Is it time to look beyond ‘teaching for mastery’ in maths?

Few can deny that the landscape of mathematics education has drastically changed over the last decade and a half. The emergence of ‘Teaching for Mastery’ in the mid- to late-2010s, linked to approaches to maths in east Asian high-performing jurisdictions (particularly Shanghai), combined with moves back towards more ‘traditional’ approaches to teaching (sparked by the tenure of Michael Gove as education secretary), have had a profound impact on the maths teaching practices used in schools across England.

Some will say that the impact of this is clear for all to see. England’s performance in international assessments seems to be improving. For example, in the PISA tests England’s score rose from 492 in 2012 to 504 in 2018, whilst in the same period the OECD average dropped from 494 to 489. Admittedly, in 2022 England’s score fell back to 492, but the OECD average dropped to 472 in the same period (widely attributed to the impact of the COVID pandemic). Similar gains have been seen in the TIMSS results as well.

However, there are some troubling figures as well, particularly when we look at those who struggle most with mathematics. In the same international tests, the gaps between the lowest attaining and highest attaining pupils have widened significantly over the last decade (although again, partly attributable to the pandemic). The top students have improved; with the percentage of year 9s achieving the ‘Advanced benchmark’ nearly doubling (8% to 15%) between 2007 and 2023. In the same period, though, those failing to meet the lowest benchmark have risen from 7% to 9%, and even before the pandemic was 8%. In addition, although scores have risen, they have not risen ‘equally’. Since 2007, year 9 pupils have seen their scores in the TIMMS in the ‘knowing’ and ‘applying’ domains shoot up by 11 and 17 points respectively. However, in the ‘reasoning’ domain scores have only improved by 5 points. This is despite ‘mathematical thinking’ being listed as one of the five key strands of teaching for mastery (which, you would hope, would encompass mathematical reasoning ability).

It is not just in international assessments that the gaps in teaching for mastery begin to appear. Tony Staneff recently did a bit a deep dive into the last nine years of the National Reference Tests, used with year 11 pupils to decide whether there are significant cohort shifts in attainment to aid with the setting of GCSE grade boundaries. Tony found the same story, that grade 7 attainment has risen significantly even after being reset following the pandemic, whilst grade 4 has remained remarkably stable even through the pandemic years. This suggests that more pupils in year 11 are getting into position to be awarded those top grades of 7 or better, but that this is not the case for those pupils who might be aiming for grade 4. Basically, there are more pupils getting to the top, but no more pupils getting out of the bottom.

It isn’t just in outcomes that these question marks over the impact of teaching for mastery arises. There have been a couple of recent research reports that have cast doubt on how well aspects of teaching for mastery are translating into schools. The Observatory for Mathematical Education, in its 2025 review highlighted that only 39% of year 7 pupils say that their ‘teacher shows how different topics link together’, despite ‘coherence’ being one of the big ideas in teaching for mastery. Similarly, secondary teachers reported the use of manipulatives in only 7% of lessons (although representations fared better at 52%), despite representation and structure being another key pillar of the teaching for mastery approach, and widely recognised as being a useful strategy for those learners who find mathematics difficult.

Another recent report, ‘The Student Grouping Study’ by UCL also found that teachers rarely provide manipulatives, although the figure here was higher (in the region of 20%). In the same survey, teachers also reported that tasks without an obvious solution were not frequently used, despite the aforementioned ‘mathematical thinking’ being a key component of teaching for mastery.

Taken collectively it would appear that, although maths education has undoubtedly improved overall in the last 20 years, the provision and outcomes for those that struggle to learn mathematics remains stubbornly behind. And so, the question must be asked, what next to support these learners? While I believe that the principles and practices of teaching for mastery represent a sound way of learning mathematics, is it that they are insufficient to the task of improving the lot of those who find mathematics most difficult? Or is it simply that more work needs to be done to embed them in schools so that lower attainers can feel their full benefit? If they are insufficient, what else do we need to ensure teachers are doing to make mathematics education as inclusive as possible?

I think part of this has to come from shifting what we value from a mathematical education. The TIMSS data, along with several other studies looking at things like why girls tend to underperform compared to boys in mathematics, indicate that a significant part of the ‘diet’ that pupils are fed in the mathematics classroom still focuses on accuracy, speed and procedure. A mathematical education that prioritises these aspects is always going to leave a proportion of pupils behind. Those pupils who need longer to process things, who might struggle to sequence information quickly, or who simply find it difficult to engage when things don’t make sense will all falter when this is what a mathematics education entails. 

For me, we need to ensure that what is valued in the mathematics classroom is pupils making sense of mathematical ideas just as much as their ability to remember facts and carry out procedures. We need to make it a priority to show pupils how the maths they learn connects and builds on itself, highlighting all the links that exist through a focus on mathematical structure, and consistent use of models and manipulatives/ representations to allow pupils to engage with that structure. We need a curriculum that sequences these things right from the off and provides the proper guidance and support for teachers to pick up their part of the journey of school mathematics learning in a way that will reinforce what came before and ensure that solid foundations are laid for what is to follow. We need to make sure that those teachers have access to the training and development they need to deliver the outstanding education that our struggling pupils require. And we need to make sure that our schools have the workforce of high-quality teachers of mathematics that can make this a reality.

Does mixed ability teaching harm pupils progress?

