What Is Fluency In Maths & How Do Schools Develop It?
Here experienced maths lead and Third Space Learning user, Rebecca Jakes gives a clear definition of what fluency is and means, what fluency looks like within a mastery curriculum, and, crucially for other primary teachers, four proven techniques and resources that she has seen develop fluency at Key Stage 2.
When the new maths curriculum was introduced a few years ago, with its triple emphasis on fluency, reasoning and problem solving, there was a sharp intake of breath amongst teachers and leaders across the country.
The higher expectation overall alongside the introduction of a new curriculum for mastery and depth was quite daunting at first. How would the children cope? How would teachers cope?
Central to this new form of mathematics education all was this concept of maths fluency. What did it mean, how should we teach it, and would children be able to achieve the necessary level by their KS2 SATs?
A few years down the line I have recently found myself reflecting on the changes from the vantage point of being a maths leader and maths adviser across several schools and assessing which interventions and initiatives we’ve used that have really worked to develop pupils maths fluency at KS2.
Fluency Definition: What is Fluency in Maths?
Fluency in maths is about developing number sense and being able to the most appropriate method for the task at hand; to be able to apply a skill to multiple contexts.
The National Curriculum states that pupils should become fluent in the fundamentals of mathematics through varied and frequent practice. While a part of this is about knowing key mathematical facts and recalling them efficiently, fluency means so much more than this at it allows pupils to delve much deeper.
How Does Mathematical Fluency Fit with Reasoning and Problem Solving?
The mastery curriculum for primary schools places problem solving at the heart of mathematics with the main aim that every child can learn to solve sophisticated multi-step word problems in an unfamiliar context.
To enable them to achieve this, pupils must develop their conceptual understanding, mathematical thinking and use of mathematical language. This is where fluency and reasoning come in.
How Fluency And Reasoning Work In Primary Maths
Fluency in maths works through intelligent practice (rather than just mechanical repetition). Once a child has grasped a mathematical concept, the idea is that they are exposed to varied fluency activities which develop their understanding.
These activities also require them to use verbal reasoning to justify and explain their thinking in order to solve word problems in an unfamiliar context.
Making this happen in the classroom is quite straightforward when you focus on the unit you are teaching.
However we’ve all felt that frustration when children are given problems that include applying skills that have been previously taught. They look at you with a blank face, completely at a loss of what to do. (See this post on the science of memory and forgetting for more detail on what’s happening here)
So how are schools ensuring children don’t forget the basics as they move from one unit of Maths to another? Simple – they are adding in some extra time every day or week to enable them to simply practise those Maths skills that they have already been taught.
What is the Best Way to Teach KS2 Maths Fluency?
The mastery curriculum has meant that finally children are allowed to just practise until they are confidently calculating. And, over the last couple of years, I’ve witnessed how truly beneficial this can be for pupils.
Children are becoming fluent in calculations and times tables and they’re loving it!
Their fluency in calculations such as their multiplication facts has led to pupils tackling more complex problems with greater confidence and resilience.
Because they are no longer having to tackle remembering how to do the calculations needed or the most appropriate strategy to choose each time, they are able to put all their energy into how to solve their mathematical problem.
As a primary teacher and consultant I am fortunate to see the many different ways in which schools are giving children time to hone the skills needed through daily or weekly practice.
There is a lot of variation and different methods for tackling this, but the one thing that is constant between them is that they are producing good or excellent outcomes in Maths.
So what’s working?
The following are the four different approaches to improving fluency in Maths at KS2 that are used by schools in my area.
Approaches to Fluency 1: Mastery Time
As Maths leader at my previous school, Woodcot Primary, I introduced a set time each day of around 30 minutes following a carousel approach to fluency practice.
During this time the class teacher has a guided group where they either:
- Work with pupils who have not fully grasped a concept during that day’s lesson.
- Pre-teach target children.
- Work with target children on areas of arithmetic they are not yet fluent in.
