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bramflakes comments on Tutoring Small Groups of Children (for money) - Less Wrong Discussion
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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?
One of the cool teacher tricks you eventually figure out is how much time to give after asking a question. Beginner teachers always jump in too early - it seems easy to the people who already know the answer :P Sometimes you even have to add on some extra time for people to realize that this is one of those questions where they actually have to think. It can get uncomfortable for you, the questioner, but that's okay, you just have to not crack first.
Not sure how well this generalizes to puzzles. One useful tip is that there's an intermediate level of help, where you basically just ask questions to make the other person walk through their thought process out loud. "What have you done so far?" are the most common first words out of my mouth when someone asks for help.
Followed by "What do you think you could do next?"
Have lots of problems prepared over a wide range of difficulty. Start with problems you're pretty sure the student can solve, and turn up the difficulty slowly.