My name is Avi, and I'm 19.
I was similiar in some aspects to you when I was a kid, in particular being good at math (did calculus and programming at 12-13), getting in trouble, being bored in school, reading a lot, having trouble with emotions.
I hadn't had an explicitly rational upbringing, and only recently (9 months or so) got into it after a chance encounter with HPMOR.
I'll try to give advice on the things you asked. Bear in mind that I didn't actually try any of this when I was in school, it's mostly what I would advise my younger self if I had to do it over.
So, you mention being bored in school. There are at least three possible scenarios for that, which should be solved differently:
I don't really have anything for 1 aside from the standard "force yourself to pay attention", maybe others can help.
For 3, you could consider asking (or having your parents ask) to be skipped a class, or ask to be allowed off, if you really know everything that is being taught. (I haven't taken any real math classes since sometime around 7th grade. I'd take out books from the library and just go through them. Also someone gave me a bunch of old Martin Gardner books about math, which are quite interesting if you can find them.)
If you absolutely must be in a class where you already know what's being taught, try finding math questions to think about that you can memorize, so you can work on them without looking like you're doing something else. Try http://brilliant.org/ , and find your level. You should be able to easily memorize a few questions each day, and work them out mentally throughout the day, perhaps writing down the answers during recess or something. I've done this myself sometimes, when I had to wait for a bus and it would be awkward to read something while waiting.
For 2, you should carefully consider how likely it is that you already know, at 10, what kinds of things are likely to be important, better than whoever planned your curriculum. If you really feel that way, respond and I'll come up with something for that, but I do think it's unlikely.
Thanks! I'm the 3rd scenario in my case, and I joined that Brilliant website. It seems to be helpful so far. I do have to participate in classes where I know everything, so what I'll end up doing most of the time is having my dad send me to school with special math worksheets that are at my level that I can do during math class.
I already have some Martin Gardener books, and will be ordering more, as you are not the only person who recommended him.
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