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.

Over the last two years we have had the pleasure of working with a wonderful group of students from the University of Oxford on the Maths in the City project.  In fact, as you will have no doubt realised from our previous posts about the project, these student volunteers have been vital to the success of the project.  Over the last two years they have:

• come on maths hunts in London and Oxford to take pictures and get ideas for mathematical sites;

“If you have other students who can present like these two, mathematics outreach is in good hands.”

•  created mathematical sites as examples for a public competition;
• brainstormed new ideas for the tours and developed existing ideas further in workshops;
• helped out at a competition event, engaging with visitors and assisting with the inaugural the tours;
• trained as guides, learning storytelling and communication skills as well as the content of the tours;
• lead 35 tours (reaching around 450 people): 31 for the general public, 3 for school groups, one for university students and one for university alumni;
• provided feedback on tours, suggesting improvements in their design and content;
• and used social media to promote the project and interact with the growing community, enabling us to reach an audience of over 2,000 people on Twitter and around 500 people on Facebook (this online community meant many tours were filled within days of being announced through our website and social media).

“The tour guides were absolutely delightful – if the two young presenters find mathematics too restricting, a life on the stage is clearly an option :)”

We were very fortunate to be able to build on the success of M3, the group of volunteers founded by Marcus du Sautoy to visit schools and science festivals promoting mathematics.  The core group of these students that were actively involved in Maths in the City grew from eight students in 2010 to around twenty in 2011.

In order to make the most of the time and enthusiasm of these volunteers, we discovered it was important to keep the following things in mind over the course of our project:

• Availability: We had to accommodate their schedules and manage expectations of how much time they could contribute during busy periods in the university calendar (eg. most were busy with exams in Trinity (summer) term) and holidays.
• Travel costs: It’s not fair to expect students to pay for travel between cities for all elements of the project (workshops, training, as well as the tours themselves).  This restricts access to the project for some potential volunteers.
• Reminders: The students are very reliable but they do have busy lives.  We put in place a system of reminders, checking they were aware of upcoming events they were involved with (say a fortnight before and again a few days before), sending all necessary information (eg. meeting place, time, expected participants, tasks for the day).
• Backup system: It’s good to build in some redundancy, for example having three volunteers for each tour if you really only need two so it doesn’t matter if someone drops out but this wasn’t always possible.  We were lucky enough to have paid staff who were always available to back students up if one of them was unable to run the tour.
• Use their strengths: The students were very happy to work hard in the workshops and other events but didn’t necessarily have time between events to work individually on the project.  We focussed on priming them for a workshop or event with material they could use on the day but designing the workshop so it didn’t matter if they hadn’t been able to read the material beforehand.  We realised their strength was generating ideas in a workshop, which the project team then developed into full resources that the students would go on to use on the tours.

“The tour guides did a wonderful job at putting across often complex mathematical concepts in simple straightforward language”

Some of the previous points are specific to a project that requires volunteers to travel to and run events.  We’ve learned, however, that there are some factors that would help any volunteer-based project succeed.  Here are our top tips for making the most of your volunteers…

• Emphasise what they will get out of the project: As well as asking them to help us we also made it clear what they would gain from their involvement – communication skills, experience in public engagement and science communication and an excellent addition to their CV.
• Have them involved from the ground up: Some of the students have been involved in the project from the very first meeting.  We have tried to involve them in as many aspects as possible and kept them informed of how the project as a whole was developing, as well as the parts they were involved in.  Not only did this build their expertise, which was a great benefit for their and other student’s involvement in the project, but it also created a sense of ownership of the project for the group of volunteers.
• Give them ownership: We fully supported their growing sense of ownership.  They we acknowledged at all times, on all material, as being a core part of the project, we asked for, and responded to, their feedback.
• Let them jump in at the deep end:  After giving them initial training, we made sure they felt fully supported.  For example the week before the initial run of pilot tours a team member and the kit were available every afternoon for practice runs.  We also gave them the project mobile and help numbers to call so they felt like they had backup on the day.  Then the project team essentially stepped back and handed the responsibility over to them – they lead the tours themselves with very little assistance from the project team.  Expecting the best of them seemed to give the students confidence which grew each time they worked face-to-face with the public.
• Use peer to peer teaching: After initial training workshops, the best way of training new guides has been to team them up with an experienced guide and learn from them on the job.  Not only has this meant we can continue to deliver tours while taking on new guides, it seemed to give both the experienced and inexperienced guides confidence in their abilities.
• Have a variety of involvement: Students could volunteer at any time during the project, they could attend and contribute to any of the workshops and they could volunteer to lead or just assist on tours or to join our online team.  This meant that people could be involved in whatever way felt most comfortable for them and for whatever time they could contribute.  And often once someone was involved in one aspect (say attending workshops or assisting on tours) they gained the confidence to participate in other ways.
• Say thank you: We regularly acknowledged, individually and as a group, the efforts of the volunteers involved.
• Let them eat cake: We provided snacks and drinks at workshops and meetings wherever possible.  We also covered their lunch on the days they ran tours (they could claim up to £8 in expenses). Although this might seem a frivolous thing to include in a budget this was an important part in the success of our volunteer team.  It encouraged people to come to meetings, particularly when they ran over lunchtime or in the evenings.  Providing snacks and drinks also creates a positive atmosphere around the project as it is a physical manifestation of our respect for the volunteers and a recognition of their efforts and commitment to the project.  We couldn’t have done it without them.

