Research School Network: Making the Most of Manipulatives Carefully considering the correct manipulatives.

Helen Wright, a maths consultant at Aspire Educational Trust, discusses the importance of carefully considering the correct manipulatives.

Consider for a moment, the maths area in a typical primary classroom. It might contain a wide variety of manipulatives. If you are lucky, there will be counters, cubes, Cuisenaire rods, Numicon, Dienes; trays full of brightly coloured equipment that are regularly used by children during their maths lessons. Whatever resource you use to plan your maths curriculum, I’ll bet manipulatives form a big part of it. The EEF Guidance Report, Improving Mathematics in Key stages 2 and 3 states such equipment provides insights into increasingly sophisticated mathematics, helping pupils engage with mathematical ideas.

Don’t assume, however, that just because manipulatives are out and being used by children, the maths you want them to learn will be learnt — understanding does not travel through children’s fingertips. Recommendation 2 in the EEF report explains that manipulatives are just tools, and how they are used is essential. Purposeful use and a clear rationale for selecting a particular manipulative to teach a specific mathematical concept will yield the greatest impact.

When sequencing content within a unit, it is important to consider which resources to introduce first and which will enable children to explore the concept more deeply. Ball explores this in her model, Domains of Mathematical Knowledge for Teaching. ​‘Knowledge of Content and Teaching’ (KCT) combines knowledge of teaching with knowledge of mathematics. As teachers, we must evaluate the relative advantages and disadvantages of particular manipulatives, considering their strengths, limitations, and potential distractions to ensure a coherent sequence

Let’s return to that well-stocked classroom. Consider for a moment, which manipulative you would choose to teach the above column subtraction with an exchange.

There is, as we have already mentioned, plenty of choice. Dienes, Unifix cubes, Numicon, place value counters, colour counters, bundling sticks and 10p and 1p coins will all offer a different perspective on the problem of exchange. Each of these manipulatives has been carefully designed with a particular purpose in mind. Each offers a unique quality and opportunity to expose the structure of exchange within subtraction.

Dienes clearly demonstrate base 10, allowing children to exchange one ten for ten ones. Exchanging one for another can create barriers for children as they might not understand they represent the same value. Unifix cubes connected in lines of ten could be used. These offer the opportunity to break connected lines of cubes into individual ones, exposing the exchange in a slightly different way. However, experience suggests that as a lesson progresses, the lines of ten sometimes become lines of eight or nine, as children build, take apart, and rebuild. Colour counters or base 10 counters do a similar job, but the ​‘ten’ is the same size as the ​‘one’, and not ten times the size, this can lead to possible misconceptions.

To make the most of manipulatives in the classroom teachers need to consider the following questions when planning:

- What are its strengths? How does it help children to notice what is important and how does it connect to the mathematics involved?
- What are its limitations? What are the distractions? What might children notice that will hinder their understanding? How might I overcome these?
- When and how will I remove the manipulative? After all manipulatives are a scaffold, a bridge to independence.

Making the most of manipulatives will involve developing a clear rationale which explores not only how and when they are used, but also how they will connect with the mathematics being taught and how they help pupils to understand mathematics by illuminating the underlying general relationships. It will involve considering the relative strengths and limitations of resources on offer and will plan for when the scaffold will be removed.


References:

Ball, D.L., Thames, M.H. and Phelps, G. (2008). Content Knowledge for Teaching: What makes it special? Journal of Teacher Education, 59(5), pp.389 – 407. doi:https://doi.org/10.1177/002248….


Guidance Report IMPROVING MATHEMATICS IN THE EARLY YEARS AND KEY STAGE 1. (n.d.). Available at: https://d2tic4wvo1iusb.cloudfr… [Accessed 2 Mar. 2025].


Guidance Report IMPROVING MATHEMATICS IN KEY STAGES 2 AND 3. (n.d.). Available at: https://d2tic4wvo1iusb.cloudfront.net/production/eef-guidance-reports/maths-ks‑2 – 3/EEF-Improving-Mathematics-in-Key-Stages-2-and‑3 – 2022-Update.pdf?v=1740928047.


[Accessed 2 Mar. 2025].