: Are you having fun? The wonderful world of manipulatives. How manipulatives can enhance the teaching and learning of maths.

When used effectively, manipulatives are a powerful tool for teaching maths. They are the bridge to connecting ideas and developing secure mathematical concepts.

I will never forget a session when I was working with a group of year 2 children who were struggling with maths and needed targeted support.

I had the idea to use a fancy car garage and toy cars to support the idea of counting, counting on, cardinality etc. by sending cars down the ramp and hiding them in the garage. I was fortunate to be able to video the session which I initially thought went amazingly well.

When I watched the video back, I was shocked! The group was clearly having a great time playing with the cars, but, there was absolutely no maths happening!

On reflection, I realised that there needed to be a clear purpose to the use of this, or indeed any manipulative, in order for the children to make links with the mathematical concepts and ideas.

I think we can all identify turning points in our practice that influenced our teaching; this example was certainly one of mine, and the moment that my passion for the use of manipulatives began.

The potential of using manipulatives in mathematical learning is huge.
There is an abundance of research that has shown pupils who use manipulatives during mathematical instruction outperform those who do not (Moyer, 2001). Research also shows the positive impact manipulatives have, on children of all ages, in deepening conceptual understanding. But, as Ball stated in 1992, ​‘these materials are not magic and understanding does not travel through the fingertips and up the arm’.

Recommendations from the EEF.
The EEF Recommendations for both Early Years and KS1, and KS2 and KS3 state that we need to ​‘ensure that there is a clear rationale for using a particular manipulative or representation to teach a specific mathematical concept’ and also ​‘ensure that children understand the links between the manipulatives and the mathematical ideas they represent’.

Making Connections.
Manipulatives also help us to make connections. Haylock and Cockburn outline four key components of mathematical experience: concrete, symbols, language, and pictures. Their research emphasises the importance in building a network of cognitive connections between them.

Concrete experiences (representations of knowledge through action) are often the missing link within this model. Manipulatives are a gateway to mathematical talk, support abstract learning and provide pictures and representations to support working and long-term memory.

Manipulatives can show mathematical structure.
Specific manipulatives such as Numicon, Cuisenaire Rods or Algebra Tiles are very effective in providing concrete experience and showing the structures within the mathematical concepts.

Cuisenaire Rods can help us to see the structures of additive reasoning and number bonds or the commutativity in multiplication bonds.

Learn more here: Using Cuisenaire rods: modelling additive and multiplicative relationships – YouTube

Numicon helps young (and older) children to see the structure of odd and even numbers or fractions.

Learn more here: Making Numbers Real – Introduction to Numicon – YouTube

Algebra tiles are a collection of square and rectangular tiles that can be used to represent expressions containing both numerical and algebraic terms.

Learn more here: What are algebra tiles?

In summary.
The abundance of rich, engaging ideas around the use of manipulatives can only impact and deepen learning, and expose the structures and ideas behind the underlying mathematical concepts if they are carefully integrated and embedded into our mathematical pedagogy. This requires explicitly teaching pupils how to use manipulatives and providing effective teacher modelling.

Then all pupils can experience the real power of manipulatives.

Key take aways;

- It’s ok that the pupils / students we teach have fun and engage in using manipulatives, but ensure that there are links between them and the mathematical ideas they represent.
- Make connections between the manipulatives, the pictorial representation, symbols and the mathematical vocabulary.
- Just give it a go, the results will be amazing!

Links to the EEF Recommendations for Improving Maths;
Education Endowment Foundation. (2020). Improving mathematics in Early Years and Key Stage 1, pp. 20 – 25. Available at: EEF_Maths_EY_KS1_Guidance_Report.pdf
Education Endowment Foundation. (2017). Improving mathematics in Key Stages 2 and 3, pp. 10 – 13. Available at: EEF-Improving-Mathematics-in-Key-Stages-2-and‑3 – 2022-Update.pdf

References
Ball, D.L. (1992). Magical Hopes; Manipulatives and the reform of Math education. American Educator 16.
Haylock, D and Cockburn, A. (2017). Understanding Mathematics for Young Children. Sage Publishing.
Moyer, P.S. (2001). Are we having fun yet? How teachers use manipulatives to teach mathematics. Educational studies in mathematics journal.