Edit: Pretty good points in the replies. Probably a lot of latent jealousy on my side in this. I should have thought on this more before commenting.
Of course, this depends so much on the person in question. Acceleration can be great for some people and awful for others. But it’s not about ‘enjoying being a kid’ — that’s something I hear a lot, but I enjoyed myself a lot more in the higher grades where I was actually learning material I found interesting.
Ironically, I found it decent preparation for life, though, which seems to be occasional bursts of furious activity punctuated by long stretches of repetition, which could easily become boring. I ended up becoming very good at taking responsibility for making my own life interesting.
Oh yes… I also spent considerable time teaching myself interesting topics. It’s a good skill to have. But I was still bored a lot of the time, and being able to do the interesting stuff in school too was a much better experience for me.
I will say one of the things that always made me laugh was that at each milestone, like finishing elementary school and starting middle school, my parents would try to tell me now it would be different, because I was at a higher level. I remember pointing out to them all the same doofuses from the previous years were moving up right along with me, and it wasn't just that I was ahead of them, but that I was faster, so this didn't seem to help. I never did understand why they thought that would work!
The best school system I ever attended rigorously divided classes between social and academic --- for social classes (gym, health, social studies, homeroom) one attended at one's grade level, while for academic classes, (English, other languages, science, math) one worked at one's grade level (but with a cap of 4 grade levels through 8th grade, so a 4th grader couldn't take high school classes) --- after 8th grade this cap was removed, and students could take any classes which they could qualify for academically. To facilitate this, some teachers were also accredited as faculty at a nearby college, and if necessary arrangements were made either for college professors to come to the school and teach, or students travelled to the college.
Most students graduated with at least a little college credit, and many received a college degree along with their high school diploma --- until the Mississippi State Supreme Court decided that it was illegal because it conferred an unseemly advantage on some students with no corresponding compensation for students who were unable to avail themselves of it academically.
This is such a great idea! And it sounds like it works well in practise, too. I’ve often pondered the idea of separating classes by ability rather than age, and this is a really practical method of achieving it.
A similar idea is to group children by reading level which makes classes function more smoothly since students finish reading assignments in similar periods of time.
It was "innovative," in a way I think we're coming to regret, to suggest that all 8-year-olds (for example) must be at the same level across every subject, and none of them should ever be taught alongside a group of mostly 6- or 10-year-olds.
Of course this all came to a head when I was a junior and the school system couldn't find a teacher for Calculus for myself and the couple of other students who wanted it which pretty much killed my college prospects, so aced the ASVAB, DLPT, and EDPT and enlisted.
My mom, annoyed at not having her afternoons free, gave me math learning materials to keep me busy. Since she wasn‘t a teacher, she didn’t really know what she was doing and I ended up entering first grade reading at a fifth-grade level and doing math at a third-grade level.
I really should have been skipped ahead at least a year, if not two. The first-grade teacher had me teach the gifted kids in the back of the room while she taught the rest of the class, the second-grade teacher didn’t really know what to do with me and I was bored out of my skull as a result (first and second grade swapped between the two teachers at lunch time with the first-grade teacher focusing on reading and writing, the second-grade teacher focusing on math and science).
One of the ones that fascinated me was dated from when I was in 2nd grade. It was a big printout with rows and columns. Some of them contained numbers, but most of them just said "PHS."
It was an oddly folded poster-size thing, and once I finally got it open, I found out the numbers were grade levels, and "PHS" stood for "Post High School."
I had been 8 when I sat for this test. My parents had staunchly refused to accelerate my education.
And they continued to refuse for ten. more. years.
I might recommend that parents not send their children proof if they went out of their way to stymie them.
And you avoided being bullied ? Nice!
I’ve not pushed him into any of this (I really would prefer that he not pursue programming as a career as I fear that we’re heading to a dark ages of software development, but he can do what he likes).
His twin sister, meanwhile, has been demanding that I teach her social studies so I’ve been doing my best to give her bits and pieces of history and government from my memory. She doesn’t demand the math, but I’ve noticed that she is paying attention during the algebra on the walk lessons as she’ll occasionally jump in with an answer herself.
My purely selfish side wouldn’t object to them skipping a grade as my ex-wife seems committed to them doing K–8 in private schools (even though our local public schools are quite good except at the junior high level, but 6–8 is hell at any school) and skipping a grade would save me a year’s tuition expenses.
Your kid would also probably really enjoy The Number Devil, a breezy novel about a kid who gets trapped in his dreams with a devil who won't stop telling him about elementary number theory, using various dream-world props.
If you want more problems after that, there are a lot of great puzzles in Kordemsky's The Moscow Puzzles https://archive.org/details/moscowpuzzles3590000kord_m9a0, or you could take a look at Fomin, Genkin, & Itenberg's Mathematical Circles: Russian Experience which your kid could probably just about handle.
There are also some great puzzles and games explained at the website of the Julia Robinson Math Festival, https://jrmf.org which can be played with fairly basic easily available materials.
It was also similar to how I taught my home educated kids - do fun stuff. It worked very well. Both love maths (and hugely enjoyed studying in general). My older daughter is doing a degree apprenticeship in electronic and electrical engineering[1] and the younger one got a 9 in IGCSE maths[2] and plans to do A level maths and further maths[3]. The younger one hated maths while she was in school, which is common, and which is the problem Lockhart was trying to solve.
This is not about pushing kids or making them prodigies, it is about making them enjoy what they do, which leads to higher achievement and and happiness.
That said, not all prodigies are miserable. Ganesh Sittampalam who broke the UK record for youngest graduate taught himself for fun until he got into university!
[1] UK term for degree paid for by employer done while working (and getting paid). Good for parental wallet!
[2] UK exams sat at 16. 9 is a top grade.
[3] Closest American thing is APs.
Truth be told, some of the kids loved it - but those were the kids that were really passionate about math, for the sake of math.
But you also had a bunch of kids that seemingly hated every second of it. So why did they do it?
- Some had pushy parents that wanted them to excel in extracurricular activities. Think typical tiger parenting...
- Some had big ambitions about certain schools, and felt that they had to compete on a national level in something, in order to stand out in the selection/application process.
Granted, this was over 15 years ago. A couple of years ago I checked up on some of the kids (LinkedIn), and the most passionate kids were either now math/physics Ph.Ds, or Ph.D track.
While that's true, there's lots of parents who don't believe it, or don't care if the end result isn't actual mathematical genius as long as it's some sort of distinction. (I'm in the happy position where my parents encouraged me to pursue the paths that I enjoyed, which wound up with some acceleration, but my getting in the local newspaper meant that we were besieged by the kind of parents who do just want to push their kids towards some pre-determined "success.")
I think that's a very optimistic view of the outcome of this sort of thing, although it could be that I just didn't describe the parental behavior well. This wasn't parenting telling their kids "hard work is worth it!", but parents who decided on the specific honors that their child would achieve, and would permit no deviation from the path, as a result of which most of these kids either burned out before achieving their goal, or rebelled, usually in self-destructive ways, as soon as they were given a little freedom from parental control.
Different parenting styles work for different people, but for me (as a child in the US in the '80s) I think that my parents did the best possible thing, which was to instill in me lessons about the value and importance of hard work, but to make it clear that, in the end, the decision about whether I would pursue those values was up to me. It probably helped that, despite the many other advantages I enjoyed, my family was insufficiently well off to represent a guaranteed financial fallback for me, so that I knew that, one way or the other, I'd have to make my way in the world—which made it particularly appealing to me to be able to find a way to earn my keep by working hard for something I loved.
It may be more likely but not impossible.