I think I was better than most kids at math, particularly algebra, but those kids grew up and caught up and I suspect many of them are as good or better at math than I am. I know nothing about child psychology or anything adjacent, but I honestly think a lot of "advanced child" stuff is just maturity.
That makes me think back to my elementary school, where a lot of the kids who got into the "gifted" program just happened to be, surprise surprise, some of the oldest kids in their grade.
At that age the better part of a year in brain development can be exactly the "edge" one needs to excel. And then it can become self-reinforcing when kids gravitate toward the areas in which they dominate their peers.
ETA:
Should add that this carried on through high school, and since I finished my math two years early, I took college-level courses for math the last two years.
My son is diagnosed with ADHD and high IQ and labeled "gifted". He's very immature, has absolutely no method, is very impulsive and can't maintain focus for more than 20 minutes. He seems very much less mature than his peers in anything.
Yet, he just understands and remembers every single thing at school much better and faster than his peers. So I guess technically that makes him "gifted" but it's not a very useful gift. It just creates problems at school because he gets bored quickly but cannot be given more work to do because he gets exhausted quickly too!
I read recently a title of an article that said "gifted children are special needs children" and that marched my experience.
My friend's child is profoundly gifted (160+ IQ). He is 12 years old and finishing Calculus and next year will be taking college math courses. His friends are a year younger than him and have qualified for AIME since they were 8 years old.
Giftedness is very real, and it's not just "maturity". Their brains are different. Seeing them squabble over math problems, it's like watching people talk a different language.
My mom would have none of that, and demanded I be put back in 4th grade.
And so I was, and it was like I wasn't gone for a single day. The class had not advanced at all.
This was quite unlike university, where I didn't dare miss a single lecture.
You should have learned roughly what is in this book at grade 7, it includes algebraic expressions, angles, ratios, unit conversions, statistical concepts like mean, mode, bar graphs, probability of dice and coins and so on.
https://archive.org/details/newenjoyingmathe0000jose/page/4/...
Then in grade 8 you'd go on to do those kind of things but a bit more advanced. Most people just forget how much math they learned and think they learned all that in high school.
Agreed university is much harder though.
I remember it very well. I thought it was crazy they were still doing the times tables.
> this book at grade 7
I don't recall any of the grades going all the way through the book. My high school had an impressive course catalog. It looked pretty rigorous! But taking the classes, how sad they were. The textbook is not a reliable indicator of what was taught - it's more like wishful thinking.
I remember taking sophomore geometry. The teacher gave out a test at the beginning of the year, to measure where the kids were. Apparently I got it all right. The teacher asked me if I'd taken geometry before? I said no, the test was just obvious. It was really sad.
Now, before you think I am some kind of genius, nope. When I arrived at college it was a full on disaster for me. I had no idea how to study. I was way, way, way behind my peers. I needed a lot of help, bad. My roommate sighed at how ill-prepared I was, and coached me through a lot of classes, otherwise I would have been flunked out.
Have things gotten any better? I doubt it. Even Harvard was forced to add a bonehead math class to try to get their incoming freshmen up to speed.
Don't get me wrong. I enjoyed going to school. My friends were there, and we had a great time. Especially in high school, when we worked on each others' cars. I'm still a motorhead.
Anyway, if that’s the scale, it still can fit with the “doesn’t lead to exceptional outcomes”. I am a perfectly competent software person, and maybe I even understand some of the mathematics behind it better than the average programmer, but I am still basically just an “adequate” worker, and honestly I am afraid that I have more or less peaked career-wise. I am sure that some prodigies do great but the article seems to indicate that they’re rarely exceptional at adulthood.
[1] honestly I think that IQ is stupid and that it’s dumb to try and distill something as complicated and multi-faceted as intelligence to a single dimension or even a couple dimensions is pretty reductive.
I was an air force brat, and so attended many diverse public schools.
I took 2 years of honors physics in high school. College freshman physics blew through that in 2 weeks. And then I was in deep doo-doo.
I am eternally grateful to Prof Ricardo Gomez, who kindly took the time to coach me one on one. I never thanked him for that, one of my many regrets.
When I went to college, it was definitely tougher, but I was able to pass the freshman physics and multi variable calculus courses first time around, without significant tutoring.
This kid and his cohorts, they hear a concept for the first time, and they just get it. Then when it comes to doing the problems, he might struggle a little but then he gets it. He is getting 95% in calculus and the only reason he lost marks is because he made sloppy mistakes.
As a former gifted child who was emotionally immature and gifted, I hope your kid gets the guidance I never did both to understand his adhd and how it impacts him, but also emotional compassion for himself and from parents about how hard adhd can be
I like to think I’m pretty clever, but I almost certainly would not have gotten 160 if I hadn’t gotten the practice test.
Many are more expensive in time and money, but you may find fairly cheap alternatives.
Worth a shot at least.
It is not uncommon to hear objectively bright and hard working young people wonder if they have become dumber or if they have been a fraud the entire time, after they leave their high school where they enjoyed being a star student and move to a nice university where they compete with the brightest mind of the entire world. They are not dumb, just not mentally adjusted to an environment where they don't get to be the number one no matter how hard they try.
I'm in my mid 30's. I'm happy enough where I am now; my biggest issue has historically been focus and apathy more than understanding concepts, much to the frustration of my teachers in high school. I was that frustrating kid who clearly understood the concepts perfectly fine, and was even fairly active during class, but I wouldn't do my homework so the teachers would be forced to give me bad grades.
I obviously don't blame the teachers for this, they're doing what they have to, but I do sometimes think that the system is a bit too one-size-fits-all, even still. I took advanced classes in high school, I got very high ACT scores (36 in English, 34 in math), but I still have always had middling academic performance because the teachers would be stuck giving me crappy grades.
For reasons slightly involving skill but mostly involving luck, I managed to cobble together a successful software career even after dropping out of college the first time around, worked without a degree for almost a decade, and eventually worked as a practicing software engineer at the senior level at BigCos. I have a bachelors now, and even a masters, and some graduate PhD work (though I didn't finish that, too time consuming while working full time), but these all came after I had established a decent career.
I think that being a little clever [1] certainly helped me through this, but what I think helped me more than anything was the fact that a) I had a geeky hobby of learning how to program when I was fourteen or fifteen that never really went away and that I was able to fall back on and b) dropping out in 2012, which just happened to be the year that pretty much everyone got a smartphone and consequently there was a huge demand for programmers and they were willing to overlook a lack of credentials.
My life has turned out fine; not perfect but certainly better than most people on this planet or even this country so it's hardly worth complaining over. I do wish I had taken school more seriously as a teenager because then I would likely be able to have move into a more mathy-theory-based role, which I seem to be unable to do as of right now [2]; it feels like I'm playing a game of catchup, which isn't impossible but it definitely is harder than if I were able to focus on school full time.
Dunno why I decided to dump my life story at you. Just one of those days I guess.
[1] Though as I said in the sibling comment, probably not nearly as clever as the tested IQ suggests.
[2] No matter how many I apply to, it seems. It doesn't help that every researchey role now is for AI/ML theory which is cool but pretty far from my expertise or the kinds of math I've studied or have any expertise on.
Nothing to do with prodigies of course.
And every child is different because it's often not just ADHD but also other things.
But we're in a much better position now to help him.
My main point is that from my experience "gifted children" very often come with all other sorts of problems that put them in the category of special needs children and it's not just that they are mentally one step ahead of their peers.