Mixed Ability Groups: The Case for a More Egalitarian Maths Classroom
Mixed Ability Groups: The
Case for a More Egalitarian Maths Classroom
The other day one of my year 10 kids asked what set they were in and I told them set four to which they said “oh god! Is that the bottom set?".I said it was but that didn’t mean they couldn’t do well. I explained that I didn’t believe in setting and that as a department we were no longer setting at KS3 to which they said how lucky they thought those kids were. They asked if they could move up and I said they could but that they were lucky to be in such a small class (eight students) and that it would be a bigger group in set three. One of the girls remarked how awful the set three she had been in the previous year had been, how it had been loud and how she hated it. I explained that lots of the time students who have trouble with behaviour end up being put in lower sets. They said at least if you move up it gives your confidence a boost but then immediately the same girl said but it ruins it when you move down.
The lesson was lovely and I felt like I really taught them well that day and that they were really engaged and learning- but at the end of the day that might not matter that much because they think of themselves as bottom set, limited by their ability, rather than having a growth mindset. Their insight into setting was amazing, they hated the experience being in lower sets had given them, of noisy uncontrollable classrooms and their new experience of a smaller group which was a positive learning environment seemed entirely novel, even surprising to them. They were for the first time able to get the teachers attention and were, dare I say it, even enjoying maths, an experience they had not previously been afforded.
While, over the
past 30 years, other subjects have transitioned to mixed ability groups, maths is still
predominantly set in this country (71%). Even in schools which have introduced
mixed ability in Key Stage Three, rarely is Key Stage Four mixed with the
structure of the foundation/higher GCSE preventing mixing being a viable option
for most schools. There are various arguments presented against mixed ability groups
for maths, chief among which is that it will have a negative affect on
attainment, particularly for Key Stage Four students, and the threat of a bad
set of GCSE results understandably makes schools highly risk averse to dramatic
changes such as this. There are also criticisms that mixing groups would leave
students at the top and the bottom squeezed out, with higher attaining students
becoming bored with work that is too easy and students who need greater support
being unable to access work. Many teachers simply find that teaching mixed ability
is harder and that they can't create lessons that are tailored for mixed
ability as well as they can for sets.
My school recently started
mixing our KS3 maths classes (beginning with year 7 in 2020/21). This was
initially a response to the pandemic with the idea of keeping year 7 in their
forms so as to avoid opportunities for transmission between classes. I had
never taught mixed groups before and (nerd that I am) I did some research on how
to best deal with a mixed class. I was quite concerned about how to pitch my
lessons but decided that it was important to scaffold for the low
attainers while having materials to challenge and engage the high
attainers. I quickly decided that I didn't want to lose my mixed ab class (who
I had developed a strong relationship with) and there were other staff who felt
the same. I found that I really enjoyed teaching the group and began to see
lots of benefits of mixing the students while also seeing the negative impact
of setting on students in other year groups. As a result we have kept the
previous year 7s (now year 8s) mixed and have also not set the 2021/2022 year 7s. I
have continued to research the setting vs mixed ability debate and have
become somewhat of an advocate for mixing. Within my
department there are various different views on mixed ability vs sets and I
expect that if we see a downturn in attainment from our current mixed groups we
will set them again. I want to use this blog to challenge the arguments against
mixing, in particular that of its negative impact on attainment and also
propose the benefits that can be gained from it, in particular its positive
impact on students' experience of maths and in the ways it makes the classroom
more egalitarian.
History of Setting in
England
The conception that maths needs
to be set is rooted in the old fashioned understanding of attainment being
simply a function of natural ability rather than of hard work, reflection,
collaboration etc. Setting has part of the English system since the 40s and was
introduced with the argument that students of a similar ability would be better
taught if they were in a group with students of the same ability
(Nursat, 2017). Research has ousted this view by showing that ability can change, and has promoted the idea of developing a growth mindset where everyone can
improve. This allows students of all attainment bands to focus on their progress, meaning that high attainers should no longer be content with their
success but look to challenge themselves and improve.
While other subjects over the previous few decades have abandoned setting in
favour of mixed or streamed ability maths has been kept set.
