I read this in the mid-nineties in what seemed to be new hardback book, but some of the other anthology stories seemed 'of the sixties'.
The narrator was recounting his experience visiting some alien world and getting told about their education system. Basically the poorer performing students are hanged as an incentive to the others to work harder.
This has resulted, after generations, in having a world of very high educated and quick learners. An example is the narrator needs new spectacles and a typical passing student is called over, utilising normal household items he diagnoses the lens strength required, makes and polishes the glasses and presents them to narrator, all within (I think) eight minutes.
Narrator witnesses a few more examples like this, including the ability to create a ftl spacecraft out of kitchen white goods within thirty minutes, then he returns to Earth.
On Earth he discusses the educational system with an enquiry board and the consensus is there is nothing to fear from the aliens, a typical Earth student is capable of building such an ftl spacecraft in less than twenty minutes
Answer
"The Primary Education of the Camiroi" by R. A. Lafferty.
Also the answer to Trying to find a short story (maybe two in the same collection) about Alien education versus Earth
If a child has not learned to accept discipline by the third or fourth grade, he is hanged.
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It was rather revealing to us that the little boy was able to test Miss Munch's eyes, grind lenses, make frames, and have her fixed up within three minutes.
The ending is not as optimistic as you recall.
Not one Earth child in five could build a faster-than-light vehicle and travel it beyond our galaxy between now and midnight.
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