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It would be interesting to see what tokenadult has to say about this. Myself, I do not know enough to form an opinion. One point of confusion I have is I do not think these comparisons can be meaningfully made due to certain dependencies. If the U.S. is leveraging its innovation momentum and absorbing the top Math people from the countries that score highest on Intl. Math Tests then one cannot properly state that those teaching methods are not important.

On the other hand; openess to dissent, open culture and ease of doing business can act as a positive attractor of creative talent, suggesting teaching prowess is meaningless beyond some threshold level. As such, optimizing on teaching instead of "cultural tolerance of dissent" may be missing the forest for the trees. Consider Signapore. It scores high in Education, GDP per capita, ecomony and business; it has a very low friction to business and top Math scores yet does not score so well in innovation. So maybe culture is key. Too much respect for seniors may deter trend bucking research programs.

Either way, as other countries develop noteworthy institutions, improve economies and lower barriers to business they will be better able to retain talent and perhaps we can fiinally factor out what variables are key.