Case Study: UK Mathematics Trust Competitions

Audience group: Lower secondary or Middle school, Upper secondary or High school, Sixth Form or Junior College

Audience interest level: Engaged

Topics: General maths, Problem solving

The UKMT aims to advance the education of young people in mathematics, in particular, by organising and running mathematics competitions.

Origins of the Project

The original challenges were run by the UK Maths Foundation, which was run single-handedly for 8 years by a reader at the University of Birmingham. As the challenges grew in success, there was need for a bigger organisation, and the University of Leeds took it over in 1996. They employ a small admin team, but the rest of the organisation is made up of volunteers.

The first Maths Challenges took place in 1988, and there are now three levels of challenge - junior, intermediate and senior.

Practicalities

The test is delivered as a multiple-choice paper, with questions written out and a separate answer sheet. The papers are sent out to schools in advance, and while it does have to be done on a particular day, unlike public exams there’s not a specified time.

Some schools enter whole year groups, while others hand-pick - most schools set by ability in maths, and maybe the top two or three sets might be entered, but it varies a lot between schools. Typically around 2500 schools enter the competitions each year, resulting in 250,000-300,000 students doing the junior and intermediate challenges, and more like 100,000 doing the senior challenge.

We give out certificates to the top 40% of participants. The top 7% get Gold, then up to 20% would get Silver, and between 20%-40% would be Bronze. Some schools might run it more competitively than others - it’s up to the individual teachers. Our aim is to give them the sort of experience they don’t normally get in the classroom - we put a bit of humour into it as well. For many students it’s just 1 hour a year and probably soon forgotten, whereas those who go on to do follow-up exams or the mentoring scheme or summer schools can get a really positive experience from it. Many schools send details of successful candidates to local newspapers for publicity purposes.

There’s also a junior and senior team challenge, where schools are represented by teams of 4 - they start off with a local round and can then qualify through to a national round.

While the administration of the competition itself - contacting schools, sending out the question papers, feeding them into the optical mark recognition machines and collating the results - is undertaken by the employed staff at the university, the mathematical work, setting the questions is done by a team of volunteers, consisting mainly of maths teachers and a fair number of university staff, most of whom are retired.

The content of the questions isn’t necessarily anything harder than topics they might come across in their curriculum, but aims to enrich and show them different materials. There’s very little technical stuff - it’s more about problem solving, and hopefully more interesting. Even with a limited amount of technical ability needed, it’s still possible to ask some really quite difficult questions.

Volunteers also form the board of trustees which sits above the admin staff, who are responsible for overall policy. The vast majority of our volunteers are very committed. I’ve been a volunteer since before UKMT existed - I actually wrote to complain about one of the questions on the papers, and was invited along to Birmingham and that’s how I got involved.

Every year I organise a meeting where we set draft papers for the junior and intermediate challenges. We have to write new questions every year - it gets harder and harder!

For higher-performing candidates, there’s a follow-up paper at each level which consists of longer questions - typically 6 on a paper for a 2 hour exam which require full written solutions. The marking for this is done by a team of 50-60 of us who get together in a hotel in Leeds and mark them over a weekend.

This is often a good way to find new volunteers for question setting - they come along to a marking weekend first. We also sometimes pick up volunteers when they bring a team along to the team challenges, and talk to our staff there about getting involved.

As well as the competitions, we also run a mentoring scheme for bright students who want to get more interested in maths, so they can be paired with a mentor. We also run summer schools for the higher performing candidates. Usually a week long, we started with just one a year in Birmingham and now there are six, including a couple in Oxford and two or three in Leeds.

At the top of the pyramid, there’s the International Mathematical Olympiad, held every year with teams of 6 from about 150 different countries. We’ve hosted that twice - Glasgow in 2001, and Bath in 2019. The highest performing challenge participants can make it into the team for the Olympiad, via follow-up papers and quite an exhaustive selection process - it’s not the ultimate goal, but for higher performing candidates the GCSE syllabus doesn’t do them justice at all, and it’s an opportunity for them to see that there are far more interesting things in mathematics than what’s on the syllabus.

