# data[].attributes.body
still some of the best problems around

# data[].attributes.attachment_link.readable_text
Our latest Primary and Secondary features challenge you to think flexibly

More exciting activities can be found on the Primary (age 5-11) and Secondary (age 11-18) student homepages

See if your solutions to our recent problems have been published
Primary
Secondary

For regular updates, sign up for our Newsletter

# data[].attributes.attachment_link.title
NRICH - Mathematics Resources for Teachers, Parents and Students to Enrich Learning

# data[].attributes.attachment_link.description
Our latest Primary and Secondary features challenge you to think flexibly More exciting activities can be found on the Primary (age 5-11) and Secondary (age 11-18) student homepages See if your solutions to our recent problems have been published Primary Secondary For regular updates, sign up for our Newsletter

# data[].attributes.body
What it says on the tin

# data[].attributes.body
Condensed research articles perfect for faculty meeting discussions

# data[].attributes.body
Only just found this but it is fascinating

# data[].attributes.body
Has a massive library of resources including a set of scanned in SMILE cards -best resources ever IMHO

# data[].attributes.body
Everything ICT lots of free resources and an interesting blog

# data[].attributes.body
5 a day, practice questions, videos

# data[].attributes.attachment_link.description
Welcome to Corbettmaths! Home to 1000's of maths resources: Videos, Worksheets, 5-a-day, Revision Cards and much more.

# data[].attributes.body
Maths game subscription site

# data[].attributes.attachment_link.readable_text
In either paper form or online, Times Tables Rock Stars is a carefully sequenced programme of daily times tables practice.

Each week concentrates on a different times table, with a recommended consolidation week for rehearsing the tables that have recently been practised every third week or so.

This format has very successfully boosted times tables recall speed for hundreds of thousands of pupils over the last 8 years in over 16,000 schools - both primary and secondary - worldwide.

The TT Rock Stars Worldwide Community of Schools

"Wait, are we doing #TTRockstars?"
Nods
"Get in!"
Fair to say our trial is going well!

@parky_teaches
Classroom conversation

A challenging Yr 8 pupil left my lesson today determined to become a 'Rock Hero'. TT Rock Stars- what a motivational tool!

@burls70
Cape Cornwall School

I've struggled every year with motivating my class to learn times tables with varying degrees of success but I feel that this has had the biggest impact by far. And I have great recorded evidence as well.

Mr Davies
Raynsford CofE School

Engaging, competitive and improves their arithmetic.

Damian Hinds
Education Secretary

A Selection of Multi-Academy Trusts using TT Rock Stars

# data[].attributes.attachment_link.description
In either paper form or online, Times Tables Rock Stars is a carefully sequenced programme of daily times tables practice. Each week concentrates on a different times table, with a recommended consolidation week for rehearsing the tables that have recently been practised every third week or so.

# data[].attributes.body
The best methods for studying any subject

# data[].attributes.attachment_link.description
We are cognitive psychological scientists interested in research on education. Our main research focus is on the science of learning. (Hence, "The Learning Scientists"!). Our Vision is to make scientific research on learning more accessible to students, teachers, and other educators.

# data[].attributes.body
Excellent starter generator

# data[].attributes.body
So much stuff... read the maths gems

# data[].attributes.attachment_link.description
Resourceaholic - free resources and ideas for teaching secondary school maths

# data[].attributes.attachment_link.description
Almost 10 years after it started, the aim of this website remains the same: to get everybody enjoying their maths a bit more. Whether you are a teacher looking to plan a great series of lessons, or a student looking for some extra help with a topic, hopefully mrbartonmaths.com will have something fo…

# data[].attributes.body
Maths teacher at Michaela school

# data[].attributes.body
Jo Boaler

# data[].attributes.attachment_link.description
At youcubed, we inspire, educate and empower teachers of mathematics, transforming the latest research on mathematics learning into accessible and practical forms.

