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Notes -
Try https://mathacademy.com/ ? I'd guess that the enrichment vs acceleration concern has more to do with classroom management than the best interests of a given student.
It's legit, it even got someone like me hooked
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I was a gifted maths student as well (unsurprisingly, given that IQ is 70% genetic in the top half of the distribution) and I definitely benefitted from enrichment over acceleration. The kind of superficial understanding of calculus available to a 75th percentile 16 year old or a 99.9th percentile 11 year old just isn't that valuable. (I learnt calculus again at 13 in what was technically a regular classroom, although it was the top set an a selective private school, and that time it took).
I eventually got my Applied Math PhD and became the sort of Math
SnobConnoisseur who insists that it's not real calculus until you at least throw away that Riemann crap and use Lebesgue integrals ... but I have to admit there's a ton of students who will do science or engineering or medicine where they would greatly benefit from solidly understanding "superficial" Calculus. If you never quite grokked delta-epsilon proofs, but you understood numerical integration well enough that you could have properly reviewed the discovery of "Tai's Method", that's a better understanding of calculus than at least that medical journal (and that author, and some of her collaborators) had at that time.For either acceleration or enrichment, though, it needs to be periodically reinforced to be worthwhile, and that can be the tricky part. I took an Algebraic Topology class for fun as a college MechE-but-advanced-at-math, was amused by simplicial complexes and exact sequences and so forth but couldn't see what any of it was really useful for, promptly forgot it all because I never used it for anything for a couple years ... and then ended up in a math PhD program where I had to relearn a chunk of it just to understand some of the best visiting lecturers. I assume Mary Tai was the same way: nobody ends up in medical research without taking at least Calc 1, and if she was smart enough to reinvent the trapezoidal rule then she was surely smart enough to understand it as it was taught in Calc 1, but she probably never used it again for years and so had completely forgotten it when she needed it. Being able to rederive ideas you forget is IMHO one of the nicest aspects of math, but it is better to have a fuller toolbox of things you don't have to reinvent, and the more "enrichment" you get, the more connections you can make between ideas, and the easier it is to remember long-unused ideas via their more-obscure connections to more recently used ideas. With narrow acceleration in one subject, you might get so far ahead there that you don't get the same reinforcement schedule that other kids get via the usual connections to other subjects.
Learning on your own makes it a little easier to get some of that reinforcement from "standard" curriculum material, though. A standard high school Physics class won't be based on calculus, because most of the kids who want to take it won't have learned calculus yet, but if you know you're not most kids and you've got basic Calc 1 under your belt then you can just study calculus-based Physics instead, getting in more science and reinforcing math skills (and getting what I'm told is an impressive AP credit) at the same time, and learning something that's still on the critical path for a lot more science+engineering career tracks than e.g. group theory would have been.
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Khan Academy is also good for acceleration, to a sufficiently self-motivated kid.
And you're right, the trouble with acceleration in general is all about the difficulty of teaching 15 kids to potentially 15 different levels at once. With enrichment you can teach the whole class the basics, then teach the quicker half of them "enrichment" extras while the slower half drills the basics into place, then teach the whole class the basics of the next standard material ... but if you instead accelerated the quicker half of the class straight into the basics of the next standard material, then you're stuck, aren't you? You've now got two separate classes, with nothing that you can teach them both at the same time, not if you're relying on a 15:1 student:teacher ratio rather than a 1:1 student:computer ratio.
All that said, there's lots of valuable things you can teach kids, even in mathematics, that would count as "enrichment" rather than "acceleration" vs a typical "get them the standard high school diploma" curriculum. Most of them that come to mind for me are somewhat impractical, aimed at mathematician-brained rather than engineer-brained kids (I guess the standard curriculum is standard for a reason?), but Boolean logic might be a good choice and can be taught from scratch, and vector geometry is IMHO simpler and more practical than a typical high school geometry class despite having little in the way of prerequisites.
I'd suggest @MadMonzer focus on the ways to build things that get gradually more complex than Lego. Technics vs regular Lego, perhaps, or 3D printing with a simple CAD tool for design? Perhaps programming? Even with nothing physical to it, writing a simple little game scratches that same "I built something" itch, and you can get a Pi or Arduino or whatever to add physicality.
And if you lump the fast students in with the slow students from the next year up, that still doesn't work well to sync the curricula, as now you have a classroom with two groups of people who vary quite dramatically in how quickly and readily they learn the subject.
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