This is rooted in an archaic view that maths is a hierarchical subject based on
whether one is "good" or "bad" at maths (Linnchevski,
Kitscher, 1998). This has been created because in maths there are
"right" and "wrong" answers. In English a student can
always have some positive feedback on a piece of writing, in Art there is
always something that can be praised in a composition. In maths, students who do
not understand a concept are likely to get every question they are given on it
wrong and this builds a negative/positive dichotomy were students think they either "can do maths" or "can't do" maths. This is
reinforced over generations. It is a perennial bane of maths teachers when
on parents evening they hear a parent tell a child "I could never do
maths". This manifests itself in setting in our education system where we
think that higher and lower attaining students are unable to work in the same
educational setting. The English system has also hung onto setting in maths
because of the perceived occupational purpose of maths. Previously students were
allowed to leave school at sixteen and therefor a maths GCSE became a key part
of getting a job, this led to the split between the higher and foundation GCSE
which requires setting of some sort at KS4. This also led to
the idea that maths for high attaining students is an academic pursuit whereas
for low attaining students it is something they have to do rather than
something they might enjoy.
Negative Impact of
Setting
There are however significant
negative impacts of setting students in maths classes. Every teacher knows that
a second to bottom or bottom set is often not a class where students are given
appropriate work and nurtured by an education that fits their need. They are,
in short, hell. These groups are noisy, unproductive and immensely difficult to
teach. This is because they are created using tests and students who are not
low ability but are badly behaved are gradually shifted to the bottom classes
as they miss content and make less progress due to their poor behaviour. This
means that lower sets are actually a 1-2 hour exercise in behaviour management
rather than in teaching. Rather than having 3-4 behaviourly tricky kids out of 24 a
low attaining set will have something more like 12 out of 24. This means that they are able to misbehave
more as the teacher is unable to deal with all of them at once and other
students who would work better in a higher set also misbehave. An enormous
amount of energy has to be expended in controlling misbehaving students and
very little teacher time is left to help students learn maths. This means that
those students with poor behaviour only get worse and those low attaining
students who do want to learn do not get enough support from their
teacher.
The teacher will also have much
lower standards with a lower set than a higher. Whether that is towards the
amount of work produced, the effort put in, behavioural expectations or home
learning, it is impossible for a teacher to have the same standards with the
top set as with the bottom, despite none of these things being a function of
'ability'. There are less high quality discussions had in these classes, not
because students can't contribute but because the teacher is focused on keeping
behaviour under control. There are also likely to be less problem solving
opportunities with classes mainly completing drill work as this makes the class more manageable.
Collaboration is also much less likely to occur in sets with only
30.1% of teachers using pair work most of the time in set classes (compared
with 52.% in mixed) (Francome and Hewitt, 2020). As Linchevski (1998) put it
"low-ability classes lead to low-quality teaching" and this creates an ever widening attainment gap between top and bottom.
Further unless students are
right on the cusp of the set (and want to move up or avoid moving down) they
begin to see themselves in the fixed mindset of being a set three/set four
student and stop trying. "what is the point" they say, "I am bad
at maths", "we're bottom set so it doesn't matter". They can't
develop the growth mindset they need to improve (Francome and Hewitt, 2020) and
develop a negative perspective of maths. This is also true of teachers and
research has show that sets can make teachers label pupils and not expect them
to improve (Francome and Hewitt, 2020). This fixed ability mindnset can
negatively effect all students (not just low attainers) as it it encourages
students to see a wrong answer as a bad thing and not as a way of
improving and indeed studies have found that high, middle and lower
attaining students have a more negative attitude towards maths in sets than in
mixed groups (Francome, Hewitt, 2020). Setting based on 'ability' lowers the self esteem of low attaining students by making them feel they are
worse than others and means they do not feel welcomed or valued in maths
(Nursat, 2017), when they often the students who need the most support.
There are also intrinsic
problems with the concept of ability grouping. Research has found that there is
no good way to set students and that even the best tests rarely produce
groupings that truly reflect ability (Nursat, 2017, Skov 1986). Rather, when we
set by 'ability' we are really setting by attainment. Many students are put
into the wrong group because of issues such as behaviour, prior knowledge, poor
mental health etc. and Black and Wiliam (2006) estimated that at least 50% of
students are placed in the "wrong set". Further, there is rarely much
to separate a student a the top of a set with one at the bottom of the next set up and the choice as to which set they are in is therefor arbitrary. There have
been arguments that students who are at the top of a lower set actually do
better but this is not born out in research which has shown that being in a
higher set raises attainment (Linchevski, 1998). So by setting students we are
arbitrarily giving some of them an advantage and some a disadvantage. This results in an extension of the achievement gap between higer and lower attainers over time. Further setting by attainment has been found to
often select along sexist, racist and classist lines (Francome, Hewitt, 2020,
Skov, 1986) which has a negative impact on the affected students and also means
that maths classrooms do not have as a wide a range of backgrounds and
perspectives featuring in discussions. Indeed, as Nursat (2017) has laid out,
all classes are mixed and the idea that a
class' ability is homogenous is pure fantasy. Different personalities, prior
knowledge, SEN and EAL needs can dramatically alter classes and thus teacher
should be differentiating and supporting for mixed ability anyway. By pigeon
holing classes as "top" or "bottom" set we are assuming
things about our groups which are not accurate and this can lead to lazy lesson
planning.
