Mastery, Setting & Mixed Attainment


I posted the image above on Twitter recently.  This was a result of my thinking around the practical issues of implementing the curriculum in real schools. The views I express in this article are not popular or fashionable.  I do attempt to be balanced in this blog, although I clearly have a bias.  

In this blog I am relating entirely to the context I am knowledgeable of: mainstream, comprehensive, secondary maths in Scotland.  I’m not talking about England, about primary or any other context.  

An issue which is always at the forefront of the debate in education is that of mixed attainment versus setting.  I am reluctant to enter the debate publicly, however, I hope my thoughts have some merit.   

I have no argument against mixed attainment with vibrant, excellent learning and teaching which is responsive to the needs of all pupils.  Indeed if the debate was between mixed attainment or an enactment of the curriculum which has the attributes listed in the right column of my table above, then I am in favour of mixed attainment every single time.  I know there is some good work going on in some schools in Scotland, who are making mixed attainment work in their contexts.  I have the utmost respect for secondary departments who are making this work.  My personal ideal would be having mixed attainment groups in maths, with all pupils working together on the same tasks, all of the time.  However, in my career I have mainly taught in situations with setting.

In this blog I suggest that there is a third option beyond mixed attainment or rigidly set classes following a conveyor belt curriculum.

A common sentiment is that not being in favour of mixed attainment is to be against “social justice”.  It’s possible to have other perspectives and still be aligned to pursuit of “social justice”.  

What happens in some schools clearly isn’t good enough.  A conveyer belt curriculum, unresponsive to the needs of pupils is still common in schools.  “This week we do topic X, next week we do topic Y.”  This often happens in schools where pupils are set.  This pays no attention to the fact that pupils may not have had adequate time to marshal the ideas and master the key skills involved.  The curriculum says it is time to move on, so the class move on.  Also common in setting is that the weakest teacher, or the NQT end up with the bottom sets.  This is clearly not aspirational or genuinely aimed at closing the gap. Those classes need an extremely skilled teacher to help move pupil learning forward.  So, if conveyor belt approaches and segregation of those who can achieve and those who can’t is what setting is all about, then I’m very much against it.  I firmly believe that all pupils can learn mathematics.

I’ve had the privilege of being all over Scotland this past 14 months and have seen countless lessons in both primary and secondary.  By upper primary the gap between low and high attainers is very wide (SNSA data confirms this).  I have witnessed some mixed attainment teaching work, and some lessons where pupils get practically no one-to-one time with the teacher and are doing work which is completely inappropriate.  Just because one is working in a mixed attainment context doesn’t mean that things improve.  Certainly, the majority of our primary schools work that way and the gap doesn’t close over the 7 years.  It is exacerbated.  (I don’t blame primary teachers for this – the reasons are complex and beyond the scope of this blog).  

Before I continue I feel that it is important to state that Mathematics IS different to other subjects.  The work at the various curriculum levels is quite different!  The gap upon arrival at secondary is 7 years.  This is a vast difference.  Mixed attainment where the gap is 1 year is quite different to such a wide range.  This is one of the reasons why I think mixed attainment is something which almost always works in early primary.  However, from what I have seen, generally, a move towards some form of setting later on in primary *might* be beneficial.  Pupils need to be taught the correct content.  Every pupil deserves attention and focus. 

“Every class is mixed attainment”, of course.  

Frequently teachers in other subjects make negative comments about maths teachers with regard to setting versus mixed attainment.  However, when the chips are on the table, these same teachers are the people who complain about multi level teaching in the senior phase! 

In maths, there are hundreds of objectives to cover.  Our BGE is vast, is both hierarchical and a complex non-hierarchical web.  If pupils aren’t making deep progress, fast, from day one there is no hope of achieving well.  You don’t hear about pupils “crashing Higher maths”.  That can happen in other subjects – even the sciences, but it just doesn’t happen in maths, as pre-requisite knowledge and skills is so vital.  In maths, Higher really does start on the first day of S1. (I forget who said that to me recently, but I liked it).  

The next issue to consider is that the skillset involved in teaching mixed attainment groupings is quite different to that of homogeneously grouped pupils.  If a department are to move over to mixed attainment teaching then a significant amount of CPD and professional learning is required to make this work.  Similarly, significant time is required to build up an appropriate scheme of work. If these conditions are met and the team is very good then I know mixed attainment can work.  However, if they are not, then the attainment impact isn’t going to materialise.

The “evidence” in favour of mixed attainment isn’t nearly as comprehensive as is often made out.  Indeed, Mark McCourt list a range of criticisms about the research in this area.  Mark also discusses the EEF summary, which is often quoted, but is deeply flawed.  

The following paper offers some interesting insights:  http://www.leeds.ac.uk/educol/documents/00001359.htm 

A complete set of data containing all the explanatory variables was available for 3481 pupils. The analysis suggested that pupils made more progress if they were not in mixed ability schools, and there was some evidence that set schools strengthened the relationship between Key Stage 2 and Key Stage 3 scores.

