Education Endowment Foundation:How I wish I’d used manipulatives to teach maths

For years, I avoided using manipulatives in my classroom. I hadn’t used them as a student, and I didn’t know how to use them effectively as a secondary teacher.

I thought I was helping students by jumping straight into formal notation, streamlining their learning with rules and procedures. However, in doing so, I was often papering over confusion with shortcuts instead of building conceptual understanding.

As highlighted in the Improving Mathematics in Key Stage 2 and 3 Guidance Report, I now see them as purposeful scaffolds – temporary, targeted supports that make mathematical structure visible and allow for meaningful progression from concrete understanding to abstract reasoning.

I used to go straight to the abstract

When introducing new topics, I used to begin with abstract rules or procedures:

“Here’s how you expand 2(x + 3)… Just multiply the 2 by the x and the 3.”

Then I’d work through a few examples and have students practise independently. Students copied steps and got the right answers – on that day.

A week later they’d write 2x + 3 instead of 2x + 6. I would reteach and the cycle repeated. This reflected Soderstorm and Bjork’s (2015) findings about learning vs performance. Students were able to perform procedures but didn’t grasp the concepts.

This pattern repeated across topics: directed numbers, rearranging equations, factorising. After repeatedly seeing the same misconceptions resurface during Year 11 interventions, I realised that my teaching needed to change.

My students didn’t have misconceptions; they had a lack of meaningful understanding.

Today, I see manipulatives not as a simplification, but as a way to reveal mathematical structure and deepen understanding. The EEF (2021) states that

Now I begin with ​‘the why’

When introducing expressions like 2(x + 3), I use algebra tiles, ​‘We’re building two groups of x + 3.” (Figure 1)

Students lay out one group of one x tile and three unit tiles, then another group of one x tile and three unit tiles and the reason they are multiplying becomes apparent.

They can see why two groups of x + 3 would not be 2x+3 (Figure 2) but rather 2x+6. Students aren’t memorising rules — they’re understanding them. We’re no longer passively doing maths — we’re seeing, representing, and experiencing it.

Manipulatives aren’t a crutch; they are a foundation

I used to think manipulatives were an add-on, perhaps something for the struggling few. Now I see them as essential for all learners. Used well, manipulatives make the abstract visible, uncover relationships, and build lasting knowledge. They don’t dilute the maths – they build it.