Gareth Roberts is passionate about mathematics. Just five minutes spent in his company proves this. With a long track record of mathematical experiences it’s not surprising that he seems to live and breathe mathematics in one way or another.

‘Essentially I spent my career in mathematics teaching. ‘ He says. ‘I was involved in university teacher training and as a maths adviser to a local authority. This was a formative period for me as I learned how children learn or, in some cases, don’t learn maths. As I spent time in these educational settings I developed a feeling about just how much teachers are able to draw out of children. I especially learned a lot from primary teachers regarding the process of teaching. It was obvious how some really helped pupils to acquire concepts while others were quite successful at seemingly putting pupils off maths. This might come from societal pressures or just poor teaching. It was formative.’

‘Then I was sucked into an administrative role within universities and suddenly there was not enough time for maths.’ ‘It’s only when I retired 10 years ago that I returned to my first love. This actually came about through pressure exerted by my grown-up children. They were adamant I should return to maths. ‘ You have to do something about this dad’ they kept saying. As a consequence I started writing a book in Welsh whose title translates roughly as ‘Everybody Counts’

The aim was to write a popular book that set out to explore the relationship between maths and culture through Welsh eyes. This might sound strange but you will be surprised just what pertinent observations can be drawn within this area. Did you know for example there is a traditional and a modern way, of counting in Welsh. In the traditional way you would say eighty-four as ‘four and four-twenties’ using twenty as a base. This is not an uncommon method of counting and it’s actually used in many languages across the world and is common to all the Celtic languages. It also turns up from time to time in English: think of the quote from the Bible *‘three score years and ten’.*

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However, in the 1950s, a new system was adopted when maths began to be taught in schools through the medium of Welsh. Now you only hear the traditional version in very specific contexts. So if I asked you how old you were and you said 40, in Welsh you would be more likely to say two twenties rather than four tens. The traditional way is still linked most strongly to ordinal numbers: first, second, third and so on. Telling the time on a clock, or telling your age puts numbers into a kind of order and so they are likely to be expressed using the traditional method. But now Wales has adopted a modern decimal method of counting. So now we use one ten one for 11, one ten two for 12, one ten three for 13 and so on. This method is clear and is easily picked up by young children. It also has a great advantage over English because the method emphasizes the value of the digits in the order they’re written. By comparison, children who learn their numbers in English have to struggle to understand words like eleven and twelve because these words don’t actually tell you what the number really is. So children learning how numbers work in English have more difficulty than those learning in Welsh.

In Germany there has been a campaign trying to persuade Germans to change the way they say numbers. They say 9 and 20 (neun und zwanzig) for 29 rather than 20 and 9 (zwanzig und neun) and some argue that the method hinders children’s early understanding of place-value. But attitudes and current practice are too entrenched so, in reality, nothing is likely to change. But the Welsh have fully adopted their modern method and experiments with young children learning in Welsh, have shown that they have an advantage compared to those learning in English, because they catch on to place-value quicker as they have a pattern to follow.’

Anyway the book was successful even though it was initially quite difficult to publish as there are few examples of books on maths in Welsh. So that was an interesting journey in itself. It was different because it was a book that wasn’t about Welsh history, poetry or music! So after its success I was not let off the hook. The kids said: ‘ you must hang on and do something else.’ So I set daily maths puzzles on Twitter as @GarethFfowc. Ask yourself, who gets up at 7.30 and tries to do a maths puzzle? The responses are always very revealing. For example, analysing the gender of those who get involved early in the morning has allowed me to gather a sample of over 1000 people. When I ask people what they imagine the gender split might be in this Twitter group it’s amazing. Their stereotypical thinking ‘more men…. maths is for men etc. women don’t like maths’ is blown away in practice. There’s a 55% women to 45% men split. It has been fascinating to see what you discover when engaging with individuals regarding why they follow the daily puzzle.’

One day a woman came up to me in an event. I guess she was in her 40s and ran a business in south Wales. She told me she followed me but never answered my puzzles directly. I asked her why. She said: ‘because I don’t want to reveal my answers to the public.’ I said ‘So why follow me? ‘ Her answer was straightforward: ‘I run a business in Swansea and get an early morning injection of caffeine to get my mind going. I like to do the puzzle in my own time and space with no pressure, without anyone leaning over my shoulder saying: ‘what’s the answer?’ That relates to the pressure at school where I would cower in the corner and not be given time to think about the answer. People need space and time not being hassled by over zealous teachers. They need to take ownership to do their own maths and not someone else’s maths’

Gareth was then asked to adapt the book into English where its title became: ‘Count us in’. This book takes the form of a series of stories. They are inspiring, pertinent and sometimes even sad. An example that stands out goes back almost 40 years. In 1980, Gareth Roberts went to a primary school near his home in Bangor in his role of maths adviser. He sat down with 5 year olds playing a game with multilink cubes. Gareth put 5 cubes on the table and hid three of these under his hand. He then asked the group how many were left on the table. The question was then asked ‘so how many cubes are under my hand?’ The children guessed a wide variety of possible answers. Then they opened his hand to see how many were really there. One little boy said nothing through out the whole exercise. The teacher had said that the little boy, also known as Gareth, was actually very good at maths. Gareth Roberts asked him why he had not participated. He said he’d understood, but didn’t want to embarrass other children by answering over them. So together the two Gareths started building scenarios with cubes.

‘What if I gave you 100 cubes and you gave me one back. How many would you have left?’ It was too trivial a question. ‘OK, what if I gave you a million cubes and you gave me one back. How many would you have left?’ The little boy thought for only a moment before giving Gareth the exact answer. It was obvious he was a truly exceptional pupil. He then pulled out a crumpled piece of paper from his trouser pocket. In Welsh he showed Gareth what he had been reading about binary numbers. There were lots of ones and zeros on the page. Gareth asked the boy a sum involving binary numbers and he answered immediately. Gareth junior hadn’t discussed this with his infant teacher because he had sufficient sense to know she would not understand and didn’t want to embarrass her.

This little boy is now known worldwide. His name is Gareth Williams, the GCHQ mathematician who died in tragic and unexplained circumstances during a secondment to MI6 in 2010. He had been an incredibly caring and sensitive boy. As one reviewer put it: ‘The book made me think, it made me smile and, sometimes, it made me cry.’ The Guardian’s Alex Bellos said, ‘a delightful and fascinating read about the role of maths in Wales and the role of Wales in maths. Anyone with an interest in Welsh culture, maths history or education will love this book’. If you haven’t read it yet, you must!

If you happen to be in Wales on 22nd February the book is being launched at 12:30 p.m. in the Senedd, the iconic Welsh Government building in Cardiff Bay and it would be great to see lots of support for Gareth Roberts there.