The rest of the class work on whatever the focus is for that day. This is usually practising fluency in calculations or nailing the times table and related division facts they are working on.
In KS1 there is a heavy focus on number bonds and memorising number facts. Most year groups have one day of the week where children practise using online Maths games to embed number relationships.
Using this approach has seen a big impact on pupil confidence in maths and resilience. As pupils gain fluency in calculations, they are no longer worrying about making mistakes, leaving them to focus on unpicking sophisticated problems with enthusiasm.
For Year 6 pupils it has had a great impact on arithmetic scores, leaving children plenty of time to learn the reasoning and problem solving skills needed for the KS2 SATs.
Approaches to Fluency 2: Maths Meetings
Haselworth Primary School hold daily ‘Maths Meetings’ in all of their year groups.
In KS1 these focus on counting (forwards, backwards, 2s, 5s, 10s etc.) in a fun context such as ‘counting tennis’, where pupils bat numbers back and forwards with a partner. Number bonds and quick recalls of doubles and halves are also a focus in Years 1 and 2.
Read more: 10 ways to memorise number facts at KS2
KS2 Maths Meetings have more of a focus on times table facts with daily practice and a weekly test. They also have a daily fluency activity based on agreed key fluency skills for each year group.
In addition to this, Year 6 do daily Maths SATs Facts from Vocabulary Ninja and Fluent in Five arithmetic practice from Third Space Learning.
Approaches to Fluency 3: Weekly Repetition
‘Number of the Week’ sheets are becoming a common addition to fluency practice. The example here is one taken from a Year 4 class at a school I moderated with recently.
Teachers reported that the biggest impact from doing this was that pupils were able to visualise a number and its properties much more quickly in other contexts.
Fluent in Five Arithmetic Pack: Years 3 to 6 [Weeks 1 to 6]
Use on a whiteboard or print out our SATs style questions, complete with progression document & help for pupils to choose mental or written method
The sheet can be varied for different abilities or year group focus; concrete resources can be used to support learning when necessary and the pupils reportedly enjoy the familiarity of the activity.
Approaches to Fluency 4: Targeted Fluency Focus
At my new school Brockhurst Primary, each year group has a set fluency focus per half term.
During each half term, teachers provide fluency activities on a daily or weekly basis and ensure there are visual reminders around the classroom to bring it to the forefront of the children’s minds.
Every half term children take home a ‘Fluency in Maths: Key Facts’ sheet with one area of Maths to focus on, enabling parents to become involved in learning and have a greater understanding of the expectations in Maths for their child.
By the end of the half term, children should know these facts and the aim is for them to achieve true automaticity so they can recall them instantly.
Many classes also hold a ‘daily Maths mile’ where children walk or jog a mile (or however far they can get in fifteen minutes) while practising their area of focus as a class.
The Best Free Resources to Develop Fluency in Maths for Year 3, Year 4, Year 5 & Year 6
Finally, here are my recommendations for the my top three engaging (and mostly free) resources to develop fluency in maths at KS2. They’re great for developing fluency in short bursts throughout the term.
1. Fluent In Five Daily Arithmetic Practice – Third Space Learning
This free arithmetic resource is designed around the teaching for mastery approach, and the daily activities really do only take five minutes.
In Year 4, I use them as at the beginning of a lesson and find them brilliant for sharing ideas for mental calculations. They are particularly good for children who don’t make obvious links like number bonds and near doubles and are overly reliant on written methods.
For Years 5 and 6 they provide an opportunity to practise arithmetic fluency on a daily basis, and offer the perfect chance for teachers to address misconceptions or set arithmetic targets. The other advantage of Fluent in Five is the emphasis on finding the most efficient strategy to use when solving the arithmetic questions with the ‘try written method’ or ‘try mental method’
Schools who use Third Space Learning’s 1-to-1 KS2 Maths intervention programme have access to all 36 weeks of Fluent in Five, alongside arithmetic tests, SATs papers and diagnostic quizzes.
