Maybe with the objection that the time coefficient can be different for different school subjects, because some of them are more focused on understanding things, and others are more focused on memorizing things
Possibly. It’s also the case that IQ is an aggregated measure of a set of cognitive subtests, and the underlying capabilities they measure can probably be factored out into things like working memory, spatial reasoning, etc., which are probably all correlated but imperfectly so; then if some of those are more useful for some subjects than others, you’ll expect some variance in progression between subjects. And you certainly observe that the ultra-gifted kids, while generally above average at everything, are often significantly more ahead in math than in language, or vice versa (some of this is probably due to where they choose to spend their time, but I think a nonzero amount is innate advantage).
Among the various ways to take up the extra time of the rapid learners, probably the best one is “don’t go faster, go wider”.
The term of art, for doing this within a single subject, is “enrichment”. And yeah, if you can do it, it fits nicely into schedules. “Taking more classes” is a more general approach. There are administrative obstacles to the latter: K-12 schools seem unlikely to permit a kid to skip half the sessions of one class so he can attend half the sessions of another class (and make up any gaps by reading the textbooks). Colleges are more likely to permit this by default, due to often not having attendance requirements, though one must beware of double-booking exams.
(Note: I am not saying that this is optimal for the rapid learner. The optimal thing for the rapid learner would be to… learn faster, obviously.
I think the best setup—can’t find the citation—is believed to be “taking a class with equally gifted children of the same age, paced for them”. If you don’t have that, then skipping grades (ideally per-subject) would address knowledge gaps; taking a class paced for at least somewhat gifted kids (possibly called an “advanced” class, or a class at a high-tier college) would partly address the learning speed gap, and enrichment would also address the learning speed gap, to a variable extent depending on the details.
A more realistic example would be a math textbook, where each chapter is followed by exercises, some of them marked as “optional, too difficult”
A specific way of doing this, which I think would be good for education to move towards, is to have a programming component: have some of those optional exercises be “Write programs to implement the concepts from this chapter”.
But if I had to guess, I would guess that the gifted kids who stay within the confines of school will probably lose most of their advantage, and the ones who focus on something else (competitions, books, online courses, personal projects) will probably keep it.
Subjects Not Permitted Acceleration. [...] With few exceptions, they have very jaded views of their education. Two dropped out of high school and a number have dropped out of university. Several more have had ongoing difficulties at university, not because of lack of ability but because they have found it difficult to commit to undergraduate study that is less than stimulating. These young people had consoled themselves through the wilderness years of undemanding and repetitive school curriculum with the promise that university would be different—exciting, intellectually rigorous, vibrant—and when it was not, as the first year of university often is not, it seemed to be the last straw.
Some have begun to seriously doubt that they are, indeed, highly gifted. The impostor syndrome is readily validated with gifted students if they are given only work that does not require them to strive for success. It is difficult to maintain the belief that one can meet and overcome challenges if one never has the opportunity to test oneself.
Versus:
Young People Who Have [skipped 3 or more grades by the end of high school]. [...] In every case, these young people have experienced positive short-term and long-term academic and socioaffective outcomes. The pressure to underachieve for peer acceptance lessened significantly or disappeared after the first acceleration. Despite being some years younger than their classmates, the majority topped their state in specific academic subjects, won prestigious academic prizes, or represented their country or state in Math, Physics, or Chemistry Olympiads. The majority entered college between ages 11 and 15. Several won scholarships to attend prestigious universities in Australia or overseas. All have graduated with extremely high grades and, in most cases, university prizes for exemplary achievement. All 17 are characterized by a passionate love of learning and almost all have gone on to obtain their Ph.D.s.
Though one could say this is more of an attitude and habit and “ever bothered to figure out study skills” thing, than a “you’ve permanently lost your advantage” thing. If you took one of those jaded dropouts (of 160+ IQ) and, at age 30, threw them into a job where they had to do some serious and challenging scientific work… There’s a chance that their attitude and habits would make them fail and get fired within the first few months, that chance depending on how severe and how ingrained they are. But if they did ok enough to not get fired, then I expect that, within a year, they would be pulling ahead of a hypothetical 120 IQ counterpart for whom everything had gone great and who started with slightly more knowledge.
Yet another reason for different speeds in different subjects is that gifted kids often read about their interests in their free time—which can also increase the speed in given subject.
