By Zena Martin
“The use of words for expression does not necessarily imply their useful communication… Because of this we can safely say that in verbal relationships ‘communication is almost a miracle.’” – Dr Caleb Gattegno
In recent years, there has been a resurgence in the use of concrete apparatus and manipulatives in primary mathematics teaching and learning. We have the pedagogy of the Far East to thank for this. Yet for many specialist teachers, the use of manipulatives has been part of their everyday repertoire of teaching strategies for the most struggling learners of maths for decades.
For me, and many others, there is one manipulative that rises ‘head and shoulders’ above all others. This is the mathematical rod, originally invented by Georges Cuisenaire. Cuisenaire® rods have been in existence since the 1930s and are the number one go-to resource for many specialist teachers who recognise the uniqueness and visual power of these materials.
However, there are still many teachers who do not yet feel confident in the use of this resource and will often reach for other manipulatives that appear to give a quicker short-term gain of a correct answer for children. Understanding the long-term learning benefits of Cuisenaire® is a vital lesson for every teacher of mathematics, whether new or experienced.
I concur with the view that many children with apparent learning difficulties are actually learning differences. What children with learning differences often find challenging in the mainstream classroom is the significant amount of language and verbal instruction that is employed. They require far more visual and practical input and experiences than are often provided. This statement could be echoed for most children in primary classrooms; it could be argued that they are just better equipped to cope with the absence of such visual stimulus. Here begin the seeds of quality first teaching!
Cuisenaire® rods allow children to see and internalise the relative sizes of numbers; to feel in their hands how six differs from seven, and from 10, and so on. They can see the difference of one white rod between each of the other rods. They internalise that all the blue ones are of the same length, or that it always takes two yellow ones to make an orange one.
Cuisenaire® rods have no numerical indicators. Though sometimes criticised or rejected for this (or even compensated for, with teachers and resource publishers adding markings or pictures to aid counting), the lack of numerical indicators is an essential feature for many children who struggle with number. I am sure you will have encountered children who reach the upper end of Key Stage 2, still insecure with number bonds to 10 and feeling compelled to count everything, still dependent on fingers and number lines for basic number bonds. These children have internalised that their only reliable method of calculating is to count – nothing else works for them because they struggle to ‘see’ magnitude. Of course, we know that counting has its limitations.
You can’t count rods – you have to become so familiar with them that you begin to see and internalise the ‘seven-ness of seven’ and understand its relationship to 8 and to 6, and later to 70, and so on. It moves children away from the ‘comfort blanket’ of counting and into a more secure internalisation of the magnitude of numbers and the structure of our number system. This cannot be achieved with any other manipulative that I know of as they all contain markings and numerical indicators that invite children back to their status quo of counting. They provide an understanding of the magnitude of number, a fundamental concept that eludes many struggling learners. We can immediately see how small ‘red two’ is compared to ‘orange 10’. We can create ‘staircases’ with our rods, going beyond 10 up to 20, or even to 50. This requires a lot of orange rods but is a worthy exercise in demonstrating to children not only the magnitude of number, but also an introduction to place value. Long before children encounter the traditional ‘tens and units’ grid, they need to explore what these numbers ‘look like’. For example, recognising that the number 26 is made up of two ‘orange 10’ rods and one ‘dark green six’ rod is the beginnings of an understanding of place value.
Another wonderful thing about rods is their versatility and ability to become a familiar ‘first port of call’ for most new mathematical concepts all the way to the end of the Key Stage 2 curriculum. The possibilities are endless! Commutative laws, fractions, decimals, percentages, ratios, time, equivalences, bases, and so on. There are few concepts that cannot be taught at least initially through Cuisenaire® rods. For children who are fully familiar with these rods, they give access to mathematical concepts that many might’ve thought not possible. It is a resource that can ‘open doors’ to maths for children who otherwise would struggle to access its abstract nature. Just for starters, imagine if the ‘orange 10’ rod no longer represented 10. What if it represented 100? What would the others become? What if it represented a million? What do the others become? What if it represented one? What would the others become? What if the dark green one represented one? What would the others become? I can think of no other manipulative that I can effectively do this with.
Ultimately, these mathematical rods, whether used by Reception children in continuous provision or by a child in Year 5 to close gaps in learning and access the curriculum more effectively, are teaching children algebra long before arithmetic. They are ultimately discovering that a brown rod and a red rod together are the same length as an orange rod – that’s algebra!
I am often met with the response from teachers (and occasionally specialists) that they don’t use these rods because the child or children don’t know the number that each one represents. Consequently, they will continue to encourage children to use counting manipulatives (often cubes or counters) to help them complete their work. Whilst this gives a short-term gain in producing a page of sums that stand a fighting chance of being correct, it does nothing to develop the child’s long-term understanding and internalisation of the number system.
What is overlooked here is the need for children to develop full familiarisation with these rods before their potential as a learning tool can be fully realised. This requires huge amounts of structured play involving making pictures, building structures, talking about the rods with an adult or peer, exploring their representation on squared paper, colouring them in, and so on. Sometimes, we follow this with multi-sensory flashcards that the children make so that they can reach a point where they can confidently pick up any rod and say its colour and number. Knowledge of colour plus knowledge of number equals full familiarisation. Once this has been achieved, a world of mathematical concepts can be opened up to children with Cuisenaire’s® ability to represent the number system so visually, to strengthen number sense and to be used with such versatility.
Time to dig them out of the cupboard
In the UK, these rods were used by the teaching profession throughout the 1960’s and 1970’s, particularly in primary schools. Many adults who were at primary school then remember these resources fondly and describe how they learnt and consolidated their knowledge of numbers bonds through these delightful coloured rods.
After that, these valuable resources seemed to fall out of favour, and I have heard many sad tales of boxes of Cuisenaire® rods being thrown in skips during ‘clear outs’ or moves to new premises. Many teachers at that time were unaware of what these resources were, let alone what to do with them.
But now they’re making a comeback! If you know you have these wonderful little tools in your school, that give visual access to the world of number to so many children who otherwise find the number system a mystery, then dig them out, dust them down, and explore their learning potential!
About Zena Martin
As a member of #TeamADL, Zena specialises in developing teachers and leaders in the North to be more inclusive for ALL learners. Zena facilities several SENCO Networks and is a SENCO Coach.
To find out more or book Zena’s services visit www.AnitaDevi.com
 Please note that I do not advocate children being ‘forced’ to stop using fingers or other counting aids. They will stop using them when they are confident that another system has replaced the need to rely on them.
Please note that I have no pecuniary interest to declare in sales of Cuisenaire® rods or any other manufacturer.