Why Do Americans Stink at Math?

Everyone? I love math.

Your typo is very accurate :-)

I would say that our problem in K-12 is a self-perpetuating one. The teachers were taught math badly and so never really learned it (and learned to hate it into the bargain). So then they teach it badly.

I'm not sure there's any solution except for tuning the students in to Khan Academy and suchlike programs.

My high school math teacher majored in math and then got a certificate in teaching. She wasn't a teacher who was told to teach math among other classes. She knew all the advanced stuff (beyond what a high school curriculum required), she was excited about it, she could explain things in various ways, give analogies, was available after class to ask questions and so on. And that is post-collapse Soviet Union full of corruption, poverty and other crap like that. Surely if we can spend trillions of dollars on F-35 we can get us some good math teachers...?

In this country I see a large disconnect between words "Oh kids are so very very important, they are our future, they can't play outside too far because they will be abducted and we care so much for them" and deeds: I see large classrooms, not enough teachers, teacher are underpaid, not interested in math. Funding comes from local property taxes so rich neighborhood get more money, poor ones get less.

Another thing is I remember teachers were respected. Imagine how we react to someone saying "Oh they are doctor. And then everyone nods, right, they are very successful. Or lawyer, or works for Google and so on". Why isn't teaching like that? My mom tells me someone back home thought she was a teacher, because she at her age spoke some English. And she took it as a great complement. In this country you tell someone you thought they were a high-school teacher and they might get offended. Something is very wrong here...

As for making it more exciting -- initially I studies math by repetition and it worked pretty well for me. I think works because kids are amazing at memorizing stuff. Why not first take advantage of that? Starting them out with set theory sounds all cool on paper that is not how humans learn. Multiplication table, basic patterns, even operations are fine to memorize first. Later on it makes most sense to introduce proofs, word problems (I remember doing lots of word problems, our teachers were crazy for them) and so on.

Most people "in the trenches" writing tools that would make use of the fundamentals in their field (either in the physical sciences or engineering disciplines) tend to agree that linear algebra has disproportionately little representation compared to calculus. To be fair, that is somewhat of a downstream problem from mathematics departments, and speaks more about the possibility of stagnation in the undergraduate science and engineering curricula.

fair caveat though: my PhD is in numerical linear algebra...