How to win the Maths Challenge

Simon Singh, founder of the Good Thinking Society and author of The Simpsons and Their Mathematical Secrets, believes that parents should ferociously ‘lobby their children’s schools’ if they still don’t run the annual Maths Challenge. For those not familiar with it, the Maths Challenge is a phenomenally well-organised competition run by the United Kingdom Mathematics Trust (UKMT). It doesn’t cost much to enter — £13 for ten papers (for ten pupils) — and is a massive opportunity for children from all backgrounds.

UKMT, a charity founded in 1996, aims to ‘advance the education of young people in mathematics’. It works with schools and volunteers to arrange junior, intermediate and senior challenges. There are follow-up rounds, Olympiads, team events, mentoring schemes and summer schools. About 700,000 children participate every year.

Throughout my career as a maths teacher, I have seen too many maths-savvy children cruise through GCSE content but left unfulfilled or even under-prepared for the challenges of further study. Unlike subjects such as English, history, science and geography — which can all be experienced outside the classroom — mathematics has always been harder to bring to life. It is a world that can sometimes seem uninspiring.

Over the past two decades, much attention has been given to improving mathematics teaching in Britain. How to get more girls interested? How to foster confidence in learners for both functional and abstract forms of the subject? How to use different teaching styles to spice lessons up and cultivate a deep understanding and genuine curiosity? Perhaps we will never truly solve these dilemmas because maths is a discipline: often prescriptive, sometimes applied. But the Maths Challenge does an excellent job of inspiring children who are interested.

How does it work? The junior challenge in April is aimed at years 7 and 8 (key stage 3); the intermediate takes place in February for years 9, 10 and 11 (key stage 4), and the senior in November for A-level students. Junior and intermediate papers last for one hour and comprise 25 multiple-choice questions that cover all strands of mathematics including geometry, algebra and number theory. Five marks are awarded for the first 15 questions, and six marks for questions 16 to 25, with marks lost for each incorrect answer (though this was scrapped in the 2020 and 2021 challenges). No calculators are allowed.

The senior challenge is a 90-minute paper. All candidates begin with 25 marks and either gain four marks for a correct answer, or lose one mark for an incorrect answer. Guessing is not an option. Participants in all challenges are able to earn bronze, silver and gold awards presented to the top 40 per cent that year, in the ratio 3:2:1, with gold awards typically representing the top 7 per cent.

And it doesn’t end there: top achievers qualify for the Kangaroo and Olympiad rounds, depending on the age of the participant, while senior rounds offer the chance to participate in the Andrew Jobbings Senior Kangaroo, the British Olympiad rounds, or the Mathematical Olympiad for Girls. These achievements act as entry points to the selection and training programmes for international competitions held in Oxford, Cambridge, Australia and Hungary. In other words, it is very prestigious and a big deal.

In 2004, when I was 12, my maths teacher presented a dozen of us with Maths Challenge papers, gave us an hour and explained we had ‘nothing to worry about’. We’d had no warning or preparation, but got on with it. A month later and the majority of us had earned certificates. I was never smart enough to qualify for Olympiad rounds, but took part in the challenge every year until I was 18. It was an escape from the more mundane formulae and methods found in the GCSE and A-level syllabus. It taught me to be intuitive. Now that I’m a maths teacher, I value what I learned, but I also wish my school had made a bigger deal of the Maths Challenge.

Parents often want to know whether participation in the UKMT Maths Challenge will increase their child’s chances of securing a place at Oxbridge or Imperial, or on an engineering or medicine course. There is reason to believe that it helps. Persistent success in any of the challenges is a highly prized achievement, and a certificate or qualification from Olympiad rounds at senior level will hold you in good stead on a personal statement for university applications.

In practical terms, any opportunity to solve problems in unusual contexts is great preparation for MAT (Oxford) and STEP (Cambridge) exams. There is also a long-standing association between Trinity College Cambridge and the upper echelons of the National Mathematics Summer School, which the college hosts.

But regardless of where children end up at university, being ranked in the top 7 per cent of some of the brightest students in the country is certainly something to be proud of.

That’s why at my school, an academy in east London with high proportions of children on free school meals, the priority has been to maximise participation among our brightest students and make them competitive. To help achieve this, we’ve looked to other schools to see how they have fared.

One that has often done well is Tiffin School, a boys’ grammar in Kingston. In 2019 Tiffin earned a whopping 134 gold certificates in the junior competition, out of a total of 264 participants — undoubtedly the highest in the UK that year — trebling their gold awards over a seven-year period. When I asked about the secret of Tiffin’s success, Dr Jamie Frost, founder of Dr Frost Maths and a maths teacher at Tiffin, pointed to a variety of factors, notably embedding UKMT material into normal lessons, ‘rather than separating it from the main curriculum’. He also told me that the UKMT Challenge requires ‘more intuition than mathematical common sense’. The degree of problem-solving is ‘much greater [than] GCSE content. There is not always an obvious strategy.’

We have tried to follow Tiffin’s example and our number of certificate winners has shot up, from a modest handful in 2017 to 34 (more than half of our participants) in the Junior Challenge 2021. Five of our pupils progressed to follow-up rounds in the intermediate, with one of them securing a place on the summer school programme, and two being invited to participate in the highly competitive Maths Masterclass Tutorials.

Simon Singh believes that children should encounter tricky, gritty maths problems in peculiar contexts, from as young an age as possible. The UKMT Challenges allow them to do just that. It is, in his words, a ‘very positive part of the maths landscape’ and all schools in the UK should consider it. Parents of the world unite: get your children’s schools to take up the challenge.