A new study comparing groupings of year 7 and year 8 pupils has found that teaching mathematics in mixed ability classes is less effective than placing pupils in sets based on ability or prior attainment.

The research – conducted by a team from the University College London (UCL), the Institute of Education, Brunel University and Queens University Belfast – finds that mixed attainment teaching leads to one months less progress overall for pupils (although they admit this is not statistically significant) and that the impact is particularly pronounced on high prior attainers, with mixed ability grouping costing them two months of maths progress when compared to setting.

As well as attainment, the study also surveyed pupils’ self-confidence in maths learning. It found that being taught in mixed ability classes negatively affected the self-confidence of pupils studying mathematics, in particular those with the lowest prior attainment.

This smacks in the face of established thinking in certain areas of maths education, which is that any cost to high attainers from mixed-ability teaching is more than made up for by the positive impact on outcomes and attitudes for the lower attainers. Proponents of mixed ability teaching often use this as a 'social justice' argument, stating (rightly) that low prior-attainers and those in lower sets tend to come from disadvantaged backgrounds and/or certain ethnic backgrounds and so the positive benefits for these pupils are worth and adverse impact on those that are more likely to have a more privileged upbringing.

I remember in the relatively early days of the the maths hubs hearing stories about certain hubs also promoting mixed ability teaching as being 'essential' for teaching for mastery. This seemed to coincide with key principles of teaching for mastery like 'all pupils can learn and enjoy mathematics' and all pupils working on the same mathematical idea.

Interestingly though, the heads of maths survey revealed that both those in charge of mixed ability departments and those in charge of setting departments both thought that their approach to grouping benefited lower attainers indicating a more divided opinion.

Now, I am sure that proponents of setting will take this as a victory, saying that 'if it helps the most able and doesn't have a negative impact on the least able, we should all be setting'.

Meanwhile I am sure that the adherents to mixed ability teaching will point to possible flaws in the research. Some of these are admitted in report, such as the admission that, due to the number of schools that either dropped out of the study or had to be withdrawn because they couldn’t be matched with a school with the alternative grouping approach, the study ‘may not fully represent the national population of schools’. Or the fact that the pupils in the setting schools had slightly higher prior attainment on entry, or more experienced teachers. Or more of the setting schools being rated 'outstanding' by Ofsted. Although Professor Allen has called for this to be the end of the mixed-attainment debate in her recent blog, I can see there being enough ammunition in the studies low evidence strength rating and own admitted limitations for die-hard MA proponents to continue the fight.

In my last school (an eight form entry school), we taught mixed ability in year 7 and year 8. This started many years ago when the school had its first KS4 cohort, and could no longer organise year 7 into two bands due to timetabling constraints. The best they could do is put them into quarters, with two classes in each quarter. I made the decision at this point to simply teach them in form groups instead. I knew we were a couple of years away from introducing a new scheme at KS3 that would be suitable for mixed ability teaching. Once this rolled out, we actually found that so many pupils were doing well (scoring over 80% on the end of year 7 testing) that setting in year 8 wasn't always necessary - we would sometimes put a top set or nurture group in place where the data from year 7 suggested it might be required. Ultimately, we had no real options in how we grouped year 7, and we were flexible enough to adapt to what the data told us (within reason) for when these pupils moved on to year 8.

For me, the way that pupils were grouped was much less important than the provision they were getting, and it is here that the study offers some real concerns. During the case study observations that the research team did they found that the majority of lessons rated low on the 'Teaching for Robust Understanding' framework. They commented things like ‘Typically, the focus was on procedures and methods with little focus on developing understandings of the underlying concepts’ and 'Although there were opportunities for challenging extension activities for high-prior attaining students [in mixed ability classrooms], these opportunities frequently involved mathematics that was not directly related to the lesson content and were rarely discussed in class.’

The teacher survey also paints a bleak picture in parts. Despite significant work over the last decade or more by the NCETM to embed practices such as mathematical thinking and the use of representations and manipulatives, the use of problem solving as anything but extension work, particularly those problems for which there is no obvious solution, as well as the use of manipulatives in lessons for these year groups remaining disappointing low. This is despite nearly 60% of pupils saying that they understand mathematics better when they can use objects to help them, rising to nearly 65% for the lowest prior attainers.

The study also contains some further concerning (although not necessarily surprising) statistics. Boys being about 50% more likely than girls to report that they feel comfortable talking about their mistakes in class adds to the evidence that maths teaching practice needs to change to be more inclusive of girls and support the building of girls confidence in maths (as was also highlighted in this recent education brief from UNESCO looking at recent TIMMS data). High prior attainers being 50% more likely that low prior attainers to say their parents like maths highlights the continuing theme of parental issues and anxieties around maths impacting the progress of their children.

Whatever happens with grouping of pupils, whether more schools move to setting, whether schools try and deal with the lack of challenge for high prior attainers by having a top set and mixed attainment for rest, these are, for me, secondary concerns. If this research is to be believed, the lower prior attainers aren't being served by either setting or mixed ability - they are struggling when they start secondary school and still struggling two years later no matter how they are grouped. This is what we need to deal with as a sector, improving practice so that it supports all learners in making progress, providing access and entitlement to the highest quality CPD to ensure teachers continue to develop their craft throughout their careers, and addressing wider societal issues and attitudes around mathematics. These are not entirely solvable by schools.