By the time I'll be teaching I'll have finished my Maths and Further Maths A-Levels and I would also have studied a fair amount of higher material.
Those are all good suggestions. One thing troubling me is that I want to help kids develop their problem-solving skills. Ideally I'd introduce some new puzzle and give them a few hints and they would work it out, but from my limited experience with my 9 year old cousin (who is fairly bright), it either ends up with me giving too little help (so he gets stuck and gives up in frustration) or too much help (so he's just following along with what I'm saying rather than discovering something for himself). How can I best strike the balance?
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If there will be effort put into actually building something, we might want to look into what other purposes it could serve, such as virtual (persistent?) meetups, remote CFAR sessions, etc. with features such as a "talking totem" that can be passed to enable audio from that person.
(Split from a previous comment for concept independence)
Later. Keep the project requirements small until it's working well. Get it to serve one desired purpose very well. Only then look at extending its use.
This is true for any coding project, but an order-of-magnitude more true for a volunteer project. If you want to get a programmer to actually volunteer for a project, convince them that the project will see great rewards while it's still small. In fact, you basically want to maximize intuitive value, while minimizing expected work. It feels so much better when your actual, original goal is achieved with a small amount of work than it feels when your tiny, first step is only the start of achieving your goal.