Anyone teaching fourth grade math and up should know algebra and geometry very well (and both are tested on both the SAT and GRE). Really, they all should. You have to know a lot more than your students in order to really understand their mistakes.
I agree, but instead of expecting all elementary school teachers to be generalists who can teach all subjects well, I think there ought to be some specialization, as there is in middle school and high school. Hire math teachers for elementary schools (maybe they could teach science as well), and pay them more than other teachers if necessary. The teachers' unions would oppose this, which is yet another reason they are part of the problem.
There is a lot of talk about "diversity" and "role models" in education, but almost all elementary school teachers are female. Emphasizing math skills in math teachers and paying them well could attract more men to K-6 teaching. This would be a side benefit. (I'm not saying that all or even most such math teachers would be male, just that a higher fraction of math specialists rather than generalists would likely be male.)