# data[].attributes.headline
Numeracy Ninja Free intervention resources

# data[].attributes.subject
Numeracy Ninja Free intervention resources

# data[].attributes.body
Loads of free resources

# data[].attributes.body
Mark McCourts Personal Blog

# data[].attributes.attachment_link.readable_text
In the last week alone, I have heard an Ofsted inspector call for maths teachers to move to mixed ability teaching and an apparent 'official' government body insist that all pupils within a year group should always be learning the same mathematical concepts.

This has been pretty much a weekly occurrence now for the last year or so.

The explanation must be, of course, the striking new evidence that mixed ability teaching in mathematics is more impactful than teaching maths classes in sets, where learning content is targeted at the point in the journey through mathematics that each set has reached, right? There could be no other logical or defensible reason for such influential bodies to call on schools across the country to undertake such a huge change in their pedagogy, curriculum planning, teaching methods, staffing, timetabling, resourcing or fundamental beliefs, right?

This new evidence, which puts the nail in the coffin of the old setting vs mixed ability debate, must be so overwhelming, so robust and trialed that we should all fall in line with the calls from these official bodies, right?

The trouble is, there is no new evidence. Nothing at all. Nothing to suggest an urgent and state mandated response to hurry schools up and down the land to swap to mixed ability teaching. Zero.

Well, that's kind of odd. Why would Ofsted and a Maths Hub be calling for this approach if there is no evidence to support such a call?

Mixed Ability or Setting

The discussion around how to group children when learning mathematics is as old as maths teaching itself. We should ask which is more impactful. Numerous studies and meta-studies have looked at the question and there is a wealth of published research on the issue. What does it find? Well, broadly, that there is little difference in outcome. Some studies suggest a slight improvement for low ability kids in mixed ability groups, some suggest high ability kids achieving worse results. Some suggest high ability kids doing better in setting, with low ability kids doing worse. Some highlight common practice of 'teaching to the middle' in mixed ability classes. Some studies show no impact at all. It is fair to say the broad picture of evidence in the debate is really rather fuzzy and the evidence certainly weak.

The main weaknesses in the data come from the tendency of studies in this area to conflate very different issues. Most studies looking at ability grouping, combine the practice of setting with other, non-analogous, practices such as streaming and other groupings. Prima facie it is clear setting and streaming are in no way relatable for the purposes of a robust study. The second weakness is the common practice of carrying out these studies without considering the subject specific nature of pedagogy. Studies tend to look at pupils across many subject areas, rather than commenting on the differences within studies. Where studies have gone further, for example Ireson and Hallam (2001), which looked at mathematics separately, the results are often quite different (in this particular case, showing setting improves outcomes in mathematics slightly).

There are some interesting studies underway, including a particularly notable one funded by the EEF, which should bring some more clarity to the subject specific part of the debate (though perhaps, from reading the proposed methodology, not to the differentiation between setting and streaming, which would be a great shame and missed opportunity). This will make for interesting reading when the study reports back next year.

For the moment, though, the evidence remains pretty much as it has been for a couple of decades: mixed and unreliable.

So, why change?

From the moment of coming to power in 1997, the Labour government repeatedly published commentary stating that schools should set children by ability unless there were extraordinary circumstances to justify mixed ability teaching. So strong was the belief in the efficacy of setting, both in terms of attainment and social justice, that Labour asked Ofsted to penalise schools where mixed ability practices were deployed.

Labour published statements making clear their belief was that mixed ability teaching can work, but only in cases where the teachers delivering were exceptionally good at doing so. For over a decade, Labour maintained its view and made clear to schools its beliefs. It is no surprise, then, that the majority of maths lessons in England's secondary schools occur in setted classes. As a result, most maths teachers have learned their craft in teaching maths in non-mixed ability classes. The workforce is set up to teach setted classes.

Given there is no new evidence to suggest a system shift towards mixed ability teaching, it is curious that the notion is gaining traction.