The criticisms of mixed
ability
There are however many teachers
and school leaders who are nervous about the idea of mixed ability teaching in
maths, even though it has been embraced in other subjects. Many teachers also
have the preconception that students attainment in maths is decided by their
'ability' having gone through setting by attainment themselves. Some teachers
are also worried that it be harder to plan lessons for mixed groups and that
they will find it impossible to support low attainers and unable to stretch the
top (Kerry, 1978). However, as I have already argued, all groups are mixed
and there is no set where a teacher should not be differentiating for the lower
and higher attaining students, the differences are just starker in a mixed
ability group. Further those who claim that low attaining students are not
supported well by mixed ability need only think of the aforementioned difficulties
of teaching a lower set to realise that low attaining students are not
supported well in sets. In a mixed group there will only be a few low attainers
and supporting them can be the teacher's focus in lessons. Producing scaffolded and/or
differentiated work can also allow all students in a mixed ability class to have appropriate and challenging work (Nursat, 2017, Berrill, Sampson,
1974). This creates a more collaborative space where low attaining students are
more comfortable engaging with class discussion, asking for help and,
crucially, making mistakes.
This is not to say that
teaching mixed groups is not challenging and that planning lessons that can challenge high attainers and support low attainers can be very difficult to
plan. Using resources that challenge students to use the same core skill taught
in the lesson but in a different context or in a more challenging format can
allow for higher attaining students to be challenged and also allow them to
develop independence and to develop skills like asking questions and
collaboration. It is also important not to allow high attaining students to
dominate discussion (Nursat, 2017) but to encourage all students to
participate. This can be done by cold and hot calling, rather than hands up. 'Cold Calling' (asking students questions at random is a powerful AfL tool in mixed ability classrooms as if a student doesn't know the answer or gets it wrong
it allows us to understand their reasoning. This should be pared with
encouragement that if the student does get it wrong then that is a good thing as it is an opportunity to learn (a perenial phrase of mine is "I like wrong answers"). 'Hot Calling' should be used to pick students who you
think will be able to answer the question and this can be used to build
confidence. Hands up might only be used at the end of a discussion and if I see
that a student who rarely participates in discussion has their hand up I will
hot call them because I want them to get their confidence up but otherwise hands up
is a system that widens the attainment gap. Whole class AfL, such as hinge
questions, should also be used regularly to ensure all students are engaging
with the learning and that the class is not dominated by high attainers.
Attainment
The primary criticism of mixed
attainment is that it negatively impact on attainment, particularly for high
attainers. This is the biggest fear for schools who might be reticent about
adopting mixed ability because of the importance placed on 'progress 8'.
However, this view needs to be critiqued as research shows that when introduced effectively with a staff body are committed to its success
mixed ability does not negatively impact attainment and can have a positive
impact (Skov, 1986). There is also no substantial research to show that setting
can raise attainment (Francome, Hewitt, 2020). Rather, studies that have
analysed the difference between mixed ability and set schools have found that
there is no difference in the attainment of high attaining students in mixed
ability groups (or a statistically insignificant negative impact), while middle
and low attaining students perform much better (Linchevski ad Kutscher, 1998). Indeed what we see in setted environments is that the attainment gap between the
top on the bottom widens year on year while this impact has not been found in
mixed ability groups (Linchevski and Kutscher, 1998). The obsession with the top achievers comes from the
hierarchical conception of maths and is also pushed by the Government who used maths attainment as a reason to introduce the Grade 9 at GCSE. When the Danish education system transitioned to mixed abilty schools from the 70s to 80s they
found that heterogenous (mixed) groups performed significantly better than
differentiated groups, particularly in terms of lower attaining students(Skov,
1986, see fig. 1.)
