All I can tell you is that I am very good at math and science and that I am significantly less likely to have turned out that way if in elementary school, I had been taught a lot of calculational arithmetic and elementary-algebra skills with no coherent and thoughtful attempt to teach the "concepts" or the "broader understanding". My formal educational was pretty crappy, and I would have been much better off if someone'd just given me a small office or a desk and a chair in a quiet place and access to books at the end of elementary school, so I could have skipped the whole secondary-school experience like Eliezer did, but the elementary-school math was very well done, not because the teachers were particularly inspired but rather because the design and integrated nature of the whole curriculum or plan of tuition.

Also, let us not lose sight of my reason for writing, which is to present evidence that at least in the U.S., math education for the average child changed drastically during the 20th Century.