> Paraphrased: "Sports do this so schools should also work this way."

That's actually not what I meant. Granted, though, my question, for its not so accurate writing, can easily lead to such generalization. I was wondering about a much narrower difference: Americans value toiling in sports, yet despise similar practice in STEM. Toiling is a personal choice, as no one forces a student to practice hard, certainly not in American schools. So, why is it a bad thing if a student chooses to get better, sometimes much better, at math by solving more challenging problems?

> (2) People like and accept competitive sports, so emotionally they should have the same reaction to competitive academics.

Not sure if it matters, but I do think that competition is of secondary importance here. What matters is practice makes a better student, at statistically speaking -- this holds true for both sports and academia.

> On (1), there are so many ways that STEM success is not like sports.

There are. Practice is necessary but not sufficient. And I'm not saying practicing guarantees success. Instead, it's more like conditional probability: some people will get ahead by practicing, and I don't see how it's morally wrong if that happens.

> The highest levels of STEM success are defined by doing never-previously-observed things in highly collaborative environments with no opportunity for an exact head-to-head comparison.

I'm more concerned about the majority of the students. The US is a great place for truly talented few. They have access to vast resource: clubs, communities, online groups, local colleges, and at least dozens of programs and awards.

> There is zero reason to believe that your 1,000 AOPS math problems are the best way to advance your STEM education towards real success, even though it may help you outcompete your neighbor on a single test.

I guess this is where we differ. Why does it have to be the best way? I can also say there's zero reason to believe that 10K free throws is the best way to advance one's basketball career. We choose the best way to our best knowledge. And everything has a marginal return, I get it. I was simply comparing toiling in sports with toiling in STEM. You practice until your marginal return approaches zero, and you move on to the next level fo drilling. For elementary students, it can be getting really familiar with multiplication table. For student in junior high, it could be deep understanding of algebra and calculus, for high school student, it could be entry-level research with collaboration with other people.

> Public education is a social investment in economic opportunity for its citizens. It needs to succeed for far more people, and the definition of its success doesn't stop at finding a few stars who fill stadium seats.

Agreed.

> there's a difference between rooting for the participants and rooting for the system.

This is a really nice way of putting it. I just didn't understand why on individual level, Americans value personal effort in sports yet treat personal effort in education as "elitism" or "gaming the system".

> The issue is that a similarly brilliant kid shouldn't be held back because they don't have the same awesome mom. And hey, maybe there are other great ways that three-job mom could be investing in her family and herself.

I guess this is where we differ too. I think the K-12 education of the US is so bad that it does not hold back brilliant kids, but hold back millions of ordinary kids by not pushing them hard enough. See, it's like any college entrance exam in East Asia. Passing the exam does not necessarily mean you're good, but failing it means you're a lousy student. The problem is that more than half of American students couldn't even do well in SAT, which is a very, I mean very, low bar for STEM students.