The UKMT is funded partly by sponsorship, but nearly all of the money comes from the fees we charge schools to enter their students in the challenges. We try to keep the fees as low as possible, but it subsidises all the other activities, including the summer schools, Olympiads and camps. We also publish a yearbook every year with problems from the challenges, as well as a set of books of problems collated by topic at different levels. A lot of parents buy them for their children who are interested in maths, and we make quite a bit of money from selling them.

Accessibility and diversity

The challenge papers are sent out to schools well in advance, and are in the form of 4 sides of A5, so teachers can enlarge them for pupils who need a large print version. We also offer large print versions of the paper and braille papers for free as well as a speech function on our online questions.

Since there’s a requirement for a school to have a teacher keen enough to run the challenge, it’s hard for us to reach all schools. If we don’t get an entry from a school one year then the staff at Leeds follow it up. Schools pay to enter the challenge, but UKMT have tried initiatives such as offering free entries, and sending sample materials. The collected books of problems are also a good resource for schools - teachers don’t have too look to hard for materials to interest the brighter pupils.

The summer schools are heavily subsidised to make them available to as many people as possible, and if someone had been invited and couldn’t afford the fee, I’m sure UKMT would be prepared to help financially if their school couldn’t.

The people who do the invitations to the summer schools try to get a reasonable balance in terms of gender and other factors. We ensure that half of all summer school students are girls and aim to have 80% of students coming from state schools. In the last 5-6 years at least, one of the Summer Schools we ran at Oxford was for girls only. Since we get lower numbers of girls in the International Mathematical Olympiad team - it’s rare to have a team of 6 boys, but generally there are only 1 or 2 girls - we started a European Girls’ Mathematical Olympiad in 2012, and now other countries are involved with that as well.

Challenges, Evaluation and Improvements

Since the challenge can be completed any time during the specified day, it has become more difficult to administer, with the advent of social media - particularly with the intermediate and senior challenges. There are chat rooms where candidates can discuss a paper when other schools won’t have seen it. We do liaise with the people who run those chat rooms and try to discourage them from putting anything up before the end of the school day, to try and keep some sort of confidentiality.

Up until this year we had a system to discourage guessing - the paper was organised so that the first 15 questions had no penalty for a wrong answer, but for the harder questions 16-25 you could lose marks for wrong answers. We wondered if this might be disproportionately impacting girls, since our experience has been that generally, they can be less adventurous and more reluctant to guess.

We decided to implement a trial this year in the Junior maths challenge held in April to do away with that negative marking system so there would be no penalties for wrong answers. This was very difficult to implement, largely because of COVID. We had some candidates sitting the Junior Challenge in schools, some doing the paper online in schools and some doing the paper online at home, where we could not be sure that they did not receive any help and did not use a calculator. This made it impossible to draw any conclusions from the trial.

We do evaluation via a survey following each Challenge and one at the end of the year with all schools that take part during the year. We get some feedback from teachers and students about the materials and most of what we get is positive. Occasionally a teacher will say “I don’t think that was accessible, it was using terms my candidates didn’t understand” - because we’re volunteers, we’re limited in what we can do, but we can take it on board.

We also look at the results of each year’s Challenges, particularly the statistics showing how well individual questions were answered, at problem group meetings before setting the following year’s papers.

One other part of our evaluation is numbers from year to year - when UKMT started it grew quite rapidly, but it’s plateaued over the last few years with some variation. We’ve also got a much broader range of activities than we started with - when the UKMT was set up in 1996 all we did was run the 3 maths challenges, the follow-up papers (including those which led to the training and selection of the team to represent the UK at the International Mathematical Olympiad) and one summer school a year. Since then we’ve added the team challenges, more summer schools and the mentoring scheme.

More information

UKMT website: UKMT.org.uk