There are many facets to the Maths in the City project – public engagement, connecting through social media and working with volunteers. The central goal of the project was to develop and lead mathematical walking tours of the ‘city’ – we wanted to tell the stories of the maths in the city to as wide a range of people as possible.

The people telling these stories were mathematics students, many of whom had no public speaking, science communication or teaching experience at the start of the project.  They didn’t even necessarily have experience in the areas of mathematics they were communicating but what these students did have was enormous enthusiasm about their subject and for the Maths in the City project.

In order to make the walking tours a success we had to harness that enthusiasm and make it as simple as possible to lead the tours. We found that there are four steps to designing walking tours that are simple to lead:

1. Take care of the practicalities

Minimise the amount of walking, traffic hassles

We quickly realised that if we were to have enough time for discussion at different stops on the tour we weren’t going to be able to walk very far.   It seems that the walking pace of a group of people exponentially slows down with the size of the group (NB – this may not be a mathematically rigorous conclusion!)

Keep an eye on your group size

We also found that the ideal size of a group on the tour was around 15 people.  The tours still worked well with larger and smaller sizes (we ran tours for 4-30 people) but 15 meant that everyone could participate without feeling constantly in the spotlight.

The best location to talk about a site isn’t always where the site actually is

The locations for the sites on a tour are an exercise in compromise. You need space available for a group of people to gather, the levels of background noise need to be taken into consideration, and you need to factor in the distance between the previous and the next stops on the tour.  For example our site about the Gherkin in London is on the opposite side of the river to the building, which allows the group to have a view of the skyline and has the space to build structures out of garden canes.  Similarly, our site for the Sheldonian Theatre in Oxford often ends up being outside the adjacent building due to space available on the busy pavement.

2. Make the maths accessible

Revealing the depth of simple ideas

We wanted our tours to be accessible to as wide a range of people as possible: grandchildren to grandparents, maths graduates to maths phobics, teachers and interested bystanders.  Simple concepts, such as the strength of triangles or the efficiency of hexagons, proved enticing to people who might initially think maths is daunting.  Guides then explored the deeper mathematical consequences of these simple ideas or wider applications, which provided interest for the more mathematically experienced.

“On the occasions when it started out too simplistic, the guides were happy to answer deeper questions.”

Hands-on demonstrations can make complex ideas more concrete

This didn’t mean that we shied away from sophisticated mathematics.  We found that you could make concepts like graph theory, topology, symmetry and group theory more down-to-earth by involving the group in demonstrations that illustrated and explored the ideas.

“The practical demonstrations made the concepts easy to understand”

3. Make the communication easy

Telling stories

The most important thing for us to remember has been that we are telling stories, stories that just happen to be about maths. It helped to emphasise that these stories should have a beginning (often pointing out the link to the location), a middle (revealing the maths) and an end (perhaps a surprising demonstration or revealing the maths in a wider context). We particularly tried to provide a final sentence that would provide a punchy and conclusive end to the story, enabling the guide to wrap up that site and move onto the next.

Crib sheets

Some of the stories involved maths concepts set in a historical or modern context and a number of hands-on demonstrations using multiple props.  We quickly discovered that for these more complicated sites it helped to provide a crib sheet at the end of the notes highlighting how to weave together the main points of the story with the demonstrations.

Questions and conversations

We asked our guides to think of the tours as conversations.  We suggested lots of questions in the tour notes that guides could ask to engage the group and they encouraged people to ask them questions too. We found this advice from our EPSRC mentor about asking and encouraging questions very useful:

• Start with easy questions that anyone could answer (eg. what shapes/patterns can you see on this building?) and build up questions in layers of understanding.
• Give people time to think and respond, don’t be worried by silence, it’s just a little thinking time.
• When someone answers a questions, clearly repeat their answer.  This makes sure that everyone has heard the answer and is a nice affirmative response for the person concerned.  It also is an opportunity for you to use the language they have supplied, helping you establish the group’s vocabulary and level of understanding and building from there.

People on the tour often had information about sites that we didn’t know or their questions and interests that meant the story we told on our walking tours was different every time.  The tour notes were just a suggestion and guides were encouraged to tell the stories their own way and respond to the interests of the group.

 4. It’s personal

“The tour guides were fantastic!”
“ I’m appreciating the things around us in a different way, looking afresh at things.”

In the end it was our tour guides, as much as our content, that made the project such a success.  This personal interaction with mathematicians, both on the walking tours and through our social media, has had as strong an impact on our audience as the mathematical stories we told.  For many tour participants meeting the maths students who led the tours and hearing about their personal journeys in maths has created a lasting image of mathematicians as creative, entertaining, passionate and ordinary people.  We hope we have helped people see mathematics, as well as the city, in a new light.

This post was written by Rachel Thomas, Public Engagement Officer for Maths in the City, and is part of a series of posts that discuss our approaches to public engagement.