My son is headed to Caltech for his freshman year in 10 days. :(( So, I’ll try to come up with some useful suggestions, though you’ve gotten a lot already.
These suggestions are more for now or early high school:
– Since his current interest is math, look for a Mathcounts group locally and/or a math circle. http://www.mathcircles.org/ Some of the SoCal Math Circles are pretty pushy in that Asian tiger stereotypey way, but see if he likes it. My son went to ARML competitions with the SoCal group for 3 years and loved the socializing. I’m not a super big fan of Mathcounts, because a lot of it is speed math instead of challenging. There is also the AMC 8, which leads into the AMC 10/12 and AIME.
– Read “How to Be a High School Superstar: A Revolutionary Plan to Get into College by Standing Out (Without Burning Out)” by Cal Newport. It’s an interesting balance to the test-prep market. I had my son read the relevant parts in 9th grade. Along those same lines, also read http://mitadmissions.org/blogs/entry/applying_sideways
– Some book, maybe the Cal Newport one, had a good list of questions about long-term goals. I still have DS’s answers. They aren’t goals like “attend x school” but more things they might like to accomplish during their life.
– I started a shared Google Doc in 9th grade where he kept track of things he’d done and time he’d spent that might be asked for in college applications. It was useful to refer to when he was doing college applications. It also ended up containing brainstorming about summer activities, HS class schedules and lots more.
– Investigate the high school options you have. Ask questions about early access to AP STEM classes, the math sequence, and about whether students take dual-enrollment classes at your local community college (or CSU or UC) and whether those count toward HS GPA. Basically, some schools limit kids and some make more opportunities available.
– When comparing HSs, also ask about clubs he might want to be involved in. Maybe a math club and/or science club that does competitions, a robotics club, a computer science club, etc.
– Are there students “like him” at the HSs you are considering? I don’t think it is useful to attend a low-performing school in order to be able to be the highest ranking kid. Think about their social life for the 4 years of HS.
– Have him think about what courses interest him. Don’t take courses because they will “look good” though of course be aware that colleges are generally looking for 4ish years of most of the core academic subjects.
– Investigate the courses he can take at your local community college. In our town, kids can take CC classes free as soon as the summer after 8th grade. DS ended up with 11 college classes during HS at the community college and our local UC. If the classes are significant and relevant to his interests (and he does well), they help with college applications.
– He may be able to get the SAT Subject Tests out of the way early. My son took Math II and Physics at the end of 9th grade, got 800s, and was happy to be done with that part of testing. (My son doesn’t like test prep, though, and didn’t prep for tests other than to get an idea of the time limit. Maybe your son does enjoy it.) He took those tests early because he did Precalculus and AP Physics B that year. They don’t have AP Physics B any longer; it’s a 2-year sequence now, so harder to be done with early.
– Start saving money for college now if you haven’t already. Paying for college out of current cash flow is tough for anyone.
– I’m seconding the AoPS suggestion. DS took their Precalculus class in 9th to get to a more appropriate level for him in 10th grade. In addition to math classes, they have a programming class. They used to have 3 programming classes, and DS took them all in 7th and 8th grade and then took the AP test in 8th grade. He ended up doing a lot of extracurriculars that involved programming, including competitions and physics research at our local UC.
– He could take the SAT for CTY qualification. My son took a similar test for CTY, but never ended up doing any of the CTY camps. There are some CTY camps in SoCal.
– I’m 3rd-ing or 4th-ing the lots of reading for pleasure and interests suggestion.
– Enjoy your great kid! It goes so fast!
These are for later:
– Look into summer programs that match his interests. There are a lot for math, but for some of them you have to do well in competitions. There are also a number for computer science and physics. My son did a selective astrophysics camp that is one that Caltech’s admissions department notices.
– Don’t have a dream school if you can help it. Apply to reaches, matches, and safeties that he would be willing to attend and you can afford (with merit if available). See where he gets accepted and then decide.
– Caltech requires students to attend for 4 years. A bunch of APs and college classes won’t help students finish early there. (There are placement tests you can take to place out of some classes or challenge prerequisites at Caltech.) The same is mostly true at MIT and Mudd (but without the 4-year requirement perhaps). However, the opposite is the case at UCs–many of my son’s 14 APs and 11 college classes would have counted, and he could have planned on 3 years or plenty of time to double major.
– Geography doesn’t help a bit with Caltech. They take a high percentage of kids from CA. (Yes, it probably helps for MIT and Mudd.)
– Within CA, CalPoly SLO is a less costly but still great option. It can probably be his safety if he gets great scores, a great GPA, and takes some extra classes in academic subjects. USC gives 1/2 tuition at a minimum to National Merit students they admit and a number or scholarships larger than that.
– The UCs include some really great options and are currently about $35K/year. Berkeley is probably tops for math. Don’t overlook the College of Creative Studies program in math at UCSB. http://ccs.math.ucsb.edu/ CCS is an amazing program for someone who wants to do research! UCSB has a small number of $6K/year merit scholarships. Berkeley has some $2K/year scholarships.
Feel free to PM me if you have specific questions.