reasoning.

Fluency groups

When it comes to practice and consolidation activities, the research shows that pupils are generally best off working individually. This makes sense – learners are going to be diverse in what they are fluent in, practice activities need to be individually tailored, and time on task is more focused when children practise individually. But, as I noted in a previous article, (Teach Primary 6.3 - tinyurl.com/tpfluency) the important thing here is that children are actually practising – consolidating what they are reasonably fluent in – rather than learning new material. Perhaps such tasks can be set as homework, since practice should not require a teacher to hand.

Problem solving groups

If we accept that problem solving can be a powerful way of engaging with new mathematical ideas (as opposed to applying mathematics previously learnt in a decontextualized fashion) then research shows paired work as the best grouping for developing understanding.

The findings here rest on extending the idea of ‘cognitive conflict’ into ‘socio-cognitive conflict’. Piaget introduced the idea of cognitive conflict: that learning comes about through an individual becoming aware of a contradiction in their understanding. (For example, the conflict between water poured from a wide container into a thin one looking as though it has increased in volume, but logic telling you that the amount cannot really have changed.)

Researchers now have shown that such conflict need not only be an individual act of cognition, but can be provoked by pairs bringing different perspectives to a problem. Differences in perspectives come to be resolved by the development of a joint perspective that is more complex than either child originally thought.

It seems common sense to assume that mixed attainment pairs working together may lead to the lower attaining partner advancing towards the level of the higher attaining partner, but this partner not gaining as much from the experience. Research does show, however, that even when pairs have differing levels of attainment, the more advanced child can progress as much as his or her less advanced peer – the old saw of ‘two heads being better than one’ appears to hold true.

A key issue in effective pair work is the power dynamic between the children. If one child is dominant and the other acquiescent, then working through to a shared perspective is unlikely to come about. Paired work only works well when the partners trust each other and can work well together. In fact, trust and cooperation seem to be more important considerations when selecting pairs to work together than factors such as matching attainment levels, or friendships.

Reasoning groups

Larger groups appear to be best suited to the development of reasoning and, when everyone in the class has been working on similar versions of a task, whole class dialogue can provide a suitable arena for practising this skill – even with a wide range of attainment in the participants. Just as pairs working on a problem can reach a level of understanding higher than either could attain on their own, so a larger group (including the whole class) can reach a higher level of reasoning and understanding.

One of the reasons why this is so comes from studies revealing that the person who is likely to learn most from group work is the participant asking the most questions; with the person answering the most questions making the next highest learning gains. When children present their work in a whole class setting, they can set up a dialogue that provokes questions about their solutions. These questions can then be answered both by the presenters and other children in the group.

Collectively, the class establishes a more sophisticated level of reasoning, and in the process, individual understanding improves.

Thus the plenary becomes important and, in order to provoke dialogue, needs to be more than a show and tell.

Ideas need to bounce off each other for the mathematics to emerge, which means children carefully listening to, building on – or arguing against – each other’s explanations.

A shift in perspective

Putting this into practice requires a shift in how we think about and plan for classes. One way of thinking about a class is as a collection of 30 individuals, each of whom has a specific level of mathematical understanding that has to be catered for. As I’ve noted above, this way of viewing the class probably does need to be adopted when planning activities to develop fluency.

An alternative view of a class is as a collective: the class as a whole has ‘understanding’ and ‘needs’. From this perspective, tasks for pairs or groups to work on need to be carefully chosen so they are beyond the grasp of any individual member of the pair or group. If pair or group tasks are chosen on the basis of being appropriate for the level of individual attainment, they may not be sufficiently challenging to provoke socio-cognitive conflict and the consequent deep learning. Tasks need to be chosen so that the resources required to solve them – knowledge, skills, problemsolving strategies and so forth – are not within the grasp of any single individual and accomplishing the task requires input from others.

At the same time, tasks need to be chosen so that everyone in the group can become engaged. I find the idea from NRich (nrich.org) of ‘low threshold, high ceiling’ tasks particularly helpful here – tasks that have an easy entry point (a low threshold) but the potential to engage learners in deep mathematical reasoning (high ceilings). As Lynne McClure points out in an article on this idea (nrich.maths.org/7701), one of the great advantages of such tasks is that they allow learners to show what they can do rather than what they cannot do.

The key shift in perspective regards how we view diversity. Too often diversity is cast as a ‘problem’ in classrooms, as something that needs to be reduced or managed in some way. The research into effective group work shows that diversity in classrooms is actually a good thing. Diversity – of ideas, of strategies, of reasoning – is essential to levering up understanding. We need to embrace diversity.

Much of the research I draw on here is summarised in ‘An extended review of pupil grouping in schools’ (DfES, Kutnick P, Sebba J, et al, 2005). The full report can be downloaded from tinyurl.com/tpgroups