Mixed ability groups are also more democratic and egalitarian and are thus a more ethical way of teaching maths. As I have argued, set groups lean towards selecting by gender, ethnicity and class and therefor do not produce diverse and representatitve classrooms (Skov, 1986). Mixed ability prevents that and allows for students from all walks of life to benefit from each others' experiences and share their own (Nursat 2017). Because the classes are not hierarchical and place value on progress rather than attainment it also promotes the idea that students are all valued equally as opposed to being judged on their attainment creating a more egalitarian learning community with a more positive attitude towards learning (Skov, 1986). This means students feel more comfortable in class and are more confident in engaging in discussions and sharing their opinions (Nursat, 2017). This means that students are more likely to enjoy maths lessons and actively engage in them. This encourages a more positive attitude towards learning maths with students becoming more inquisitive and resilient in lessons (Francome, Hewitt, 2020).
Growth Mindset
Mixed ability groups also help to develop a growth mindset and a positive attitude to mistake making. Because they are all mixed the class is seen as a more egalitarian collaborative space where students are more free to make mistakes without seeing it as a judgement on their ability. In fact mistake making can be more easily encouraged as a way to learn. Because the class is a more positive learning environment than sets (Skov, 1986) the students are more likely to feel welcomed and valued in class (Nursat, 2017) and therefor are more likely to be comfortable making a mistake. The strategies described above (whole class AfL, cold and hot calling) can support this and mistakes should be welcomed and praised by the teacher who may use them to discuss a misconception or to talk about a student's reasoning. This means that students will develop the idea that even though they have got the wrong answer their opinions and ideas are all equally valid (Berrill, Sampson, 1974). I know through my own mixed ability groups that when we complete AfL or assessments there is much less "who got it right"/"what mark did you get" as there is an understanding that everyone is in a different place and that these assessments are opportunities to learn. This needs to be the case for the high attainers who need to see that just because they can master the core skills doesn't mean that they will not be challenged in maths lessons. This is supported by Francome and Hewitt's study (2020) which found that 68.8% of students in mixed ability groups said that in maths lessons they discussed and encouraged mistakes, while only 45.7% of students said the same thing in sets. Further around 73% of student in mixed ability schools were found to have developed a "growth mindset" as opposed to 67% in set schools (Francome, Hewitt, 2020). Students from mixed groups interviewed as part of this study discussed the value of mistakes with oe saying "my math lessons re all about learning from your mistakes", while students from set groups were likely to talk about a paternalistic relationship with their teachers where "miss just explains everything [and we] write it down in our books" (Francome, Hewitt, 2020).
Collaboration
The negative attitude towards learning often found low attaining sets means that low attaining students are unable to access the benefits of collaboration that are normally reserved for high attaining sets. Mixed ability groups also positively encourage collaboration between students who are able to support each other (Skov, 1986). In mixed settings students are sat with students who can support them in their work, in this way students are able to use each other as learning resources and develop greater understanding of concepts by teaching them (Nursat, 2017). This does not mean sitting the highest attaining students with the lowest but pairing up students whose attainment is not drastically different and who also work well together. I always arrange my seating plans around students who I know can be great teachers for their partners and the highest compliment I can give is that a student is a really good teacher. It is often said that a complete understanding of a topic is only reached when you can teach it to someone else so by colloboarting and teaching each other students get a better understanding of concepts and misconceptions. Fancome and Hewitt's study (2020) bears this out with 52.4% of teachers with mixed groups saying that pair work happens most of the time in their classes, while the same was only true of 30.1% of sets. Mixed ability groups also bring a greater diversity of life experience and viewpoints and allows students to learn from each other's different experiences (Kerry, 1978). In this environment students can actively develop collaboration and teaching skills and can see the value of asking for help. I often find that my lower set groups are worst at this with students wanting to sit and work on their own and often being unable to articulate when they need support. The collaborative nature of mixed ability groups means that students become happier working together and more comfortable asking for help.
