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Faculty of Mathematics


The Centre for Mathematical Sciences is again busy with students beginning their undergraduate maths courses here in the Faculty. This includes the first students to benefit from the new STEP Support Programme - which aims to give all university applicants the opportunity to reach their mathematical potential by providing early and effective intervention.

"The ultimate hope is to make a real difference by levelling the playing field and to encourage more applicants from disadvantaged backgrounds and under-represented groups," says Dr Orsola Rath Spivack, Faculty Admissions Officer.

STEP is an additional mathematics examination, taken at the end of year 13, which forms part of offers to applicants for mathematics, and some related degrees, at Cambridge and a number of other universities. The content of the STEP exam is based on A-level Maths and Further Maths, but questions are designed to be more like those you meet at university in style.

Our aim is to ensure that everyone who has the mathematical potential has the tools, experience and confidence to do well at STEP, no matter what their educational background Claire Metcalfe

The new STEP Support Programme is designed to help university applicants develop their advanced problem-solving skills and prepare for sitting STEP exams. The programme is developed by the Faculty's Millennium Mathematics Project, and the resources are free and open to anyone.

"Some schools have a lot of experience at helping students prepare for STEP. We are particularly aiming the programme at students whose school does not have much experience and cannot provide much support preparing for STEP," says Claire Metcalfe, who developed the resources for the programme.

"Our admissions process aims to identify the students with real potential and motivation, the ability to think creatively in mathematics and to build on their necessary base of A-level knowledge (or equivalent) by using new concepts to solve challenging problems," says Rath Spivack. STEP is demanding, but preparing for the exam gives students a chance to engage with interesting, challenging mathematics, to stretch themselves and to develop the mathematical reasoning, independence and confidence needed in a Cambridge undergraduate mathematics degree.

"We hope that, by trying to ensure that everybody has support for STEP, many more students will be able to achieve their potential in STEP and actually enjoy solving questions, so this in turn will change their attitude to STEP," says Rath Spivack.

Bridging the gap

The main component of the STEP Support Programme is a course of free online modules for individual additional study. These are designed for students to work on weekly, starting in the summer of Year 12 (although it is possible for students starting later to catch up). Each module consists of a structured mathematical problem-solving assignment, leading to work on selected STEP questions, with support material and partial solutions to help students assess their progress and identify areas that need more work. The online resources are supported by a discussion forum staffed by volunteer Cambridge maths students and faculty staff. The online programme is free and open to everyone, regardless of which university they are applying to. Indeed the programme is recommended by many other universities too as an excellent preparation for potential applicants, including the University of Oxford.

To complement and extend the online programme, the faculty ran two full-day STEP Support events for state-school students in March 2017. Every UK state school student holding an offer from the University of Cambridge to study Mathematics was invited to attend one of these days, with 188 students from all over the UK participating in these events. These events were a very positive experience for the students involved: "It introduced me to other people from the same situation also being challenged by STEP, and was a great day of doing maths with other like-minded people," says Molly Barker, now an undergraduate in the Maths Faculty.

"For many students, their first experience of STEP can be a shock as they have never (or rarely) come across a maths question that they cannot do. By providing a gentle introduction to solving STEP questions, and by gradually taking away the scaffolding and support, we have created a course which bridges the gap between A-level and STEP," says Metcalfe.

The foundation modules, the first part of the course, are designed to gradually take students through a mathematical warm up, introducing them, from the very first assignment, to carefully selected STEP questions with lots of scaffolding to help tackle them. "I found the format of the foundation modules very good. As well as being a gradual build up, it also allowed you to reflect on the STEP question fully and understand how similar STEP questions with the same themes might be solved," says Molly Barker, currently an undergraduate in the Maths Faculty who took part in the STEP support programme last year. She also found the partial solutions particularly helpful: "When you were completely stuck on a question, it was nice to get a hint and be able to then make progress yourself, rather than having to lose the experience of doing the question by getting a full solution."

Later parts of the course, the STEP II and STEP III modules, cover material that not all students will have encountered until the end of their final year at school. "To help with this, we derive a lot of the formulae needed in the foundation modules and then we provide topic notes so that students can attempt the STEP questions even if they have not covered the relevant topics in their lessons by that point," says Metcalfe. "The topic notes were invaluable because my school didn’t teach some topics," says Barker.

The programme has been deliberately designed to be open access and free to all. "We want to encourage people to dip a toe in the water of university style mathematics, as well as support and encourage them to think about whether this kind of maths, and coming to study at Cambridge, is something they are interested in," says Julia Hawkins, Deputy Director of the Millennium Mathematics Project.

Making the next STEP

The resources were released weekly from August 2016, and have had over 250,000 page views in the last year. There were 5,500 downloads of the first assignment alone. And the most important evidence of the programme's success is that some of this year's maths undergraduates, including Barker, have noted the programme’s impact on their journey to Cambridge.

"The 'self-contained' nature of the support programme meant that what you had learnt at school didn't matter," says Barker. "You could just use the programme to fully catch up and be able to give your best shot at STEP. Her fellow student Andrew Ejemai agreed: "I found the Cambridge online STEP Support Programme very useful in my independent preparation for STEP papers."

Their colleague, Lewis Croney, was originally at a secondary school that was under-performing against national benchmarks and where few students went to university, let alone Cambridge. Croney was supported by his sixth form college and took part in the STEP Support events, and is now studying Maths at Trinity College. "I am ecstatic to be joining the University of Cambridge to study Mathematics and am looking forward to learning alongside so many like-minded people. It really is a dream come true."

"A long time ago, I was a student from a school which had no history of students sitting STEP. In designing resources for the programme I often thought about what the 18-year old version of me would have found useful," says Metcalfe. "It can be a lonely and sometimes scary experience working through STEP papers, and throughout the programme we try to build students' confidence, and hopefully make the experience more enjoyable." The programme is designed to show that rather than a barrier to entry on mathematics courses, STEP can be an opportunity to get stuck into some challenging and exciting maths at school.

"STEP questions are hard but they are also really fun to do," says Barker. Metcalfe explains that the programme has meant that talented mathematicians, regardless of their background, have access to opportunities to reach their full potential. "Our aim is to ensure that everyone who has the mathematical potential has the tools, experience and confidence to do well at STEP, no matter what their educational background."

Find all the free online STEP Support Programme resources at