Yeah, learning by reading at home definitely has a huge effect in many cases. In Terence Tao’s education, he was allowed to progress through multiple years of a subject per year (and to do so at different rates in different subjects), and since the classes he attended were normal ones, I think his academic progression must have been essentially determined by his ability to teach himself at home via textbooks. Unless perhaps they let him e.g. attend 7th grade science 2 days a week and 6th grade science the rest? I should learn more about his life.
The educational setup can also feed into the reading aspect. During my childhood, on a few occasions, I did explicitly think, “Well, I would like to read more of this math stuff (at home), but on the other hand, each thing I learn by reading at home is another thing I’ll have to sit through the teacher telling me, being bored because I already know it”, and actually decided to not read certain advanced math stuff because of that. (Years later, I changed my mind and chose to learn calculus from my sister’s textbook around 8th grade—which did, in fact, cause me to be bored sitting through BC Calculus eventually.) This could, of course, be solved by letting kids easily skip past stuff by taking a test to prove they’ve already learned it.
Possibly. It’s also the case that IQ is an aggregated measure of a set of cognitive subtests, and the underlying capabilities they measure can probably be factored out into things like working memory, spatial reasoning, etc., which are probably all correlated but imperfectly so; then if some of those are more useful for some subjects than others, you’ll expect some variance in progression between subjects. And you certainly observe that the ultra-gifted kids, while generally above average at everything, are often significantly more ahead in math than in language, or vice versa (some of this is probably due to where they choose to spend their time, but I think a nonzero amount is innate advantage).
The term of art, for doing this within a single subject, is “enrichment”. And yeah, if you can do it, it fits nicely into schedules. “Taking more classes” is a more general approach. There are administrative obstacles to the latter: K-12 schools seem unlikely to permit a kid to skip half the sessions of one class so he can attend half the sessions of another class (and make up any gaps by reading the textbooks). Colleges are more likely to permit this by default, due to often not having attendance requirements, though one must beware of double-booking exams.
I think the best setup—can’t find the citation—is believed to be “taking a class with equally gifted children of the same age, paced for them”. If you don’t have that, then skipping grades (ideally per-subject) would address knowledge gaps; taking a class paced for at least somewhat gifted kids (possibly called an “advanced” class, or a class at a high-tier college) would partly address the learning speed gap, and enrichment would also address the learning speed gap, to a variable extent depending on the details.
A specific way of doing this, which I think would be good for education to move towards, is to have a programming component: have some of those optional exercises be “Write programs to implement the concepts from this chapter”.
Oh yup:
Versus:
Though one could say this is more of an attitude and habit and “ever bothered to figure out study skills” thing, than a “you’ve permanently lost your advantage” thing. If you took one of those jaded dropouts (of 160+ IQ) and, at age 30, threw them into a job where they had to do some serious and challenging scientific work… There’s a chance that their attitude and habits would make them fail and get fired within the first few months, that chance depending on how severe and how ingrained they are. But if they did ok enough to not get fired, then I expect that, within a year, they would be pulling ahead of a hypothetical 120 IQ counterpart for whom everything had gone great and who started with slightly more knowledge.
Yet another reason for different speeds in different subjects is that gifted kids often read about their interests in their free time—which can also increase the speed in given subject.
Yeah, learning by reading at home definitely has a huge effect in many cases. In Terence Tao’s education, he was allowed to progress through multiple years of a subject per year (and to do so at different rates in different subjects), and since the classes he attended were normal ones, I think his academic progression must have been essentially determined by his ability to teach himself at home via textbooks. Unless perhaps they let him e.g. attend 7th grade science 2 days a week and 6th grade science the rest? I should learn more about his life.
The educational setup can also feed into the reading aspect. During my childhood, on a few occasions, I did explicitly think, “Well, I would like to read more of this math stuff (at home), but on the other hand, each thing I learn by reading at home is another thing I’ll have to sit through the teacher telling me, being bored because I already know it”, and actually decided to not read certain advanced math stuff because of that. (Years later, I changed my mind and chose to learn calculus from my sister’s textbook around 8th grade—which did, in fact, cause me to be bored sitting through BC Calculus eventually.) This could, of course, be solved by letting kids easily skip past stuff by taking a test to prove they’ve already learned it.