Why should you follow Mastery in Maths at KS1 & KS2? 6 real - and surprising - benefits for the whole school
Sceptical of mastery in Maths? Interested but not sure what it could look like in your class or school? This post outlines the six key benefits of adopting a mastery approach in a UK context, even when you’re not following an entire Singapore or Shanghai Maths approach. We look at how to reduce teacher workload through less in depth marking and simplifying planning; how to help children remember things they have learnt in previous days, how to help children apply their learning in unfamiliar contexts, how to raise end of key stage test results and why children become better Mathematicians through the adoption of mastery in Maths.
So, let’s kick off with the first benefit…
1. Mastery means less marking
That got your attention didn’t it? One of the cornerstones of a mastery approach is keeping your class working together so that everyone can access and master what is being taught. This provides continuous opportunities to discuss common errors and misconceptions as they occur.
Take a Year 1 class who are learning how to subtract on a numberline. The benchmark for the lesson is that you want all children to come away having made the link with their prior learning about adding on a numberline.
e.g. 14 – 6 = 8 is inextricably linked to 8 + 6 = 14.
Knowing which pupils have not made that link and why enables you to act swiftly and put a short, sharp, "keep up" session in place to give struggling learners further support. This is your detailed marking for those children.
Those children who are generally on track and at broadly the same level of understanding can have detailed marking replaced with discussion, questioning and modelling at the start of the next lesson.
Ofsted’s myth-busting document states, “Ofsted does not expect to see any specific frequency, type or volume of marking and feedback." If you are concerned with moderating books, the simple answer is to look at a progression of pages on the same concepts and you should see progress made, whether through oral or written feedback.
It’s quite a liberating experience and frees you to purely concentrate on learning, which is how it should be. Your policy can simply reflect the approach.
2. Mastery means children remember
Ever have children understand something one day, only for them to completely forget it the next? You need to make the learning deeper. Using questioning as a key strategy alongside a concrete, pictorial, abstract approach will support this goal. Teaching children to be mindful is crucial here. In other words, looking for patterns, drawing on things they already know and relating these to their current learning. It also means the teacher has to nudge the children towards what is relevant.
It’s a Year 6 classroom, round about March.
A hard working, stressed Year 6 teacher is exploring Algebra with their class. Specifically find all the possibilities where a + b = 15.
Here is a mastery influenced conversation between teacher and children:
Teacher: What do we know?
Pupil: "a" and "b" have to add up to 15.
Teacher: Okay, tell me more about 15.
Pupil: It has one ten and 5 ones. It’s an odd number. It rounds to 20.
Teacher: So which of those properties do you think will help us solve this problem?
Pupil: It has one ten and 5 ones, because the question tells us "a" is a two digit number.
Teacher: Is that right? Are you sure? Well if you say so, that does make sense. So what could "a" be then? What does that mean "b" could be?
If the children are given concrete resources such as place value counters or dienes apparatus, learning becomes de-mystified. “But they can’t have manipulatives in the test!” I hear you cry. No you can’t. But children can draw a pictorial representation.
The children in the above example could be helped significantly more. What if Algebra was discussed from Year 1 onwards? It’s a similar kind of discussion that can be built when looking at a number bond like 9 – [ ] = 7.
If children are given opportunities to discuss, reason and create with concrete resources, it will result in deeper learning that is more likely to stick, which means they can draw on it in later learning such as in the Year 6 example above.
By using strategies across school, such as training children to be mindful and staff to nudge, children are more able to remember and draw on these learning experiences. Even if some children "forget", it may well just take a quick reminder or brief example for that light bulb to come back on again.
And it will certainly mean that teachers are back tracking less, giving them more time to cover more if necessary or go deeper in key areas. In other words, to master concepts and content.
3. Mastery means raised test results
If you want your children to succeed, don’t race through content in order to cover everything for end of year tests. Don’t cram either as by doing so, your children may jump through a hoop but the following year they will suffer. Why? Because learning without any depth is superficial and superficial learning doesn’t "stick". We all know this, but it still happens due to a variety of pressures.
So what can you do instead?
It’s September in Year 4. You’ve had your class for three weeks now and are conscious that you will be refining formal written methods throughout the year. You already see a huge breadth of abilities and are questioning whether certain groups of children have the prior learning necessary to be able to reach end of year expectations.
So, you decide to focus on Number until the children really understand Place Value before moving on. You know this will mean that all children will then have a good chance of refining their understanding of formal written methods.
You decide that if you are going to have to cover some content superficially, you will make it content that will make the least difference to your class. You might find you can actually speed learning up later in the year because of their development in Place Value.
One way to raise test results is to cut down the amount of content needed to be taught by enabling children to make connections across Mathematical concepts.
So when your Year 2 teacher is working on telling time to the nearest 5 minutes, they take it as an opportunity to revisit and consolidate counting in 5s.
When your Year 3 teacher works on written methods of subtraction, they use money as a context.
When your Year 4 teacher is teaching scaling, they use it as a vehicle to not only develop their multiplication facts but they do this in the context of measures by creating the dimensions for a scaled model.