I hope you found this helpful. If you did or think we’ve missed anything, tell us by commenting below or dropping us a line on Facebook and Twitter.

This is part of a series of blog posts which discuss our approaches to public engagement on the topics of; teaching/public delivery of complex material, what makes the public participate in public engagement initiatives and using social media for public engagement. There’s also an intro post that gives an overview of the Maths in the City project.

This post was written by Rachel Thomas, Public Engagement Officer for Maths in the City.

To paraphrase Dave White in the first blog post in this series about the Maths in the City project, engaging the public is a delicate business, particularly when you want meaningful levels of involvement.

Getting involved in Maths in the City takes effort. We ran mathematical walking tours in the snow, hail and pouring rain and in most of these tours, everyone who booked turned up. Creating an example of maths in the city on our website requires registration and then at least ten minutes to post a picture and write about it. The quality of some of the examples suggest that far more time than this has been invested. We are in regular communication with followers/fans on Twitter and Facebook who don’t know the names and faces of the people behind the tweets and posts.

“Exceeded my expectations! The tour was interesting, exciting and FUN, even in the pouring rain! Thank you”

So why are all these people so keen to participate? Here are our top four reasons.

1. Everybody loves a competition
We launched Maths in the City on an unsuspecting world by announcing a competition. We offered serious prizes and the quality of entries were superb. To see a list of winners and what they won, visit this page on the Maths in the City website. The competition is responsible for 60% of the examples of maths in the city on this site.

Winners and runners up included a man from Ireland, a group from Spain and a young lady from Hong Kong. Despite the fact that we could not pay for travel, all winners and runners up attended an award day at Oxford except for the girl from Hong Kong, who sent a video message. Pictures from the award day are available on Flickr.

The winners of the Maths in the City competition, with Marcus du Sautoy

2. Everybody loves a Dave
Maths in the City has a mascot, named Maths Dave. Placed as a resource on the project website as piece of whimsical fun, the cult of Maths Dave quickly grew, as evidenced in the Maths Dave forum. (Get your own Maths Dave here.)

One maths teacher from Walthamstow School for Girls used Maths Dave in her lessons; her class did such a great job with their Maths Daves and Davinas that the teacher and two students were invited to the competition award day to receive a special prize on behalf of the class. A year later we had the pleasure of taking 60 girls from the school on our London maths tour.

The Maths Daves and Davinas created by the year 1 maths class from Walthamstow School for Girls

3. Everybody loves seeing their homework on the fridge door
The Maths in the City project is produced and managed by us lot at TALL. We also design online courses, including The Number Mysteries, which is based on a book written by Marcus du Sautoy of the same title. This course includes an assignment option in which students write an example of maths in the city, which they can add to mathsinthecity.com once it has been marked. Here is an example on Umhlanga Pier, written by a South African student. Students of the Number Mysteries course appear to enjoy the opportunity to share their work in a public place and the project benefits from a steady stream of high quality examples of maths in the city from around the world.

Add your mathematical stories to mathsinthecity.com

4. Everybody loves a delightful and articulate student who is passionate about their subject
The lifeblood of this project has been the student volunteers who have helped to design the walking tours, lead the walking tours and engage with the public through our social media channels. A journalist from the Oxford Times was so charmed by one of our volunteers that I think he fell a little bit in love. Read his article ‘Oxford by numbers’ and judge for yourself.

“I would like to thank our guide for making the mathematical concepts very clear, and the tour very enjoyable”

These are our top four reasons why we got meaningful engagement with the public. Do you have other reasons that have come from your experience in public engagement? Please tell us by  commenting below or by dropping us a line on Facebook and Twitter.

