Numbuko – Engaging young children in maths

July 15, 2016

Maths in the Early Years

Maths is crucial in the early years. It not only impacts children’s later ability [1] but it shapes how they see and feel about the subject. It is worrying to see many children, particularly girls, being put off such an important, and wonderful, area of learning from as young as 6 years old [2].

There are many ways to help children learn maths. The most important ingredient is us! As adults, we can provide resources, activities, and importantly, talk positively about maths concepts to support children’s love and learning of maths. Talk is the most important, as we can ‘mathematize’ a wide range of everyday activities [3], from counting our steps when walking, working out how many stickers we still need, to finding the best way to share biscuits equally.

Resources do play an important role, where some materials make it easier to talk about mathematical patterns than others. Numbuko blocks were developed from a long history of research into maths representations to provide the best resource to help us talk about the building blocks of maths with children.


Mathematical Manipulatives

Almost 200 years ago, Frederick Froebel, founder of the kindergarten, presented a range of ‘gifts’ [see 4]. These simple materials were intended to provide a resource for children to explore fundamental numerical patterns. His third gift for example, consisted of a set of eight blocks, offering children a means to explore how quantities can be partitioned equally in different ways.

Since Froebel’s gifts, we have seen a wide range of other maths learning materials, or ‘manipulatives’ as they are often referred to.  Whilst debates continue as to how (and even if) these materials support learning [5], one way to consider these materials is in terms of the features they use to represent number. Some use shape or length (e.g. different size rods such as Dienes blocks). Many also use colour to represent numbers (e.g. Cuisenaire rods, Numicon). Research suggests [6] that it is better to use materials with limited ‘extraneous’ features, that is, features that are not relevant to the ideas they represent (e.g. different colour unit blocks or small teddy bears).

One issue with manipulatives is the materials often limit how they can represent number. Properties such as colour and shape cannot change easily. So for example, whilst you can ‘break’ 10 into two groups of 5, you cannot (easily) break a coloured ten manipulatives piece.

Another problem, is that many of these materials are, well, slightly ‘schooly’. They often lack the fun factor that children expect from toys at home. If we want children to see maths as something fun and wonderful, we can do better at providing materials that capture these qualities.


Why Physical Manipulatives?

Many might say that you can address the problems of existing maths manipulatives by creating on-screen versions often as ‘apps’. You can, and this has created a wide range of ‘virtual materials’  [7]. The National Library of Virtual Manipulatives [8] provides a good selection.

But parents and teachers often feel that there is something missing from these screen-based materials. Indeed, interaction with screens has been dismissed as simply ‘sliding pictures under glass’ [9]. As a result, Dr Andrew Manches, the founder behind Numbuko, has spent many years researching the question, ‘What is the role of hands-on play in learning?’

The animation below provides a summary of some recent funded work [10] by Andrew at Moray House School of Education looking at how physical actions with materials may generate imagery that supports our thinking. Evidence for this possibility lies in the way people very commonly gesture when thinking and explaining maths concepts.

In summary, as well as being more accessible, more social and arguably more engaging, there are good cognitive arguments for the importance of physical rather than screen based learning materials for young children.



Numbuko was designed to address the limitations of traditional manipulatives and screen based versions. For this, they required a bit of digital magic.

Numbuko are physical blocks that when attached in a row, change colour. Significantly, they change colour according to the number attached. They are in effect like traditional colour rods, with an important difference: they can be pulled apart and added back together, just like numbers can. With a rod of ten blocks, children can explore how this can be broken into two equal groups of five, but not into three equal groups because you have one left over.

As the animation shows, there is more to Numbuko. When adding an 11th block, the colour sequence starts again. 12 is clearly made up of ten and two.  Numbuko lets children explore how numbers to 20 can be counted, added, subtracted, partitioned into fractions, made up of tens and units.