Linking across areas frees up teaching time and enables children to deepen their conceptual understanding, seeing connections with their learning in a test situation, with unfamiliar content.
4. Mastery means simplified planning
What’s the purpose of planning? To enable teachers to know what they are teaching and to give children well structured, thought through learning opportunities. So why do we need strict planning formats with multiple boxes for differentiation and plenaries that get paid lip service to or teachers fill in through gritted teeth?
Well with a mastery approach you don’t. You create one really good lesson for all your class. You spend time thinking through the best way to get children to really understand the concepts being learnt and putting in place the scaffolded learning that supports them in getting there. That support is by deliberately planned variation taught through intelligent or guided practice. These strategies sit alongside being mindful, nudging and using a concrete, pictorial, abstract approach as key strategies to enable all learners to access their learning.
A Year 5 class are starting to learn how to multiply 3 digit numbers by 2 digit numbers. Instead of traditional "differentiated activities" for less and more able, a mastery approach would utilise variation in a sequence of questions for the children to work through under the guided support (intelligent/guided practice) of the teacher.
Such as sequence could be 64 x 7, 364 x 7, 364 x 9, 364 x 90. We’ll look closer at that kind of sequence in a later blog post dedicated to variation.
How does all this simplify planning? Because your plan may just have these 4 calculations written down, a couple of key questions and an independent activity for all children to complete on it. No separate boxes for differentiated mini lessons within the class. What about plenaries? The purpose of a plenary is to ensure children are given another chance to make sense of their learning and for you as a teacher to assess where children are. By utilising variation alongside intelligent/guided practice, and occasionally pausing during independent activities, you are doing this throughout the lesson anyway.
Merely mentioning the word "textbook" instantly evokes all kinds of reactions (usually related to your own ill-experienced use of them as a child). But that is not how they are used in a mastery curriculum. Instead, they are the critical friend, the expert in the room, the alternative to doing things "the way they’ve always been done".
If your staff need support, you provide resources to do so. So an investment in textbooks can massively change the difficulty of planning and quality of learning. Staff can simply reference or cut and paste from the scheme in their planning. You will know that your staff are then using expert, quality ideas, structure and methodology freeing them to be able to put their energies into delivering, supporting and assessing children in their learning.
And they might even thank you for it.
5. Mastery means children apply their learning
The pedagogy discussed so far encompasses keeping your class working together, depth, questioning, being mindful, nudging, variation, intelligent/guided practice and a concrete, pictorial abstract approach. It is the combination of all these elements, heavily relying on greater depth and ability to reason through discussion that supports children in transferring their learning to new contexts.
"I can’t believe only a few children got ‘what fraction of the shape is not shaded?’ in the test. We did that a week ago and they all got it then.” Says a Year 3 teacher. Sound familiar?
This could have been because their learning was not deep enough, was not in the same context as the test question or the style of teaching lent itself to ticking off a "do this, then this, then this" process. I’d bet it’s a combination to some extent of all three.
With a mastery approach, the children will have had significant experience working on a range of problems such as “How many shapes can you build using 2 colours of multilink cubes? Use post it notes to label the fraction of the blue cubes of each shape.” These will be coupled with questioning such as “How do you know what the denominator is? What do you notice about the numerator? Is it true or false that the numerator will always be the amount of blue cubes? What about the red cubes?”
Whether or not it was intended that way, The National Numeracy Strategy and Primary Framework created a format of children being giving lists of objectives and success criteria that could be learnt and ticked off in fairly isolated chunks. They would then simply recall whichever set of success criteria applied to any particular test question. In practice, this fails in most schools because the children are unable to apply what they have learnt in a new context or problem. A mastery approach provides the framework of sustainability, where children are more able to apply their learning in a range of contexts.
6. Mastery means children are better Mathematicians and learners
We don’t become teachers or school leaders to push children through tests. We want to help children learn. To make a difference.
A good teacher helps a child when they find something difficult. A great teacher enables a child to persevere and see learning difficulties as exciting challenges that they, their peers and adults can help them overcome. This is a mastery approach.
A good leader gives staff resources to help them be better teachers. A great leader inspires the whole school community to make changes that will hugely enhance learning. A mastery approach is one such change.
When children can make connections in their learning, sustain their understanding and build on prior learning they are building a rich canvas of learnt experiences that makes them not only better Mathematicians but better learners altogether. That has to be the greatest benefit of adopting a mastery approach of all.
About the author
Pete Richardson is an Assistant Headteacher with a focus on assessment, technology and Maths. He's a passionate convert to a mastery approach, blending the best of Singapore, Shanghai and home grown pedagogy. Follow him on Twitter @primarypete_
From our blog: What does Asian Maths mean for your classroom?
Michael Tidd's journey to mastery: Mastery Maths in KS2
How is mastery working for you?
If your school is following or thinking of following a mastery approach in Maths, we’d love to know how it’s working for you. Increasingly schools who use our one-to-one specialist Maths tutors for their interventions are telling us that this is the framework that their pupils understand so that's what we teach. It’s been really interesting for us over the past year or so, since the new curriculum and its focus on depth and mastery to work on adapting and personalising our lessons to tie them in to what’s going on in pupils' classroom Maths lessons.