Throughout my entire career as a maths teacher, I taught classes in mixed ability and loved every minute of it. It was by pure luck that the first school I landed in as a trainee teacher was a Utopian, hippy kind of place. The maths department (by far the best maths department I have ever known) was staffed by huge intellects, all of whom were over the age of 50. Their combined knowledge on the teaching process was immense. All classes were truly mixed ability, which meant I had to learn how to deliver mathematics lessons with the lowest attaining and highest attaining, lowest ability and highest ability all in one room. It was a blast. The intellectual challenge was huge and I relished it. Every member of the maths team truly believed in mixed ability classes and had become masterful in their practices and pedagogies specific to mixed ability teaching to ensure they had high impact. Those are the pedagogies and practices I developed too and I remain thankful for that.

The Labour government's claim that mixed ability is only impactful with very specific types of teachers resonates with me. I have watched so many teachers being forced to teach mixed ability classes, without having had suitable CPD and time to develop necessary practices, which has always resulted in extremely sub-optimal lessons. Often a complete waste of time for everyone involved. As a young teacher, this used to upset me greatly, wondering why the outcome was so bad. Of course, as one learns more about teaching, one comes to realise that shoe-horning a teacher into a pedagogy is always a disaster.

So, the evidence does not support a change to mixed ability across the system, the workforce is not suitably developed to do so and forcing the issue without heavyweight CPD risks significant damage. Yet, still the call to change. Why?

Well, if it's not evidence, then perhaps it's...

Social Justice

An oft wielded argument in support of mixed ability teaching is the education for social justice angle. I loved that my classes were not segregated, loved that my pupils had equality of opportunity, loved the social interactions and what, as a young teacher, I believed to be the removal of stigma. But the social justice argument just doesn't stand up to scrutiny. Real social justice comes from becoming learn'd, from becoming autonomous and being able to lead a purposeful adult life. Yet, the evidence tells us that mixed ability practices don't result in greater gains in terms of attainment. Well, okay, but what about those pupils who would be placed in bottom sets in a setted scenario, surely they feel more included and less stigmatised? Yes, some do. But, and here's the rub, many don't. Where mixed ability teaching is forced upon teachers who have not developed necessary practices, the tendency to 'teach to the middle' leaves the lowest attaining and lowest ability pupils adrift, alienated and, most importantly, unable to learn. This returns us to the Labour government argument of mixed ability teaching only being defensible with appropriately skilled teachers.

And what about the highest ability pupils? Clearly, 'teaching to the middle' fails them. But, I have seen many mixed ability classes where high ability pupils are stretched and challenged because the teacher has sufficient subject knowledge and developed pedagogies to enable them to take a mathematical concept further and deeper than the aspirations of the national curriculum. This is wonderful to watch. Sadly, this is not common practice for two reasons. Firstly, most teachers have been trained to teach in a setted situation, where it would appear on first look that the content can be constrained to a fairly narrow inspection (more on that fallacy later). Secondly, the subject knowledge of teachers is not always sufficient to understand how to stretch a concept. This latter point is driving some of the worst practice I have witnessed in England's schools, which is also a result of official bodies erroneously spreading the myth that all pupils should learn the same content, namely the practice of keeping high ability pupils on mundane work for months on end. An increasing number of teachers and parents are telling me about their frustration at this practice, with many going further to say that officials have told them they are 'not allowed' to let the pupils progress further up the curriculum no matter how secure they are in the concepts they are being kept on. We do, of course, want to give pupils as many opportunities as possible to behave mathematically, so once an idea has been gripped, it is desirable to give the pupil opportunities to explore the concept further and more deeply, making connections and solving problems. But there is a point where pupils should move on. The idea that all pupils should be kept on a concept arbitrarily is simply wrong.

So, the social justice argument doesn't appear to be the driver either. After all, the Labour government was very committed to education for social justice too.

Ability or Attainment

The same inspector and same 'official' referred to at the start of this blog also included in their argument that the word 'ability' is damaging and should be replaced by the word 'attainment'.

There is a slight problem with this argument: the words don't mean the same thing!

Emotive language is used to try to advance this mind-numbing claim. Both people asserted that the word 'ability' is "dangerous".

This attempt to redefine language is a common tactic when trying to create a deliberate dark ages and gain control for ideological reasons.

