Public engagement, outreach and maths communication activities come in many forms - and all of these terms are used interchangeably to mean similar things, although there are subtle differences between them.

As the name 'public engagement' implies, it's meant to be two-way: public engagement can involve bringing the public in to consult/participate in experiments, especially in medicine. It's worth bearing this in mind when planning public engagement activities - mostly people think of it as just being about exposition: a chance to impart your knowledge and share your enthusiasm, but workshops can be very instructive to both sides. Doing great outreach workshops can help you go back to your work with more ideas.

It's important to remember that public engagement is often centred around, or promoted as an opportunity for, learning (whether it’s people actually learning new skills or information, or just general stereotype-shifting) - it can also just be entertainment that’s informative, or it can be straight-up lectures packed with facts for those who are keen.

Here are some crucial things to bear in mind:

• One key thing is to know your audience: their age and knowledge/ability level (both what level of education they’ve completed, and their ability level within that - is it a mixed group, or Gifted & Talented?), the size of audience you’re working with, and their background can all affect the type of engagement and need to be considered when planning.
• There are many different formats for public engagement: in-person (or online!) talks and workshops; other types of online engagement; videos/TV/radio; and written material. It can be live or asynchronous.
• The person delivering the engagement will make a difference to how it comes across. Everyone has their own style and things they like doing; you may do all, some or none of the many types of PE out there, and they often feed into each other.
• Budget can be a factor; some engagement is done alongside other work, but some people do it as a career; costs are often involved in delivery and where the funding comes from can affect the outcome.
• PE projects might have differing aims: projects are often conceived with a goal in mind, and evaluation can be used to determine if it has reached this goal.

One other thing to bear in mind is that bad engagement - whether it's delivered by people who are only doing it to tick a box, or who don’t understand the difference between delivering information and engaging people; engagement that leans on stereotypes, reinforces negative ideas, or employs bad or confusing explanations - can impact on perceptions negatively.

Particularly in maths, people can approach things with a skewed perception: thinking that the subject is difficult or boring, perceiving it as being only done by a certain kind of person, and often having a lack of confidence in their own abilities. It's important to make sure you don't reinforce those ideas by making people feel stupid, or overcomplicating things.

However: don’t be intimidated by this! Remember that you’re facilitating an interaction between the audience and the exciting cool content you've prepared for them. When done properly, it should hardly seem like you’re doing anything at all. You don’t have to be the star of the show - but you can make use of character to build credibility and engage people.