A word that seemed to be a buzz word when the new National Curriculum was published was ‘fluency’. The definition of fluent online is ‘smoothly graceful and effortless’. In looking at the aim in the National Curriculum, it seems to refer to bring able to understand why methods work in Maths (not just go through the motion of doing the method) and apply the method to appropriate questions and problems. So how do we develop Mathematical fluency in children? Do we give them a list of calculations? Or is there more required?
Recently our Year 6 began that wonderful journey of dividing by two digit numbers. Why doing this with an extra digit is such a great jump I’m not sure – maybe another focus for a future blog…
Anyway, as many Year 6 teachers will know – along with the teachers who introduce any formal methods of calculation, helping the children understand why they use these methods and the maths behind them is much harder than just getting the children to work on the mechanics of the calculation. Thus, scores and scores of children are taught the method without necessarily understanding the maths behind them. Since the introduction of a mastery approach to teaching maths, this has been improving.
This is how we tackled this challenge whilst trying to develop a deeper understanding and mastery of the calculation method.
Naturally in the first session there was already a range of confidence. Some of our Year 6 children were already familiar with and confident with long division whereas some had just about still got a grasp on dividing by a single digit number. Those children were offered the opportunity to either go and attempt a few calculations to make sure there were confident or attempt an estimation challenge involving the long division from nRich: Dicey Operations Game 6
With the rest of the children, initially after a visual representation of the method, a number of demonstrations and a discussion around how the remainders and other aspects of the method worked, the choice was again given to the children where to pitch themselves. Those who felt confident then went to try either of the before mentioned challenges where those that did not stayed in the ‘Long Division Clinic’. The Clinic involves whiteboard work, discussion and targeting from the Teacher and explaining to their peers the process they are working through with careful listening in by the Teacher.
In order to enable the children to practice the calculation and get a real-time assessment on whether they were correct or not whilst I worked with those who still needed to grasp the method we used the website MathsBot which creates instant problems and the chn could quickly uncover the answer on the IWB to check they were correct. If not, they were to analyse, with a partner if needed, to uncover the error.
2. Clinic Continues
Because of the nature of the first session being much more introductory, there is more time given now for those who are less confident to continue working in the Clinic and then try independently. By this stage also, by scrutiny of the previous lesson’s learning, some children may have been discovered who were not as confident as previously thought. These can come into the ‘Clinic’ briefly to check where any misconceptions are.
Meanwhile, those who are more confident have choices on how to push themselves further. Try some more challenging problems set by the Teacher, work on showing their remainders as fractions or decimals and finally some reasoning and problem solving problems set by White Rose Maths which develop understanding on how to apply this method to problems.
It is well documented that we learn 20% of what we hear, 30% of what we see and so on… But we learn 95% of what we teach others. So the question was for me then ‘How could I get my class to teach others in a way that will include all?’ Of course I could go down the route of whole class presentation… But if I were a10 year old child I would struggle to stand up and teach my peers the basics of long division. Teaching to groups is always fun, less intimidating. The question that method throws up is how could I accurately assess if each individual child had met the LO when different groups are teaching each other at once? To have each group teach other one by one so I could listen to every child would be too time consuming. So what?
I was led to an app called Explain Everything which was perfect. @ICT_MrP was the first to introduce this to me.
The app allows the user to create a video whilst using a drawing tool or a highlighting tool and images. This gave the perfect opportunity for the children to ‘teach’ someone how to use skills in Maths. In doing this, the children themselves become increasingly competent, developing their fluency.
This video not only gives the children an opportunity to engage in a meaningful and purposeful activity, but it can also serve as a future stimulus to remember previous learning. These are some examples:
Not only does this allow the children the opportunity to explain the workings behind the formal method, it encourages them to take it step by step and plan how to break down the calculation for someone that is new to the concept. There is also that extra incentive where they could have their work used for a huge purpose – to have on the school website as part of our calculation policy and teach others who are interested in how to use this formal method.
Considering how to group the children is key in this task. Children should be allowed the opportunity to work independently as some will feel inhibited by not being able to express their explanations with extra discussion. However, some children will not yet be fully confident in their abilities and so mixed-ability pairing is extremely useful here. This is not only enable the children to further internalise the formal method but also make peer coaching another input for all children to get this calculation approach.
4. Take on the Problems!
By this stage – most children should be fairly competent in the method or at least much more closer to grasping it than they were before. This is where the real application, the whole reason why we learn these methods, comes into play. A selection of problems are available of differing levels (strictly no straight calculations) – the children are in mixed ability pairs and take on the challenges they wish to try. This ‘Hot/Spicy/Chilli’ approach means they can start where they feel comfortable and then advance or step back where they feel is necessary. The challenges can be sourced again from the White Rose Maths documents (they have a lot of sessions when teachers are required to teach a new calculation method) and also many other areas. These challenges are completed on large, graffiti paper so that concerns about presentation or neatness can be put to one side and the maths is the main focus:
As the session progresses, the children are expected to discuss their thoughts and their answers. This will again develop children’s ability to talk through the calculation. This would be the equivalent of the ‘Ruler of Reasoning’ session in my ‘TalkMaths Approach’ shared in a recent post. The Teacher’s role is to step back and listen in to discussions. From this observation they can address any final or further misconceptions that can be dealt with as a whole class.
No approach is foolproof. There will still be children who won’t have grasped the concept after this approach – however, this will give children a pace to suit them. Faster and more in-depth if needed, slower and more probing if required. Teaching and learning formal methods of calculation is a necessary facet of maths teaching in KS2 Maths and a lynchpin in any child’s mathematical toolkit. A deeper understanding must be developed – hopefully this will help.