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gwern comments on Interesting critique of British education by outgoing advisor (warning: some politics) - Less Wrong Discussion
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I think your reading is being uncharitable; 'substantial' doesn't refer to any particular amount, just that the amounts are meaningful, which will be context-specific. (I also like the term because it isn't deceptively conflated with a technical meaning, like 'significant' is - significant could mean either substantial/import/large or meets an arbitrary p-value).
The way I see it, he's stating that basically 0% of students are trained the way he would like them (surely true), that 0% is not optimal (also surely true but I'm not sure what the optimal percentage is), and that right now, we don't even have good ideas of what is possible for the various qualities of student because the research simply hasn't been done aside from some suggestive anecdotes (true).
There's something like 15 million high school students in the USA; that's 75,000 students. How many of them are in gifted summer programs?
Overall, this manifesto was quite a read. Reading it gave me a weird sort of feeling - I didn't learn very much that was new, but it's a little shocking to see someone cover in a single place so many topics of interest to me in a competent manner and with an attitude & writing style similar to my own.
I hoped so too, but didn't have time to read the whole work (which might have settled my concerns).
The range 5,000 to 25,000 seems like a decent 50% interval to me. So yeah, it could be higher. The real issue, in my mind, is not summer but the rest of the year; it seems odd to me that we don't have boarding schools for students that are 1 in 10,000, where they can learn about a high school course a week, or do things like this.
The impression I get from his discussion of the French & Russian elite schools is that the summer courses may be better considered part of the filter for admission into those sort of schools; specifically, footnote #150:
This makes sense since cognitive testing has known measurement error, which while very low, is still problematic if you're trying to select the top 1% (or higher) of students* for these expensive schools (and because intelligence itself changes over time, so a single test means regression to the mean), and it may either spark enthusiasm for going to the advanced schools or test the child's attitudes toward it - not much point in enrolling a kid who doesn't want to be there, right?
* for example, apparently the Termite study missed out on two Nobelists because they were under the filter by some tiny amount on the test; if Terman had been able to afford a larger sample or had a slightly better test, his results would have been much more impressive, especially since Nobelists are one in millions.
Agreed that seeing someone in class is useful information, and that this is a good feeder system for elite schools. But to the best of my knowledge there is not a quality national network of elite math and science schools in the US, just a collection of local magnet schools.