I'll add to that. We fell into the secular homeschooler camp. At some point, it takes less effort to just homeschool than to spend endless time arguing with school administrators to challenge your child appropriately. "We can give them extra worksheets for homework." Oh wow, thanks.

A great resource for "mathy" kids is Art of Problem Solving. https://artofproblemsolving.com There are free resources, their math books are outstaningly excellent (well, they could use more excercizes, but the exposition is superb), and they have online classes. The online classes are run with a live chat room that typesets LaTeX. The pace of the classes is blistering, so not for everybody. But you can buy the same books for cheap and use them at home at a pace that is right for your kid.

We used AoPS as the main spine of our child's math curriculum. At the time, it topped out at about AP Calculus, I'm not sure if they go beyond single variable calculus yet. Anyway, after that a local university let our kid take multivariable calculus along side the freshman engineering students. We were lucky to have that resource. Next problem: when your kid completes multi-variable calculus at age 13, what next? We did discrete math and freshman engineering physics, and counted them toward the high shool transcript.

Which is another problem homeschooler's face -- the so-called "mommy transcript". When it comes to college applications, it's good to have somebody in addition to mom posting grades to your transcript. The Uni grades in math and physics and recommendation letters from university profs helped the college application package a lot. For that matter, AoPS is well ennough known now that it is good on a transcript.

While I'm on math resources, http://www.mathpath.org is a truly wonderful summer math camp for kids in the 11-14 age range. Great faculty, great staff. Now would be a good time to think about applying for 2018. Just so you understand the scale here: My kid spent all of their spare time for two weeks on the quailifying quiz, attempting 5 of the 7 questions, a couple of those attempts were a bit weak. (A good solid attempt at 2 or 3 will get you in.) If you think your child might like MathPath, I'd encourage you to download the quiz now and let your kid start pondering the questions.

It sounds like you are an upper middle or upper class family. There are gifted children in the US that aren't identified as such that come from lower class families who are deprived of their education. I checked the AoPs site and if you get the pre-algebra -> calculus textbooks + solution guides it's over $200. This may not sound like a lot to you (as you suggested) because it is due to your class. This is something some poor families cannot do. Even if they want to buy those books. Sending your middle schooler or high schooler to take college level classes is another sign of class status. I believe we should have schools like AoPs and the Proof School targeted not at the wealthy gifted children, but poor gifted children. I also think these schools shouldn't filter applicants out by SAT scores (since mostly gifted children from well off families seem to do better than gifted children without access to education). It seems like most places ignorantly assume the gifted only come from well-off places and put cultural barriers (such as exams) to identify them. This class advantage carries over into university admissions when the well-off students have 30-60+ credit hours from colleges coming in, as opposed to the gifted kids from poor families with 0 college credits. The former are admitted to elite schools, while the latter are denied. If you look around, these elite prep schools and elite colleges tend to lack economic diversity. Teaching advance math to gifted children of the elite, while excluding the gifted children of the poor (due to barriers of entry) do a disservice to our society as a whole.

I'm not sure why you were downvoted, as you are absolutely correct. I've lived both sides of that.

I grew up in rural fly-over land, and my little farm country high school with a very high proportion of kids on the lunch subsidy didn't prepare me very well for engineering school. Maybe one kid every other year would attempt engineering school. My pig farmer father died when I was 5, but my mother managed to stuff enough money away even in the lean years that I had money for a cheap land-grant university.

As I mentioned, I wasn't all that well prepared. I remember one night when DiffEQ homework was kicking my butt, and said to my self: "Ether get this stuff under your belt, or go home an clean hog barns for the rest of your life." I chose option A. My wife's parents were dairy farmers. She was the guru of scholarship application essays... that paid for her undergrad degree.

So, I get what you are saying. I've lived it. My wife lived it. But between us we've accumulated 5 degrees, made some good investments, been in a couple of situations where stock options were pleasantly large, and yes, work is optional right now, even living at Silicon Valley prices. Pardon me if I don't appologize for accompishing what YC and HN are all about.

So your post is a little short on actionable solutions to the problems we both see as clear as day. Here is a suggestion: MathPath has a need-tested scholarship fund so that kids that can't afford the camp can go. Tax deductable donations gladly accepted. Join me in donating. Then spread the word about MathPath -- anybody can apply.

My son is actually math challenged and also a science nerd. This is a whole other mind-boggling challenge.

I bought math books full of words off the bargain table for as little as a dollar and, after sorting things out with his father, just gave my son the stack of books to read. No tests. No written work. No problem solving. Just read these books. That finally worked and he has a good grounding in math, though he can't crunch numbers. He is, as they say, calculator dependent. But he absolutely understands important concepts. To my mind, this is vastly better than a kid who can estimate to 8 decimal places in their head, but can't grasp GIGO (garbage in, garbage out).

I hear you. Math isn't arithmetic. Exploring math from the discrete math and geometry side often is a good approach for those kinds of kids.

We pursued a statistics track.

I've actually been trying to explain that exact concept (algebra variables) to some advanced third graders. It's been surprisingly hard to get them to grasp it.

When I was a child, the first thing that made sense to me was that "x is the number that makes the statement true". That is, 100 = 100, so if 25 * x = 100, you need to figure out what value of x multiplied by 25 gives you 100. I didn't even understand the manipulations or how you would really solve for x at first, but I did understand that you were trying to figure out the number that would do that. I would just phrase it like a puzzle, like "what plus 9 equals 14" or "3 times what equals 42"?

For some reason, one of my earliest memories I have is from when I would try to show off to older kids that I understood algebra.

Have you tried analogous approaches, such as showing kids an empty box, a question mark, multiple metaphors, etc?

I find that visual approaches work well, but when you write an English letter which has already been used for other purposes, it's a little less clear.

I've always translated "x" to "?" (the value to be discovered) as a mental shortcut. The "?" symbol might be easier to interpret for third graders.

I think they are used to seeing empty boxes for mystery values.

Have you looked at the Dragon Box app?

I shill DragonBox every chance I get ;) It does a great job of teaching abstract algebra to children who don’t even know arithmetic.

I think it helped my son for me to explain that letters were just short "names" in place of the phrase "mystery number." Or something along those lines.

Like "We are just going to call it X or Y instead of the unknown number we are trying to figure out."

> A good place to promote this would be with secular homeschoolers. Those homeschooling for nonreligious reasons are often dealing with a bright kid interested in advanced subjects.

I don't see any reason to restrict this to those homeschooling for nonreligious reasons. There are plenty of bright homeschooled kids interested in advanced subjects regardless of their parents' primary motivation for homeschooling.

I am in no way restricting it, merely suggesting fertile ground to find enthusiastic early adopters who can help it flourish.

I am suggesting that the broader homeschooling community may be equally fertile ground to find enthusiastic early adopters.