By Lydia Davison, Maths Lead and Teaching and Learning Lead, Newbold Verdon Primary School in Leicester
A narrative often surfaces when it comes to the use of manipulatives in the primary mathematics classroom. In my experience, primary educators frequently talk of using manipulatives such as Numicon apparatus in the Foundation Stage and Key Stage1 – for interventions, as part of a Maths display, in a resource area for the children to dip into and pick from. However, the use of manipulatives for teaching mathematics in Key Stage 2 can often be limited.
Why are manipulatives key to learning across KS1 and KS2?
- When used deliberately and effectively, they help children to visualise, explore and represent mathematical concepts, patterns and relationships.
- They are fully inclusive and support all learners to engage deeply.
- They enable children to transition from concrete to pictorial to abstract thinking.
- EEF’s Guidance Report for KS1 and KS2 names manipulatives as powerful tools and scaffolds to support children to engage with mathematical ideas.
Why can teachers struggle to use manipulatives in KS2 alongside schemes of learning?
- As we move through the Key Stage, children are expected to learn more abstractly.
- A pressure to evidence all learning.
- Some schemes of work are resourced with worksheets. When they do suggest the use of different concrete manipulatives, schools may not have sufficient resources to make this effective.
- Educators can often experience a “straight jacket” feeling when they want to show ultimate fidelity to their scheme of work.
So, here are my suggestions on how to champion Numicon resources in a primary classroom guided by White Rose Maths planning.
How do I choose a manipulative to use? The three C’s
The EEF stipulates that educators must ensure that there is a clear rationale for using a particular manipulative. When deciding upon the manipulative to use and when to use it, these are the considerations that I personally make.
What is the context of my classroom? What are the needs of all the children in front of me? What are the needs of my most able? Do they have opportunities to ask questions, dig deeper, explore further, make conjectures?
Post Covid-19, I have really had to teach my children how to talk mathematically again – a challenge that becomes burdensome and almost impossible if teaching through a worksheet. What Numicon enables so well is communication and language within the classroom. Children engage in a mathematical experience where they explore, collaborate and create using the Shapes.
What concept am I trying to teach my children? What do I want children to see, grasp and build upon? There are some areas of Maths where Numicon Shapes really stand apart from other manipulatives: number and place value, fractions, four main operations, and position and direction. When used deliberately and developmentally from Foundation Stage to Year 6, they can really support all learners to make connections between concepts and move deeper as learning becomes more complex.
Finally, consistency is key. What representations are the children already familiar with? What have they used before in previous lessons, previous year groups, for closely related concepts? We’re always trying to minimise the number of moving parts and strip back the cognitive load for our pupils. Whilst conceptual variation has its rightful place within a mastery curriculum, too many manipulatives used can confuse children. This can prevent them from making the meaningful connections that we want (and need) them to make in order to develop those strong mental models.
Numicon Shapes are not toys: be explicit on how you want children to use them
Imagine arriving into a KS3 chemistry class, informing students of different chemical reactions and then simply providing them with the equipment to use to experiment with. Both a fire and learning hazard, and something which hopefully would never occur. Why then can we often see boxes of Numicon shapes placed in the centre of the table of our lower attaining children to use to help them? From my experience, children may be more likely to reach the wrong answer, develop misconceptions and be more confused. However, that is not a reason to not use them.
When I teach concepts with Numicon, I model exactly how I want all my children to use it, from the way I want my students to place the Shapes on the table in front of them and I narrate my thinking as I identify what is being represented. I leave no stone unturned. I then move to the “We Do”phase, where children contribute to my model, before working in pairs or groups on very similar examples to practise and develop their confidence and understanding. Spending time here benefits every learner in the classroom:
- The SEND children who need quality first teaching and explicit instruction on how to use the shapes.
- The majority of the class who need to talk, explore, collaborate and practice.
- The early graspers who can take this learning in a different direction, make connections, or generalise to find a rule.
Children will be children: How do I set my expectations?
You only need to deliver a staff CPD session on using Numicon to understand how tactile and satisfying the Shapes are for the senses. Teachers, senior leaders, learning support assistants… all making towers, shapes, patterns whilst you are delivering. When using Numicon with children – particularly for the first time – give them this chance to explore, play and wear out the novelty. However, set your expectations for behaviour and practise these routines.
“When my hand is raised, your hands need to be free. Let’s practise this.”
“I’m going to set a 30 second timer. When the timer reaches zero, the Numicon needs to be:
1) In the box
2) Lid on
3) In the centre of the table.
OK, off you go.”
(At the beginning, I’d even have visuals on the board of what this looks like, and give children longer to pack the Numicon away – it takes longer than you think!)
Remember why you opted for a planning scheme such as White Rose
Whilst following a scheme of learning or planning sequence is not for everybody, many schools and subject leaders opt for one to maximise consistency, support teachers with subject knowledge and ease workload. Stipulating the use of Numicon, where teacher exposition is as important as ever, can be challenging. In its lesson plans, WR often stipulates to use “concrete manipulatives” – leaving it up to the teacher to select which to use and how to use it.
For those progressive concepts that run consistently from Foundation Stage to Year 6, such as the four main operations, fractions, and place value, consider how you can ensure that staff are clear, confident and consistent in how to use Numicon (or another manipulative). In my school, one way that we are trying to support staff with their use of Numicon is through our calculation policy. From Year 1 to Year 6, we have demonstrated exactly how the Numicon can be used at every stage of teaching the four main operations and how it progresses to the abstract methods.
This gives teachers a sense of permission to appropriately take planning in their own direction, whilst remaining consistent with the rest of their setting. Teachers can identify previous learning steps to scaffold and support children working below age-related expectations.
Go directly to the source: Numicon White Rose matching documents
Much of the Numicon planning fits directly into the White Rose schemes of learning. Signing up for a free Oxford Owl account gives educators access to the White Rose matching charts. These are direct links to where Numicon lessons fit within the White Rose lesson sequences. Teachers with paid subscriptions to Numicon can then access the activities in the Numicon Teaching Handbooks directly. Why is this useful? It can save planning time for busy teachers and gives support to teachers who have less experience using Numicon or who are struggling for ideas on how to use it.
Use Numicon throughout the learning journey
The beauty of using resources like Numicon is their versatility. Once children are familiar and confident, they are often able to use it in new ways and apply to challenging problems. It supports them to visualise and represent complex problems without the frustration of seeing crossings out on a piece of paper. We always urge teachers to remember this when deciding whether or not to “remove” the resources from the children. Yes, we want our children to be efficient effective mathematicians, calculating abstractly and mentally. However, that can be demonstrated through concrete and pictorial understanding.
White Rose’s #problemoftheday is a great opportunity for children to work together to unpick, represent and work through challenging problems. Numicon resources can be both a scaffold to ensure access for all students, but also a brilliant way for children to demonstrate their knowledge and understanding in a creative and visual way.
The powers of social media: Take inspiration from other educators
For any teachers starting out with Numicon or wanting ideas on how to use it, I always urge them to engage with X (formerly Twitter) and the Numicon Facebook page. Teachers post images or videos on how they use Numicon for different concepts and for different year groups. Reach out, ask questions and have a go yourself!
You can follow Lydia on X (formerly Twitter) at @davisonmiss
For more insights into how to get the most out of your school’s Numicon resources with your pupils, sign up to one of our NCETM-accredited digital Professional Development workshops.