Thank you for your question, Claire. It is certainly the case that, in the UK and other Western jurisdictions, primary classes often contain pupils spanning a large attainment range. In year 4, say, it is common to find pupils who are operating at a mathematical level beyond what would typically be expected of a year 6 whilst also finding pupils who are operating at a mathematical level below what would typically be expected of a pre-school child. This is an enormous challenge for teachers to overcome.

There are approaches we can take to make such classrooms more effective, including in-class groupings, which change from subject to subject, day to day, for instance. Alternatively, when it is time for maths, we could use a common hook from which to spin off many different activities – so pupils are, in the face of it, working on the same problem, but at varying levels of complexity.

You ask about implementing a mastery approach in such a classroom. These two goals (having classrooms with very wide attainment gaps and running a mastery approach) are not compatible. A mastery cycle approach to teaching and learning relies on the group being closely enough aligned in terms of attainment to allow for the effective use of the elements of the model – that is, prerequisite quizzing and pre-teaching until all pupils are ready to progress with learning the new idea, whole class instruction, working on tasks specifically about the new learning goal (not spanning a large range of access points), ongoing formative assessment with immediate corrective teaching, extension tasks related specifically to the new idea, and testing at the specific level of difficulty of the new learning goal.

A mastery approach does not work with a large attainment gap.

This is why the main formulators of a mastery approach would often use non-grade settings – in other words, mixed aged classrooms – to enable groups to be a homogenous as possible in terms of their current attainment.

But this is not a very useful response to your question, is it? There’s little point in me just saying it can’t be done.

Primary schools can use a mastery approach. In fact, if a mastery approach is to work anywhere, then it is critical that primary schools use it. But it needs to be implemented from the very beginning.

Which perhaps brings us on to the next question...

Thank you for your question, Christopher.

It is not unusual to find implementing a mastery approach somewhat easier in KS2 than KS1 in the current system (which has been a product ofmany years of a conveyor belt approach to curriculum). I’d suggest this isbecause KS2 pupils – even those at the lowest level of attainment – have abetter developed schema of knowledge than KS1 pupils. Making sense of new ideas is only possible through constructing that sense from ideas already understood – so the older pupils have more stories, metaphors and images on which to call. The vast majority of what children learn is beyond the content of the school curriculum, so it is often a happy surprise to find that older pupils can construct new meaning in unexpected ways.

There is a fear (and I don’t use that word lightly) amongst many primary teachers that there will be professional consequence to them if they, themselves rather than the pupils, do not ‘keep up’ with the curriculum. I’ve written many times about this conveyor belt approach problem, so won’t labour the point here, save to say that it is understandable that teachers in KS1 feel they are unable to work on an idea such as number sense or place value for a very prolonged period of time. Teachers know (and will tell you privately if they feel they are not at risk of admonishment) that moving on through the curriculum content when pupils have not yet gripped obviously prerequisite ideas is a reckless and idiotic thing to do. But they often feel they have no choice.

I think we make a huge error in England by starting formal mathematics early and racing towards a view of successful mathematics learning that holds written algorithms up as the way of identifying whether or not a 4-, 5-, 6- or 7-year-old child is doing well. I suggest we would perhaps have a great deal more success in our aim for all pupils to become mathematically literate if, instead of the current fetish for standardisation of written responses, we provided an early years (up to age 7) education that focussed on truly understanding numerosity, place value, proportional reasoning and relationships between quantities – none of which is best achieved through a worship of written algorithm.

A prolonged view of early years education (as is not uncommon around the world) would, in my view, give a much stronger foundation for all pupils to construct a successful understanding of mathematics as they continue through school.

All of this can be achieved through a mastery approach, but it requires a shift in policy that takes the aim of all pupils having secure foundational knowledge in place before embarking on a more formal process of using that knowledge to develop the ability to communicate through mathematical symbolism and convention. Sadly, there is little appetite forsuch an approach in the UK.

Thank you for your question, Nilam. It’s a perennial problem, isn’t it? We all know that moment when a pupil says they are finished long before we expected them to be. Even the most careful planning and the most diligently selected tasks that take into account everything we know about the pupils in order to get the level of difficulty just right can sometimes leave us surprised by the speed at which an individual grips and overcomes the problems. This is, of course, also a pretty lovely moment –it shows the pupil has really applied themselves and worked determinedly to nail whatever task they have been set. I think there are two important responses that should come next.

Firstly, we should appreciate that some pupils absolutely love to completetheir work quickly, but that this might not always align with completing their work carefully. So, teachers take the time to ensure they have presented their thinking elegantly and with mathematical precision – we should always be encouraging pupils to treat mathematical communication with the attention it requires.

Assuming they have indeed completed the task to the highest level of accuracy and mathematical sophistication they can, then, secondly, I think it is important that all teachers have up their sleeves a range of challenging prompts that extend the task, engage the pupil in serious thought, and keep them working at the limits of their comfort zone. Thereare lots of stock responses we can quickly use that have huge impact (perhaps it would be a good idea if teacher training included dozens of these stock responses, so we all know them before facing the situation you describe?)

Some of my favourites include:

• Can you generalise your solution?
• What if this approach was applied to *insert new scenario*?
• What if the questions were posed in a different base?
• Under what conditions would your solution break down? What are the boundary conditions of the idea we are learning about today?
• Now that you have gripped this new idea, what ideas did you once hold to be true are now probably false?

I hope that is a useful starter for the list... but would love to hear other people’s favourites. Perhaps add in the comments below?

Thank you for your question, Andy. This has been addressed in the previous questions, so I’ll just briefly reiterate: absolutely not. Mixed attainment (where the gap is large) and a mastery approach are not compatible models.

We know that learning takes place at the boundaries of our comfort zone, so let’s take the education of all pupils seriously and ensure that the new ideas we are asking them to grip are at the right level for them.