Having been in charge of a mathematics society in secondary school, here are some of my thoughts on the role of a mathematics society. I would go through the possible missions / target audience of the society and the possible activities that could be held.

What should the target audience of the society be?

Of course, the expected mission of a mathematics society, at least at a secondary school level, is to “promote” mathematics to students. This may seem to be a specific enough goal. Yet I would argue that it matters a lot what kind of students you’re trying to promote mathematics to.

For example, if you are targetting underperforming students, you may try to organise classes teaching them after school, or providing free mentorship services. Only when they begin having some success at mathematics would they have the ability or interest to understand further about mathematics.

If you are targetting students who are ambivalent about mathematics, you may try to present some cool facts about mathematics, or persuade them that a deeper understanding of mathematics is the key to understanding how this world works.

If you are targetting students who are interested and good at mathematics, you may instead want to introduce mathematics at a rigorous level by publishing introductory articles to advanced mathematics or show them what studying mathematics at a university level is like.

The three audiences mentioned above are very different in nature, and it’s highly unlikely that your mathematics society would be able to focus on all of them. As such it has to focus on one or two.

My recommendation: Focus on students who are interested and good at mathematics

Helping underperforming students is a great idea, yet teaching requires training, especially when the committees of the mathematics society are just secondary school students themselves. You would also need to cooperate with the school authority to genuinely find out those who need help.

Arousing interest in mathematics for the general student population is also a very oversaturated market. With so many great content creators on youtube, what more could a secondary school mathematics society do than just sending out hyperlinks to youtube videos? (This should however definetely be done as much as appropriately so in chat groups)

As such, I believe focusing on students who are interested and good at mathematics should be the priority. This could mean holding events introducing what studying mathematics in university is like, or providing opportunities for students to learn ahead in maths together. I would argue despite having to compete with universities’ outreach programmes and other online resources, secondary school mathematics society have a place to fill.

Firstly, a maths society could leverage its alumni network. No matter how many times you hear how great it is to study mathematics from university websites or online chat rooms, it would never be as trustworthy nor as inspiring as listening to an alumni share their experiences.

Secondly, committee members would be more motivated to organise events for the society. Committee members are almost by definition interested and able in mathematics themselves. They too would be interested in how to push their mathematical knowledge further and what studying mathematics in university is like. They would be motivated to contribute to the society since they would themselves benefit from it.

Consequences

Suppose you do believe that the society should target students who are interested and good at mathematics, how would this shape the activities that the society holds?

Firstly, events should be more technical in nature. Events should strive to emulate what studying mathematics at a university level is like. For example, mathematics could be exposed in a more abstract or rigorous manner. The mathematics discussed also need not have any real world or physical applications.

Secondly, events should focus on facilitating social interactions between participants. As events become more technical, there will be fewer participants. This is very natural. After all, how many students in a secondary school are truly interested in mathematics? Yet this is not necessarily a bad thing. Fewer participants mean a possibility for more interaction. Get people to know each other. Form support networks for mathematics competitions or university admissions. Close-knitness is what makes any society special.

What activities could be held?

1. Physical or Online Talks

It’s incredibly easy to host a talk. You only need a guest, a venue and an audience.

Of course, some talks are easier to plan than others. The easiest talks to plan might be experience-sharing sessions. You could invite an alumni who is studying / has studied mathematics at university and talk about what it was like and have a QnA session afterwards. Alternatively you could ask an alumni to do a talk on a bit of mathematics they find interesting (which would take a bit more planning).

Interactivity is crucial. As the attendance numbers wouldn’t be that large it’s important to get attendees to interact with the guests. The guest would also feel that they’ve resonated with a smaller audience more deeply.

Personally, I’ve found these experiences to be far more convincing than official “testimonies” from universities. (which naturally sounds more like advertisements)

2. Gatherings

It could be as simple as a simple lunch gathering or an afterschool meetup. Provide free food / drinks and get people to do maths together. Make sure junior members don’t feel alienated and actively look out for those with potential who may one day take over the society, and make sure they don’t feel alienated! Get teachers / alumni to show up to make things interesting.

Arts and crafts are also an option – get people to make paper dodecahedrons / icosahedrons. Or you can get board games like Catan, Risk or Rummikub.

3. Whatsapp / Discord / Messenger … group

It’s not that hard to keep it active. Post about snippets of maths you’ve found. Post about all the outreach programmes universities are doing. Post about the activities the society is going to hold.

4. Wildcard

Innovate! Come up with new stuff. Build new traditions.

Conclusion

Ultimately, focus on the people. Get people to form life-long friendships. Build support networks between generations of mathematicians.