I agree about the overall structure of educational systems vis a vis grades, although there is apparently some evidence that being tested periodically helps one retain information.

Thanks, I hadn't seen the things that the linked NY Times article discusses before.

Actually, in fairness, I don't think he's generalizing; I think he's observing one example. My interpretation of the statement as prescriptive may not have been intended.

As you remark, equating "show your work" with "reject mental insights and alternative approaches" is too strong. My suggestion was that to the extent that he's drawing such an equivalence, he's likely to be generalizing from one example.

But in line with what you say above, the essay that the quote is from was written as a personal reflection rather than a careful analysis and so the quote is most properly viewed as an offhand remark reflecting on his own experience.

Of course, if it's to be included on this list, it should be expected to be interpreted as prescriptive.

I cited Thurston for a description of his own experience with school math.

I wonder whether my lack of preconceptions about the source of the quote was helpful or harmful here. (My guess is "no." ;))

Sure, makes sense. I was just giving some background in case you're curious. I personally found the essays that I linked above well worth reading.