(And when you’ve done that, keep your eyes peeled for the rest in our series of posts on our approaches to public engagement. Topics to come are; teaching/public delivery of complex material, community facilitation/the use of social media and the management/encouragement of volunteers. We’ll be announcing them on Facebook and Twitter.)

For the last two years I have been the Creative Director of the ‘Maths in the City’ project. At the helm was Marcus du Sautoy, that maths guy from the TV and Radio who also happens to be a member of my Continuing Education department here at Oxford and the Charles Simonyi Professor for the Public Understanding of Science. The idea for the project came from discussions Marcus had with secondary schools in London. The overall aim being to ‘engage’ the public with maths by demonstrating how the science of numbers is integral to the urban environments most of us inhabit. The 2 minute video below gives a flavour of what it’s all about.

Funded by the EPSRC (who fielded an excellent and experienced mentor for the project)  via a public engagement grant the project ran a series of walking tours around Oxford and London which anyone could attend for free. The tours were highly interactive (string, chalk, sweets, springs, sticks, marbles etc.) and designed to interest people of all ages with potentially a very basic understanding of maths. The guides for the tours were all maths students drawn from Marcus’ cabal here at the university called M³. An important aspect of the project was giving these students the opportunity to practice their public speaking skills at the sharp end of maths-communication i.e. in a street with a group of strangers that have  random levels of subject understanding. To support and promote the tours we built a nifty website. Nifty because it allows anyone in the world to create a maths ‘site’ and, if they so desire, a tour of their own. The M³ group used the site to help author our main tours of Oxford and London. It also gave us an opportunity to run a competition to increase the visibility of the project and to help populate the website with maths from around the world.

The officially funded part of the project is coming to a close but I’m happy to say that the M³ group will continue to run and develop the tours. Overall the project was a great success:

• over 2500 people engaging with us via social media
• over 460 people attended mathematical walking tours of Oxford and London
• over 130 examples of ‘maths in the city’, from around the world, posted on www.mathsinthecity.com, the vast majority from members of the general public.

Having a world renown mathematician and broadcaster as a figurehead certainly helped promote Maths in the City but the project team who were all assigned 1.5 days a week or less were the real behind-the-scenes workers: designing the details of the tours, putting together the website, encouraging an online community, training the tour-guide students and generally dealing with all the nuts-and-bolts involved in running public walking tours. What I am most proud of is that we designed multiple ways to engage with the project, for example:

• To promote the project and to give it a ‘friendly’ face (we don’t underestimate how daunting contributing to an Oxford University project might be for some) we provided cut-out-and-keep template of our logo/mascot ‘Maths Dave’. Much to our delight people began to submit photos of their very own versions of Maths Dave.

Maths Dave’s in Turkey

• People could submit a mathematical site from their city. These ranged from elementary maths such as this site on triangles (one of our competition winners) through to sites such as the ‘Squeaking Labyrinth’ (which is certainly beyond me) and everything in between.
• The tour ‘sites’ were essentially neat chunks of teaching material (all openly licensed as ‘Open Educational Resources’) which all included great hands-on activities. The project used the tour sites to give ‘stationary’ walking tours or ‘talks’ as they are normally known as part of public lecture series i.e. you don’t have to take the walk to get the maths. One of the most widely appropriated was the Sheldonian Roof site which inspired a whole morning of teaching at one secondary school culminating in this spectacular model.

No glue was used!

• If balancing a ridiculous amount of rulers across desks is not for you then there was always the geeky banter to enjoy over on our Twitter stream and Facebook page or the opportunity to read about the project in one of our many write-ups including the New Scientist.
• The hub of the project’s activity was of course the physical tours themselves. I went on a few to check everything was running smoothly and remember a six year old and his older brother happily helping to make triangles, rectangles and hexagons with a loop of string in one of the quads of St. Johns college while the adults discussed the shapes which most efficiently tessellate on a two dimensional plane.

A maths student leads a London tour across Millennium bridge with the aid of Maths Dave on a stick.

Engaging the public both online and offline is a delicate business especially when your tour-guide group  is made-up of volunteers new to public speaking, trying to complete Oxford degrees and acting as the public face to an institution which has very refined views on ‘reputation’ and ‘credibility’. Instead of writing a dusty report on the project which would end its days in unread pdf purgatory on the outskirts of a funding council website we have chosen to write a series of blog post which discuss our approaches to public engagement on the topics of; teaching/public delivery of complex material, what makes the public participate in public engagement initiatives, community facilitation/the use of social media and the management/encouragement of volunteers. Watch @daveowhite or @mathsinthecity as we release the posts over the next few weeks. I hope they will be insightful for those of you considering public engagement projects.