These collaborative group which are more positive about mistake making and encourage a growth mindset are also more likely to produce students who enjoy maths. Enjoyment of maths is heavily dependent on attainment and for many students it is their least favourite lesson. As discussed above a lot of this can be put down the the fact that students have a negative experience of getting answers wrong and feel judged because they are put into "ability" based sets. Because mixed ability groups encourage wrong answers and do not put pressure on students to get into a good set in order to feel valued students feel more comfortable (Nursat, 2017) and can enjoy maths even if they do not find that they are good at it. Further students in middle or lower attaining sets may not be in a positive learning environment and therefor learn to associate maths with negative experience. Mixed groups create more positive learning environments which mean that a student's enjoyment of the subject is less heavily associated with their attainment. The focus on growth in mixed ability groups and improvement can mean that students can see their progress as an achievement to feel proud of, even if they are a low or middle attainer (Francome, Hewitt, 2020) and thus enjoy their lessons.
Concessions
I will admit it is important to provide nurture support for those students who cannot access the curriculum, ideally in a way that would allow them to return to normal classes such as through booster sessions. This is also the case for high performing students, who should be encouraged to extend themselves in maths clubs, extra sessions (either in or out of lessons) and through participation in maths challenges such as the JMC and IMC. This means that these students are still being challenged and encouraged to excel rather than just being able to coast through lessons. Finally the reality of the way the Maths GCSE is split into foundation and higher means that for most schools it will be impossible not to set at some point in KS4, at what point in KS4 this happens should be decided based on the context of the school and around the Scheme of Learning. We set at the start of year 10 but I have heard some schools not setting till year 11 or even till the start of term 2 in year 11. I would argue that necessity is just another way in which GCSEs negatively impact teaching in England but that is an argument for another blog post.
Conclusion
When I began teaching maths I was all for sets, they were how I was taught and I had done well, and I struggled to see how content could be pitched for both high and low attainers. It was only when mixed ability was forced on me by COVID that I started to see and understand the benefits of mixed ability. Working closer with low sets also showed me how detrimental they can be for children and this inspired me to go away and research the field of mixed ability vs set classes. I have found that all the work that was going on in the research was reinforcing and expanding the observations I had made myself, that sets can be terrible for middle and lower attaining students and that actually there is no such thing as setting by ability. This system has created groups which are hell to teach and which learning is much harder, while also imposing the idea that maths is a hierarchical subject based on ability rather than one where it is possible to improve. The make up of sets are often formed around class, racial, and gender lines and this also means that they have a negative impact on the achievement gap and do not reflect an egalitarian society. They teach students to hate and fear maths and have little to no benefits. Mixed ability addresses many of these issues, reducing the achievement gap and allowing students to collaborate and improve their growth mindsets. Most of all it is more egalitarian and democratic and allows students to enjoy maths, whatever their attainment. I dread the day when I have to set my mixed ability classes, I know how hard it will hit the confidence of some of my students who have shown real improvement and how I will know that the sets they join will not be positive learning environments. Schools do seem to be going in the right direction on this and teacher attitudes also seem to be changing. However the GCSE system may mean that mixed ability from 11-16 is unattainable without serious changes to examination practices in England. Mixed ability however should become the norm rather than the exception for KS3 and when this has successfully implemented it will be easier for departments to consider changes to their KS4 approach. Mixed ability is by no means perfect and it is certainly challenging for teachers who have always taught sets, but with adjustments for context, it can create a more democratic, growth orientated and happier maths classroom.
Works Cited
Linchevski, Liora, and Kutscher, ‘Tell Me with Whom You’re Learing and I’ll tell you How Much You’ve Learned: Ability versus Same-Ability Grouping in Mathematics’ in Journal for Research in Mathematics Education Vol. 29 (1998), pp. 533-554
Nursat, Dil, ‘Overcoming the Challenges faced in a mixed ability Classroom’ in Journal of Humanities and Social Science Vol. 22 (2017). pp. 9-14
Skov, Poul, ‘Mixed Ability Teaching’ in Scandinavian Journal of Educational Research Vol. 30 (1986) pp. 84-95
Kerry, Trevor, ‘Bright Pupils in Mixed Ability Classes’ in British Educational Research Journal Vol. 4 (1978), pp. 103-111
Berrill, Renée, Sampson, George, ‘A Method of Teaching of Mathematics to Mixed Ability Groups and the Changing Role of the Teacher’ in International Journal of Mathematical Education in Science and Technology, Vol. 5, (1974), pp. 47-51
Francome, Tom and Hewitt, Dave ‘“My math lessons are all about learning from your mistakes”: how mixed-attainment mathematics grouping affects the way students experience mathematics’ in Educational Review, Vol. 72 (2020), pp. 475-494
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