Building the Fun Factor

Numbuko aims to compete in fun terms with all toys children have at home. For this we considered how to make the most engaging construction toy, whilst keeping the maths representation. Numbuko blocks join magnetically. Better than that, they join magnetically but don’t repel (email us if you are curious). A session with children of all ages with our non-digital prototype was very positive. Below is one child’s creation.

We also wanted our colour-changing rods to build in all directions. So we have created a simple rule, add a block to the end a row, all blocks will change colour; attach a block in a new direction, you’ve created a new row.

The result is you create an exponentially high number of configurations. Clichéd, but the possibilities really are endless (okay, not endless but we are having difficulty calculating the end for a given quantity of blocks and are looking for some gifted mathematics to help us).


Powering Numbuko Blocks

Early on, we got feedback about the concerns of how to charge Numbuko blocks, or worse, change batteries in each one. Our solution, make it so they don’t require batteries or plugging in. Numbuko blocks are powered by light in the room, they are solar charged, not that you would know from looking at them.


Numbuko and Talk

We started by saying that talk is the most important ingredient, which is why we are calling this project PlayTalkLearn. Numbuko aims to provide an open ended creative resource that helps parents and practitioners to talk about children’s play. Rather than referring to the colours, we encourage adults to talk numbers. “Let’s see if you can make a giraffe with 10 blocksAhh you only have 8, you need 2 more. I was wrong, we needed one less than 10. Well done! Can you give half the blocks to your brother now. Ooh, there’s one left over”.

Sometimes, it does help to have some structured activities. However, we are extremely mindful to encourage creative thinking. So we are creating puzzle cards. We are creating three types of cards, Make, Change, and Explore.


Where We Are Now

We have patented and testing our prototype colour changing blocks, and look forward to sharing them soon with children and parents for feedback. Please email us if you are interested in becoming a test pilot!

To move forward we are also looking for the right investors who share our vision of a trusted early learning company. For this, it is invaluable to evidence interest in our blocks. So we would love to encourage anyone who supports Numbuko to sign up to our newsletter via our website, or follow our developments through Facebook. And we really would love to hear your thoughts.




1.         Sylva, K., et al., eds. Early childhood matters: evidence from the effective pre-school and primary education project. 2009, Routledge: London.

2.         The Scottish Government, Making Maths Count – Interim Report, National Profil-Raising Group for Mathematics, Editor. 2016.

3.         van Oers, B., Emergent mathematical thinking in the context of play. Educational studies in mathematics, 2010. 74(1): p. 23-37.

4.         Theissen, R., Frederick Froebel, AIMS Educational Foundation, Editor. 2005.

5.         McNeil, N.M. and L. Jarvin, When theories don’t add up: Disentangling the manipulatives debate. Theory into Practice, 2007. 46(4): p. 309-316.

6.         Uttal, D.H., K.V. Scudder, and J.S. DeLoache, Manipulatives as symbols: A new perspective on the use of concrete objects to teach mathematics. Journal of Applied Developmental Psychology, 1997. 18(1): p. 37-54.

7.         Moyer, P., J. Bolyard, and M. Spikell, What are virtual manipulatives? Teaching children mathematics, 2002. 8(6): p. 372-377.

8.         NLVM. National Library of Virtual Manipulatives. 2007; Available from:

9.         Victor, B. “A Brief Rant on the Future of Interaction Design.” 2011  8th July 2014]; Available from:

10.       Manches, A., Interaction, Embodiment and Technologies in Early Learning. 2013, Economic Social Research Council: University of Edinburgh.



AndrewManches2Dr Andrew Manches – Andrew has 16 years’ experience in education, initially as a primary teacher then as an academic. Andrew was an infant teacher and now holds a prestigious Chancellor’s Fellow in the School of Education at the University of Edinburgh. He researches the role of interaction in the way children think and learn and the implications for new forms of technology. Andrew has worked on a wide range of projects in learning technology and leads the Children and Technology course at the University. Andrew and his partner have two children aged 2 and 3. Party time starts at 5am daily.
Numbuko Website

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