Persuading maths undergraduates to take up teaching is a problem.
Encouraging pupils to love the subject is a struggle. So trying to get undergraduates and secondary students to sit in a classroom on a Saturday morning sounds like the impossible.
But it has been achieved at the maths masterclasses run by the Universities of Bristol and Bath and the University of the West of England.
The masterclasses have been running since 1990 and enthusiastic and committed teachers have been involved from the start.
Now, undergraduates have been invited to play a part in the project, run to develop innovative teaching and learning in mathematics.
It's a Saturday morning at the University of Bath in Swindon and five undergraduates are leading a masterclass on the mathematics of castles with a group of 60 Year 7 and 8 pupils. The hall is quiet as student lecturer Ben Stephen explains the engineering of medieval fortifications.
"What we're trying to do is create a kill zone - to get people trapped," he says. "How do you funnel attackers into a space where you can effectively destroy them? Remember that one arrow slit only gives you a 45-degree cone."
This is his first solo teaching exercise and there's no doubting his expertise and enthusiasm.
"To try to show children that lots of things around us are governed by maths is a real challenge," he says. "We're not really here to teach them, we're trying to unlock what they can see."
Ben Stephen and his fellow undergraduates are potential pioneers, says Chris Budd, professor of applied mathematics at Bath University.
"The Smith report, released last February, identifies a shortfall of around 3,400 specialist maths teachers in maintained secondary schools in England," he says.
"Smith suggests undergraduates as paid classroom or marking assistants as a way of helping solve the problem, and he underlines the need for universities and schools to work together, very much as we've been doing at Bath."
Chris Budd used an award from the National Teaching Fellowship Scheme of the Institute of Learning and Teaching to set up a "communicating science to the public" module as part of Bath's mathematics degree course.
Each year, 10 undergraduates follow a semester-long programme of workshops, brainstorming, planning and preparation sessions, which culminates in their leading their own Saturday classes for gifted and talented schoolchildren.
Sarah-Jane Rhead likes being an ambassador for her subject and developing her communication skills. Like some of the other students, she's considering a career in education. "I'm so pleased and refreshed to see people enjoying maths and science," she says.
In small workshop groups, the children tackle sheets of puzzles and design their castles, with students and teachers on hand to advise.
"Remember that the best height of a rampart is the distance from the rampart to the ditch, times tan," says Karina Binns, before settling down to explain ratio to a pupil who's unsure.
Most can't wait to get inventing. "Our Great Fort of Terror has double-helix stairs," says 12-year-old Matthew, making a presentation to everyone at the end of the morning. "First of all, we've got a ditch, then a hill, a maze with people shooting into it, and a portcullis with windows in a curved shape. We've got a convex and symmetrical perimeter fence.
These turrets get all the vision, then we have a keep inside."
Claire Bailey, who teaches maths at St Joseph's School in Swindon, is encouraged by the sessions. "The kids have really put the ideas they've learnt into practice," she says. "There's a good buzz, and they will go away with a positive outlook on maths. The students did well, especially considering they're not trained."
Bath University's work is part of the Wessex Masterclasses group, covering Swindon, Bath and Bristol. But Chris Budd points out that the work going on in the West Country is only part of a much bigger framework.
"The Royal Institution arranges schools masterclasses all over Britain," he says. "It is in everyone's interests to encourage young mathematicians, and any teacher who wants to organise something locally will find help and advice forthcoming."
The five students relax as the children leave the hall. "I've enjoyed doing this, it's a new experience and it meant I had to be organised," says Jo Foster.
Chris Budd has no doubt that the scheme is worthwhile: "Here at Bath, we've seen that if you involve undergraduates it undoubtedly makes maths more exciting for schoolchildren. What better role models could they have?"
Masterclasses around the country: www.rigb.orgrimaineventsprogrammeformaths.jsp Wessex masterclasses group: www.bath.ac.ukribbm