The greatest problem with the mixed ability vs setting debate is the fanatical tribalism of those at the extremes of both sides (of a debate that the evidence suggests there isn't a fag paper between). Trying to discuss mixed ability or setting is often difficult because the debate is shut down by no-platformers, who will not accept any challenge to their beliefs, no matter how unsupported those beliefs are by evidence. Using words like "dangerous" is a way of shutting down debate. Who would want to be a "danger" to children?

Ability is not a dangerous word, it is a very helpful one. As is attainment. The difference between these words, in an education discussion, is really important and formative.

Attainment is the point that a pupil has reached in learning a discipline. It can change; pupils can unlearn as well as learn. It is not precise. But it is very useful in determining appropriate points on a curriculum from which to springboard pupils to new learning. We, as educators, continually assess these attainment points so as to best ensure the curriculum we are following can adapt and flex to what has been understood or forgotten. Knowing the prior attainment of pupils (rather than what has been previously presented at them) is crucial if we are to ensure pupils are learning appropriate new ideas and concepts.

Ability is an index of learning rate. It is the readiness and speed at which a pupil can grip a new idea. It can change; as with all human beings, pupils will make meaning from some metaphors, models or examples, more readily than they will of others. In maths, for example, we often see pupils quickly understanding some numerical pattern, say, who then take a long time to grip a geometrical relationship. An individual can have a high index of learning rate during some periods of their life and a low one at others. Again, as educators, we are continually assessing ability so that we are best able to judge the amount of time, additional practice, new explanations or support that a pupil needs in order to really grip an idea. Knowing the ability of a pupil (rather than wooly ideas of engagement or enjoyment) is crucial if we are to ensure that pupils are learning new ideas and concepts for the appropriate amount of time (rather than some arbitrary amount of time presented on a scheme of work).

Current attempts to abolish the word 'ability' from education's lexicon are deliberate in trying to remove nuance from the debate. The fanatics do not like nuance!

For more on index of learning rate, see J B Carroll (1963) and B S Bloom (1969).

All classes are mixed attainment and mixed ability

One issue with the practice of setting pupils is the assumption that those setted classes are now homogenous. They are, of course, not. Setting is merely a way of narrowing the attainment range within a class, not removing it altogether. With a narrower attainment range, teachers may focus their attention on fewer aspects of a concept and spend a greater amount of time with a greater number of pupils on the crux of the matter. The class will still contain pupils who need to access the concept at a lower entry point and those who have already gripped the focus of the lesson and can be stretched further in their thinking. The teacher must still be aware of the prerequisites and the possible areas for extension. The narrowing of the attainment range is a mechanistic way of maximising teacher focus. The range of abilities in the class is also always present in setted classes. Pupils will grip ideas at different speeds through different metaphors and explanations. This is true of the highest attaining and of the lowest. A common misconception is that pupils in low sets have very similar index of learning rate. They don't. There will still be pupils who grip ideas very quickly, because the ideas are being pitched at the right level for the pupils and the examples or models have resonated. Similarly, there will be very high attaining pupils in the top set who take a long time to grip an idea because the way in which it has been communicated has not allowed them to make connections to already known facts and ideas. The teacher must be aware of these attainment and ability ranges when working with pupils arranged in sets. The effective mixed ability teacher appears to be more alert to these differences, the ineffective mixed ability teacher ignores them and teaches to the middle. There are pros and cons in both approaches!

The impact of attainment range

Advocates of mixed ability teaching will often argue that the attainment gap does not matter - it can be any size. This is easy to dismantle reductio ad absurdum; would one advocate a class containing an individual who cannot count and another who is red hot at advanced Fourier Analysis? Of course not, so there is a range where the defence falls apart. The debate is really about how wide that gap can be and still maintain efficacy with a highly expert teacher. Those who refuse to engage with the nuance of the debate, choosing instead to maintain a fanatical stance of insisting the range can be of any size, serve only to weaken the argument for mixed ability teaching. I see many schools addressing the issue through logistical solutions such as having a top set and bottom set, but then six mixed ability classes between. This hybrid approach is a way of taking some account of the normal distribution nature of a year group. I would welcome research on these hybrid approaches so the impact can be better understood.

