How to Develop Mathematical Fluency at KS2
The increased mathematical fluency in pupils with a range of abilities makes it a very effective intervention
Year 6 & Key Stage 2 Phase Leader, Northumberland
What is mathematical fluency?
Fluency can be tricky to define, but broadly speaking it refers to a pupil’s ability to know and recall mathematical facts efficiently, and to perform mathematical activities accurately and quickly.
Why is fluency important in maths?
In its truest sense, fluency is much more than just knowing facts. It’s the ability to flexibly choose the most appropriate method for the task at hand, understand and explain these methods and, ultimately, quickly arrive at the correct answer.
It gives gives pupils the ability to develop number sense and delve deeper into maths and in order to:
- Understand the flexibility needed to succeed
- Choose the most appropriate method for the task at hand
- Apply their skills to multiple contexts
- Explore the different ways that a maths problem can be approached
Plus, fluency is essential for KS2 SATs success:
Without a strong level of fluency, pupils often take up time carrying out mental questions using a written method leaving them unable to complete the whole arithmetic paper.
The reasoning papers require pupils to demonstrate deep understanding rather than just mechanical repetition. By focusing on building fluency throughout KS2, pupils are exposed to varied activities and contexts through which to develop their understanding.
How to develop fluency at KS2
One of the most beneficial things for pupils is, quite simply, the chance to practise – just practise – until they are confidently calculating.
Then, when pupils move on to more complicated problems, they’re building on a solid foundation. As primary teacher and maths consultant Rebecca Jakes says, “One of the most important things I’ve witnessed over the last couple of years is how fluency in calculations has led to pupils tackling problems with greater confidence and resilience“.
When pupils are quickly able to recall number facts and simple calculations, this reduces the cognitive load: how many demands are placed on their working memory. For example, two digit column addition of 25 + 58 is much easier for the pupil who automatically knows that 5 + 8 = 13. They’re not having to waste working memory calculating 5 + 8.
How Third Space Learning supports all KS2 pupils to develop mathematical fluency
We help schools provide more opportunities for regular practice through our programmes of 1-to-1 interventions and high quality resources.
Schools choose which pupils they’d like to receive 1-to-1 support and, during their weekly online 1-to-1 lessons, tutors work with their pupils to practise their calculations, dissect maths problems and explore the different ways they can be approached.
By working with each pupil to identify the calculations required and encouraging them to verbalise their thinking and the steps they could take, tutors help pupils build mathematical fluency and deepen their understanding to become both procedurally and conceptually fluent.
Alongside this, Third Space Learning schools get access to hundreds of resources which enhance whole-class teaching and support pupils to achieve fluency in maths.
Four techniques to develop mathematical fluency at KS2
- Allow time for regular practice
Drill and memorisation is a great way to reinforce this and creating a set time during the maths lessons or school day for this can be really effective. If you feel it’s getting repetitive for your pupils, you could explore more game-like, fun activities. These are a great way to keep pupils engaged and motivated. For example, try creating your own songs or actions to add to your times tables or number bonds chants.
As well as through the 1-to-1 lessons, schools signed up to our programme also get access to additional opportunities for fun fluency practice across Years 1-6 through the resources in the Third Space Maths Hub. Our most popular resources include ‘Fluent in Five’ (quick-fire daily arithmetic problems to build number fluency in 5-minutes a day) and all the fun games and activities in our Ultimate Times Tables Resource Packs
2. Don’t neglect conceptual understanding
Practice in isolation is not enough. A focus on conceptual understanding is vital to ensure pupils have understood the underlying maths behind a problem and aren’t just reciting learnt number facts. Keep an eye out for pupils who are struggling during your regular practice sessions and ensure they have the chance to address any gaps or misconceptions.
Because they choose which specific pupils they’d like to receive the weekly 1-to-1 lessons, our intervention programmes allow schools to easily provide more targeted support for these pupils without having to take the focus away from regular practice for the rest of their class.
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3. Practise in varied contexts
Pupils who may have shown a level of fluency in a particular concept can still find it difficult to use those skills in different types of questions. For example, a pupil may be comfortable with times tables facts, but then struggle to apply these when calculating the area of a shape.
Where possible, try to include opportunities for pupils to use and reinforce a range of skills across the maths curriculum and make it clear to pupils when they are using skills that they have already learnt. Exposing your pupils to this kind of variety across the term and year helps them develop true mathematical fluency.
Because pupils have the same tutor for each of their 1-to-1 lessons, the tutor is able to review which topics a pupil has previously learnt but is struggling to apply to new contexts. They’re then able to use this information to personalise each lesson to allow opportunities to apply skills to different contexts.
4. Observe and assess
Accuracy is a key element of fluency in maths so it’s important that teachers are using assessment during lessons and picking up on mistakes or inaccurate answers if and when pupils reach them. Giving pupils the responsibility to check their own accuracy through self-assessment is also a great way to boost fluency.
However, in a class of 30 it can be hard to always pick up on where each pupil is in their understanding. Through our weekly 1-to-1 lessons, pupils benefit from someone monitoring, reviewing and building on their answers in real-time. Tutors are able to spot and address and gaps or misconceptions as soon as they arise, ensuring a consistent focus on both accuracy and mathematical understanding.