They also have an amazing video CPD library in their online Maths Hub which is my ‘go to’ when I’m introducing a new area of Maths or if I have a pupil or group of pupils who can’t grasp a concept.
Many of the games and activities on Mathsframe are free and come with a range of support and challenge.
I particularly like the ones shown above for children who are still building conceptual understanding (but also for those who have learnt a method but don’t actually understand what they are doing).
As a paid member, you also have access to assessments and variations of problem solving questions.
3. Prodigy Game
My class would play prodigy all day long if I let them. It’s free and takes minutes to set up. As a teacher, all you need to do is set tasks regularly to match what the children are learning in class or to revisit prior learning.
Each pupil has a login and they have to solve maths problems to move through the game.
They can meet other people from their class but not anyone from the outside world so it’s also pretty safe. It’s great for home learning; the only drawback is getting them to stop playing at the end of a session.
Other resources to build Maths fluency at KS2
If you’re looking to embed fluency in Maths, there are many more resources out there to help. The overwhelming favourite is Times Tables Rockstars which will give your pupils the confidence, speed and accuracy they need to fly through the Year 4 Multiplication (Times Tables) Check.
How I Teach Mathematical Fluency to Year 3 and Year 4
So, after seeing so many approaches to developing fluency and number sense, what have I done in my own practice? The answer is simple – I’ve shared it and used it.
In Year 4 where I am based, the teaching team were reflecting on the ‘use it or lose it’ issue that arises when an area of Maths is mastered but not returned to.
So after sharing the ideas I have seen we decided to incorporate our favourite bits into one model:
Sticking with the carousel model, each day pupils practise the mathematical concept or fluency they are focusing on in addition to the fluency focus from previous terms until they’re giving accurate answers every time.
On one day they have a guided group with an adult (either class teacher or LSA) and if need be the teacher pre-teaches or works with small groups of pupils who haven’t grasped concepts in that day’s Maths lesson.
One session is on laptops and the ‘Maths facts’ session is using the weekly repetition example shown above.
Having just read Clare Sealy’s amazing blog on teaching telling the time, we are now thinking about swapping one of the activities to one based on fluency in reading time.
As Clare quite rightly said, we all tear our hair out when trying to teach time but only do so once a year. Maths Express is accompanied by using ‘Fluent in Five’ at the beginning of each Maths lesson or as a morning challenge when children arrive at school.
Why have we called it Maths Express? The Year 6 teacher and Maths Lead at Brockhurst had given this name to her sessions and we liked the sound of it. Some of the boys in our year group are mad on trains so we decided to use it too.
The children love the sessions and one child commented, ‘I know why it’s called Maths Express. We are all on the train together heading in the same direction and we want to get to the same place.’ I couldn’t have put it any better myself.
- What is Maths Mastery? Techniques and Procedures
- Maths Mastery strategies and resources to support your maths teaching
- Ultimate KS2 Checklist Of 33 Mental Maths Strategies
How Third Space Learning supports the development of maths fluency
Each of the lessons in our interventions provide a journey through each concept. They begin with a recap of previously learnt topics that link to the current lesson, using real world examples and deep questioning to introduce and develop the pupil’s knowledge of the topic. Pupil and tutor then work together on procedural fluency for the topic of the week, building towards more complex problems as a pupil masters the concept. This process gives us a great opportunity to work on misconceptions as they arise, and the tutors can assess and use this knowledge moving forward.
Do you have pupils who need extra support in maths?
Every week Third Space Learning’s maths specialist tutors support thousands of pupils across hundreds of schools with weekly online 1-to-1 lessons designed to plug gaps and boost progress. Since 2013 we’ve helped over 60,000 primary school pupils become more confident, able mathematicians. You can learn more about our interventions or request a personalised quote for your school to speak to us about your school’s needs and how we can help.