How big can the range be? This is really the question. We know that all classes are actually mixed attainment and ability, and that setting is simply a way of reducing the attainment spread to bring about efficiencies for teaching. The typical attainment range in mathematics at aged 11 in England is 7 years of learning. Every secondary teacher knows this; we all know 11 year olds who can do some pretty sophisticated mathematics and some who can't yet count to 10 reliably. Should these pupils be in the same class? Should these pupils be forced to be in the same class with a teacher who does not subscribe to the approach and has not been trained to be impactful in such a setting? Is it possible to be impactful across all pupils when the attainment range is 7 years? These are the questions schools need to ask.

Mixed ability and Mastery

I have written extensively on mastery and trained more schools in mastery approaches than any other organisation in the UK, so I will not rehearse the arguments for mastery here. It is however, worth highlighting, yet again, that mastery has nothing whatsoever to do with mixed ability. Indeed, most mastery approaches throughout the last 100 years have embraced non-grade settings, where pupils are of mixed ages. This is to create classes that are as homogenous as possible (a key aspect of mastery efficacy).

So, really, why change?

The inspector mentioned in this blog was once a teacher. They did not teach mixed ability. Yet, they now are encouraging schools to undertake a root and branches review and a huge amount of work to move to an approach that will not change their outcomes. There must surely be a reason these people are saying these words, yet I have never heard anyone articulate a defensible argument for the upheaval. Do they actually know why they believe what they espouse? (note: the 'official' at the event added, "off the record, I don't think this is right")

My humble advice

The outcomes in both mixed ability and setting can be great. The outcomes in both can be awful. It is the practices, structures, logistics and pedagogies that bring about efficacy or not. But do not for one minute believe there is any requirement upon you and your school to change. There isn't. The national curriculum is quite clear in its aspiration that the majority of pupils should learn the same content. Of course they should. The population of pupils is a normal distribution, so the majority around the mean are broadly similar in both attainment and ability. But majority simply means any number larger than 50%. Not all. There are many, many pupils who should be learning different materials, either because they are not yet equipped to learn the material of the majority or have far surpassed the majority.

I really loved teaching mixed classes. But I have a pedagogy and you have a pedagogy and they are not the same and they do not have to be the same. If you, as a whole maths department, want to teach your classes in sets, do. If you, as a whole maths department, want to teach your classes in mixed ability groups, do.

Just don't do either because you are blindly following the blind.

# data[].attributes.attachment_link.description
In the last week alone, I have heard an Ofsted inspector call for maths teachers to move to mixed ability teaching and an apparent 'official' government body insist that all pupils within a year group should always be learning the same mathematical concepts.

# data[].attributes.attachment_link.description
Explore mathematics with our comprehensive courses. Lesson content that reveals new approaches to learning will help you understand rather than just memorize solutions.

# data[].attributes.body
Incredible collection of problems

# data[].attributes.attachment_link.readable_text
Unfortunately, my father Don Steward passed away from Covid-19 on 3rd May 2020.

Throughout his working life he was passionate about improving the teaching of mathematics and has requested that all of his work remains freely available.

As per his wishes, I have uploaded all of his work to this Blog in the pages section which contains links to google drive where slides and presentations can be downloaded for free.

Don has also requested that those who use his work make a discretionary donation to charities supporting education in Africa.

We have set up a Justgiving fundraising page to support this wish below:
https://www.justgiving.com/fundraising/jessesteward

Many thanks for all of the kind messages we have received which are of great comfort to myself and the family.

Kind regards,

Jess

# data[].attributes.attachment_link.description
Unfortunately, my father Don Steward passed away from Covid-19 on 3rd May 2020. Throughout his working life he was passionate about improving the teaching of mathematics and has requested that all of his work remains freely available.

# data[].attributes.body
Sets of interesting problems