Research School Network: Making best use of manipulatives What does the evidence say about the use of manipulatives?

In this blog, Heather Martin, Executive Assistant Principal of Christ the King and St Cuthbert’s Catholic Academies and Assistant Maths Hub Lead for Abacus North West Maths Hub, reflects on how using the evidence from the EEF’s mathematics guidance reports has helped to develop the use of manipulatives and representations across her schools.

Manipulatives: what does the evidence say?

Manipulatives matter. Used well, they can be powerful tools for supporting children in engaging with mathematical concepts. However, like most resources, they need to be used purposefully and appropriately in order to have an impact.

While evidence is clear that manipulatives should be used in the teaching of maths across all key stages (EEF, 2017, & EEF, 2020), it isn’t just about making them available to teachers and children. Planning for which manipulative to use when, and why, is critical, as is the teacher’s role in introducing and modelling their use. This can be a balancing act: we know that children are unlikely to learn mathematical concepts if they are simply given manipulatives and encouraged to do with them what they wish (Bruner, 1966), while we also know that overly restrictive, moment-by-moment instructions about exactly what to do with manipulatives can backfire as well (Brown, 2009).

So, using manipulatives requires skillful, knowledgeable practitioners, and leaders who are willing to give the time and resources needed in order to implement change.

The ​‘what’ and the ​‘why’

We have always used manipulatives across our schools, but engaging with the evidence led us to question whether we had always used them well.

It was clear to leaders that there was not always a shared rationale for manipulative use, or consistent training for teachers, which meant that we did not always select appropriate manipulatives, and variation across the year groups sometimes left children confused and struggling. This lack of clarity also made it especially difficult for new staff to understand which manipulatives to use and why.

Mapping manipulative use

Initially, our maths leaders considered where teachers and children would benefit from deliberate and consistent use of a particular manipulative. We drew upon external expertise both through our local Maths Hub, and through high-quality resources such as those from the NCETM. Teachers were a key part of this process, and we collaboratively developed a scheme of learning detailing when manipulatives should be used, and examples of their use in supporting the teaching of key topics across all year groups – from Early Years to Year 6.

As part of this, we ensured that we were very deliberate about our rationale and shared this with colleagues. For example, in Year 2 we don’t initially use place value counters, as these involve unitising which can be conceptually tricky: we use Base 10 blocks (or Dienes blocks) first before moving to place value counters when children are ready. Discussions about this and similar decisions at the planning stage help embed our rationale, and support teachers in understanding the ​‘why’ alongside the ​‘what.’

We also recognised the need to buy enough manipulatives for every classroom in the school in order to make them available and to make it easy for teachers to use them.

A collective endeavour

Mindful of the need for implementation to be a collective endeavour, we continue to engage teachers in the process through ongoing professional dialogue. Despite our schools being one-form entry, working across two schools means that teachers can work together in year group pairings, utilise a shared calculations policy, and engage in regular staff meetings at which manipulatives are discussed. Making use of manipulatives is also a focus of lesson drop-ins and coaching conversations.

We have certainly seen an improvement in the quality of manipulative use because of this work, but progress is ongoing. Recent conversations have focussed on when and how to take a manipulative away from children, as well as thinking about the language used with children to ensure we always ask what a manipulative ​‘represents’ to bring attention back to the underlying mathematical concepts.

Through continuous collaboration as well as using research evidence to inform our practice we’re making manipulatives matter for everyone.

References

Bruner, J. S. (1966). Toward a theory of instruction. Harvard University Press.

Brown, M., McNeil, N., & Glenberg, A. (2009). Using Concreteness in Education: Real Problems, Potential Solutions. Child Development Perspectives
3: 160 – 164.

EEF (2017). Improving mathematics in Key Stages 2 and 3 [guidance report].

EEF (2020). Improving mathematics in the Early Years and Key Stage 1 [guidance report].