This study has a section particularly focused on mathematics, which makes this an interesting point! It continues…

High attaining pupils in mathematics at Key Stage 2 do better at Key Stage 3 if they are in a set school, whereas low attaining pupils do better if they are in a mixed ability school.

Why might this be?  My conjecture is that the best mathematicians, the best teachers very often end up with the top sets.  The weaker or inexperienced teachers often end up with the lowest attaining groups.  I’ve never seen the weakest teacher in a department being given the top set Higher, but frequently asked to take “2nd bottom S1”.   Which class needs a good teacher more?  Those lowest attaining pupils could have a great experience, being taught the correct mathematics, at pace, with a great teacher.  

Mixed attainment can work, but sometimes doesn’t.  Setting can work, but sometimes doesn’t.  The third view is Mastery learning as proposed by Bloom, Carroll and others.  It puts the pupils front and centre of all considerations.  It is about responsive teaching.  However, to do this homogenous groupings have been central to effective implementations.   


The model above, from Carroll, captures some key ideas. Pupil’s academic achievement is related to pupils being given adequate time to learn the material (we can acknowledge pupils have different rates of learning), the quality of teaching, the barriers to learning and the active engagement of the pupil in the work.  These are variables, which we can actually influence.

We can work with partners in the school and elsewhere to try to help overcome barriers to learning, although this very complex and mainly beyond the control of maths teachers. 

However, we can give pupils the time required to achieve.  If we have curricula that states “two weeks for fractions”, then we are failing to cater to the time pupils need to learn.  Real differentiation is adjusting the time allowed, to learn the required material. That is the biggest lever we have.  We can allow pupils more time to develop the understanding.  People often say we are in a massive rush, but I’ve argued against this in many talks and in previous blogs – there is no rush.  We can save time by not teaching line symmetry in P3, 4, 5, 6, 7, S1 and S2 for a start!  Or we could use coherent models which permeate the entire curriculum – thus reducing learning time required, overall. 

We can always strive to teach better.  We can seek out effective pedagogies, learn more about effective models and immerse ourselves in the understandings of questioning, assessment, task design and selection etc etc.  The focus on improving learning and teaching or curriculum, as I’ve often said, should be central to every DM.

We can develop a real growth mindset in pupils.  Rather than putting up pretty posters or having motivating speakers, we can give pupils a chance to really develop a growth mindset, by giving them opportunities to achieve high levels of success, fairly regularly.  As Thomas Guskey has said “Don’t try to convince learners that they should have a growth mindset- change their experience so they develop it themselves.” Gordon Carrier et al talk about how prior achievement and success in learning results in students being more motivated and, frequently, being able to  demonstrate more perseverance. 

Ultimately, if teaching is a purposeful activity then it should have some impact.  Pupils should perform beyond expected progress.  If pupils sit, say, a CAT standardised test and then perform exactly as predicted in later schooling, does this mean the school/pupil have achieved well?  Maybe the pupils has, but I’d question the schooling.  Surely our job is to help pupils achieve better than the pre-determined?  There is a plethora of evidence and case studies which suggest that mastery learning can help to genuinely raise the attainment beyond expected levels for our pupils.  We can see the bell shape curve move in a positive direction.

We can use standardised scores to evaluate the quality of experience of pupils, but should not use them to predetermine pupils future outcomes, either consciously or implicitly.

So what about setting?  Being pragmatic, I think the best option is somewhere in the middle. My inclination is now towards really flexible and fluid setting, where classes are mixed, but only within a level. In a typical secondary school there are some classes working at Third, some at Second and one at First/Second Levels.  Within each of those 3 categories there would be classes which are not “hard set”. For example, with the Third Level classes try to keep all of the pupils progressing together, and the classes would be mixed amongst that level.  While there will be a gap, it will be manageable. The aim for the other classes is to actually close the gap – by really specific targeted intervention planning, using evidence based progressions to help these pupils access and succeed with the secondary curriculum proper, in coming years.  In this approach I’d hope to try to obtain some of the benefits of setting and some of benefits of mixed groupings.  

Not having rigid timelines can be logistically difficult.  But just because it is hard doesn’t mean it isn’t worth the effort to try.  Our teaching should be responsive to pupils and so should our curriculum.  Flexible scheduling goes hand in hand with the highest of aspirations for all pupils.  

 This is about social justice.  There is a big difference between having rigid setting, weak pedagogy and low aspirations versus a responsive dynamic mastery curriculum which utilises some form of setting to maximise effectiveness of teaching.  For me the debate should, in secondary be, mixed attainment (regular curriculum) versus setting (mastery curriculum).  

Mastery is one model of schooling, there are others.  This is the one that’s improved things for pupils in my department previously and I feel more confident about making work in future, than any other. This mastery cycle from Mark McCourt which captures much of the work of Bloom and others.  This blog is not an explanation of the implementation of mastery – I have attempted than in other blogs and Mark has written an excellent book on the subject!  

I hope that my arguments show a commitment to raising achievement for all pupils. 

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