Research School Network: What can we do, when the maths ​‘ain’t mathing’? Tracey Adams discusses using EEF’s Math guidance to enhance manipulatives and representations in her teaching and school.

What can we do, when the maths ​‘ain’t mathing’?

In this blog, Tracey Adams reflects on how using the evidence from the EEF’s Mathematics guidance reports, have helped to develop the use of manipulatives and representations, within her own practice and school.
In the busy world of schools, it can be tough to step back and view the broader picture. With staff often stretched, finding time to focus on personal professional development, outside of formal training sessions (INSETs), can be challenging. As a school leader, engaging with resources from the EEF has significantly impacted my approach to teaching. The ​“Improving Mathematics in Early Years and Key Stage 1” and ​“Key Stage 2” guidance reports have been essential in helping me understand the transformative role that manipulatives and representations can play in teaching Maths, both in my own practice and for others.

Why do we need to use manipulatives and representations?

The one recommendation that sits across all of the EEF Mathematics guidance reports is the need to focus on the use of manipulatives and representations, whilst exploring the crucial link to problem solving. The guidance reports explain that they are great tools for underpinning pupils’ conceptual understanding but to get the most out of them, there must be a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept (EEF 2017).

The understanding I gleaned from the guidance, pushed me to experiment with representation, in my lessons. At that time, I was a Year 6 teacher and I began with thinking blocks and used them to help my pupils understand ratio. As I explored this tool, I began to see its potential across a range of mathematical topics. My understanding of how representation allows for greater mathematical thinking and discussion also began to grow.

Why are Manipulatives and Representations Important?

A key takeaway from the EEF Mathematics guidance is the emphasis on using manipulatives and representations, while also making strong connections to problem-solving. Many disadvantaged students face unique challenges in learning Maths, including gaps in knowledge, anxiety, and misconceptions. According to the guidance, manipulatives and representations are effective tools for deepening students’ understanding of Maths and overcoming these barriers.
The guidance stresses, that to maximise their benefits, teachers must have a clear reason for choosing specific manipulatives or representations, when teaching particular mathematical concepts (EEF 2017).

Shifting My Practice

The insights I gained from these reports, pushed me to experiment with using representations in my own lessons. At the time, I was teaching Year 6 and I started by incorporating bar modelling to help my students understand the concept of ratio. As I explored this tool, I began to see its broader application across many areas of mathematics. I also began to appreciate how representations could promote deeper mathematical thinking and encourage more meaningful classroom discussions.
The results were striking. My students quickly became more confident in their ability to talk about Maths because they had a visual representation to discuss. They were no longer just solving problems mechanically; they were able to explain the reasoning behind their solutions.

Building Collaborative Practice

This year, as a Headteacher and Maths Subject Lead, I continue to lead my team in exploring manipulatives and representations. We have been working on how to select the most effective tools for each stage of learning — from Reception through to Year 6. We have also focused on how these tools can help us ensure that conceptual understanding is thoroughly embedded. To do this, we concentrated on one key concept — addition — and explored how different year groups can approach it using manipulatives and representations. This collective exploration, has allowed us to map out a clear and consistent learning journey for our students, ensuring that every child has the support they need, through carefully chosen tools, to scaffold their mathematical thinking.

Empowering Student Exploration

Using manipulatives and representations offers students the opportunity to express what they see and crucially, to understand why math works, not just how it works. This visual approach sparks curiosity and invites deeper questions, whether students are in the early years or approaching more complex problems in Key Stage 2. In turn, this process of exploration and discovery helps students find answers, boosting their confidence and success in math.

So, to ensure that we don’t get to the point where the maths ​‘ain’t mathing’, we must equip students with the tools to visualise and verbalise their understanding. In doing this, we give them the chance to become more confident, inquisitive and capable learners. When students can confidently ask and answer questions through this kind of exploration, they are likely to feel more successful and more engaged in their own mathematical learning journey.

Key considerations when using manipulatives:

- Ensure that there is a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept.
- Enable pupils to understand the links between the manipulatives and the mathematical ideas they represent.
- Try to avoid pupils becoming reliant on manipulatives to do a type of task or question. A manipulative should enable a pupil to understand mathematics by illuminating the underlying general relationships, not just ​‘getting them to the right answer’ to a specific problem.
- Manipulatives should act as a ​‘scaffold’, which can be removed once independence is achieved.
- Manipulatives can be used to support pupils of all ages.