I have a 9-year-old who really loves math. He seems to have taught himself through about high school Geometry by reading library books. His 8th grade brother who just started Algebra 2 thinks the younger one knows about as much math as him. I accept that it's not reasonable to expect his school to teach him anything in math (he's in a 2-years-ahead gifted program and all the other subjects suit him fine), but I asked him if he would like me to give him stuff to work on at home, and he was really excited about the idea.
Does anyone have any materials or strategies to suggest? We tried Art of Problem Solving pre-algebra briefly last year (like maybe 4 or 5 evenings), but he's not excited by math contest type problems and the concepts are not presented in a very interesting way. He likes things like graph theory, complex numbers, formal logic, game theory, different dimensions, probability, topology, etc., which he read about in library books. For fun he does things like figuring out how to make logic gates with dominoes and finding the volume of polyhedra. He wants to learn calculus and prove Goldbach's conjecture.
At the same time, I know he has some holes in his knowledge because he didn't learn anything formally. Like, a few days ago, we discovered he can explain to you what the quadratic formula and factoring are for but he didn't know how to factor (we told him and he was doing it in his head in 5 minutes). (He does have all the basics like exponent rules down though.) So I would like to teach him more systematically. But still keep it interesting and fun. If there's anything that doesn't involve screens that would be preferred (he's a serious screen addict).
I thought in the past I could keep him happy with like math circles and Vi Hart videos but he wants to learn new stuff--like, make forward progress rather than just play with the same ideas. Does anyone have any encouragement or warnings? What happens when an otherwise normal kid finishes high school math before getting to high school?
