# Mixed-ability Maths Groups Influence Pupils’ Mindsets, Teachers’ Mindsets and Teachers’ Beliefs and Practices

**Written by Tom Francome**. Tom is a PhD student and a Senior Enterprise Fellow at the CMC at Loughborough University. If you are interested in this blog post and would like to get in touch, please email him directly at T.J.Francome@lboro.ac.uk, or comment below to start a conversation.

The Coronavirus outbreak showcased the adaptability and resilience of teachers. As students across the country returned to classrooms for face-to-face teaching, one consequence of social-distancing measures is that many mathematics classes are now mixed-attainment groups – a practice uncommon in UK secondary schools. The prospect of mixed-attainment mathematics classes might daunt some teachers. However, this can be viewed as an opportunity, rather than a problem.

Setting and streaming are not effective strategies for raising attainment. Everyone in Scandinavia teaches mixed-attainment mathematics, but there are fewer examples of good practice in the UK, so little evidence of benefits to encourage sceptical stakeholders. This “vicious circle” of factors deters UK secondary schools from teaching maths in mixed-attainment groups and maintains the status quo of ‘ability grouping’, which depends upon the misguided beliefs that abilities are ‘fixed’ and can be assessed accurately. Usual setting practices mean up to 50% of pupils are put in the “wrong” set and are rarely moved. This can have dire consequences:

*“If three pupils with the same scores on entrance to school were placed in different sets, one in a top set, one in a middle set and one in a low set, the performance of the pupil in a top set would be significantly higher and that of the pupil in the bottom set significantly lower.”* (Ireson, Hallam, Hack, Clark, & Plewis, 2002, p. 311)

It is desirable for pupils to believe that mathematical ability increases as a result of effort and effective teaching (a growth mindset). The alternative is that you have a ‘fixed’ ability which is preserved by avoiding challenges and potential failures. Of course, growth mindset interventions do not tend to work beyond the short-term; perhaps suggesting that long-term structural changes may be needed to promote and maintain growth mindsets. Unfortunately, research suggests setting practices can create fixed mindsets. Effectively telling some pupils:

“You’re good at mathematics… so you don’t have to try.”

or

“You’re not good at mathematics… so there’s no point in trying.”

Following on from this research, we conducted a small-scale study looking at the effects of setting versus mixed-attainment groups. We compared beliefs and practices in mathematics in two schools: School M taught in mixed-ability groups and School S taught in setted groups. We surveyed 286 year 7 pupils (age 11/12) and 12 teachers via questionnaires, lesson observations, and interviews.

Teachers of mixed groups believed more strongly that effort could increase ability, compared to teachers who taught setted groups. Pupils in both schools reported growth-mindsets but the beliefs were stronger for mixed-attainment groups who had stronger views that intelligence is improvable, were more strongly motivated by ‘learning goals’, and had stronger beliefs that effort led to improvement. Pupils in both schools wanted challenging work, wanted to learn through mistakes and wanted to discuss their work with others. Data suggested that pupils in mixed-attainment groups were more likely to be given or seek out challenging work, and to believe these tasks would help them learn.

Teachers from both schools expressed similar beliefs about the way they worked with pupils, but this was not supported by the pupil feedback. Mixed-attainment lessons tended to involve pupils discussing ideas collaboratively in pairs/small groups, using mistakes and misconceptions as learning opportunities, and using substantial tasks (i.e., bigger and more challenging tasks, which were accessible at different levels, and may generate more mistakes). Lessons with setted classes tended to involve pupils working mostly on their own, following methods shown by the teacher, and closely following textbooks/worksheets.

“I like discussing my answers with other classmates because I like to see if we came up with similar strategies” (Pupil M29)

“I work hard and I sometimes make mistakes but [the teacher] helps me learn from them.” (Pupil M117)

“My maths lessons are fun and interesting. My maths lessons are helping me get better at maths” (Pupil M12)

“In my maths lessons we always have a worksheet to do but before we start our teacher gives us some examples on the board.” (Pupil S100)

“In my maths class I sit alone and get on with my work” (Pupil S127).

“I’m always doing work at my level” (Pupil S135)

Our observations corroborated the pupil reports and showed that pupils in the mixed-attainment groups spent a far greater proportion of time working collaboratively.

Our observations corroborated the pupil reports and showed that pupils in the mixed-attainment groups spent a far greater proportion of time working collaboratively.

Whole class | Work alone | Consult peers occasionally | Work collaboratively | |

School M (mixed) | 38% | 2% | 25% | 35% |

School S (sets) | 49% | 22% | 24% | 5% |

Table 1 shows that pupils in both schools spent similar proportions of time in whole-class teaching and consulting with peers (such as checking they had the same answer). The vast majority of the remaining time was spent on individual work in School S and on collaborative work in School M.

A small study like this cannot be generalised but it raises some important questions. Can mixed-attainment groups encourage teachers to believe in pupils’ ability to improve mathematically? Can mixed-attainment groups change teaching practices in ways that support the learning of all pupils? When teachers work with mixed-attainment groups, they have to take account of pupils’ prior experiences in their planning. Teaching “at a particular level” is unlikely to succeed and so offering substantial tasks can allow each pupil to feel challenged mathematically. Different ideas arise and need discussion beyond ‘the answer’ so collaboration can be genuine. Pupils are more likely to make mistakes working on substantial tasks than following small steps and this allows greater opportunity for pupils to learn from their mistakes. Such a variety of pupil perspectives allows for greater opportunity to make connections between the different mathematical aspects of their work.

In contrast, setted classrooms can give teachers false impressions of the pupils being “at the same level”. This may lead to more procedural teaching where pupils are more likely to reproduce steps without error. This often means pupils do not feel challenged, and do not gain the benefits which come with learning from mistakes. There can also be less variety in the mathematics taking place within a lesson and so less opportunity for making connections between different topics. A consequence of this is that the actual experiences pupils have of learning mathematics, and their beliefs about what mathematics is, may be at odds with the beliefs expressed by teachers within the school.

This study also offered some evidence that grouping practices could influence pupils’ mindsets, teachers’ mindsets and teachers’ beliefs and practices when teaching mathematics. We found that both the experience of learning mathematics and pupil outcomes were improved if pupils believed they could improve, were less reluctant to engage with challenging problems, and persevered following setbacks (growth mindsets). ‘Mixed’ pupils had stronger growth-mindsets, ‘mixed’ teachers held more ‘connectionist’ beliefs and also had stronger growth-mindsets. As one mixed-attainment teacher said, “*I think the most important lesson for anyone to learn in maths is the harder you work at it, the better you’ll do*” (Teacher M4).

If current circumstances necessitate mixed-attainment groups, then we hope that this leads to more collaboration between teachers, generates more good-practice examples of mixed-attainment teaching and makes the transition to mixed-attainment groups less daunting for other schools. What started out as a pandemic-induced necessity, may just be the catalyst we need for improving pupils’ experiences of learning mathematics.

For further details, see: Francome, T., & Hewitt, D. (2018). “My math lessons are all about learning from your mistakes”: how mixed-attainment mathematics grouping affects the way students experience mathematics. Educational Review. https://doi.org/10.1080/00131911.2018.1513908 Available for free: *here*

###### Centre for Mathematical Cognition

We write mostly about mathematics education, numerical cognition and general academic life. Our centre’s research is wide-ranging, so there is something for everyone: teachers, researchers and general interest. Jayne Pickering, a research fellow at the CMC, runs this blog and edits all posts. Please email j.pickering2@lboro.ac.uk if you have any feedback or if you would like information about being a guest contributor. We hope you enjoy our blog!