I doubt that SAT math scores are much higher for secondary teachers than elementary.
I agree that secondary teachers who are not math teachers probably had lackluster SAT math scores. But actual math teachers, especially high school math teachers, need to take quite a few college math courses to be certified, at least in my state.
The thing that drives me crazy about high school (and college and grad school) instructors who have zero understanding of math is that their grading can be completely wonky. As in, they give a ton of low point assignments, take off a "few" points for extremely trivial things on each one, and then artificially increase the value of those assignments by making them worth some large percent of the grade. I've seen this happen over and over at all levels.
Or here's another one. I've also seen this at all levels, but the most disturbing place was at a graduate school of education at a major state university. They had a grading rubric for written work that defines the values 0-10 like this:
9-10 Excellent, 6-8 very good, 3-5 satisfactory, 0-2 unacceptable
And then they averaged these scores and expressed them as a percent. The course grades were awarded as follows:
94-100 A, 84-93 B, 70-83 C, 0-69 F
According to this scheme, a student could get a mixture of "very good" and "excellent" scores and still fail the course.
Why even have a grading rubric if you're not going to use anything but the high end? And this isn't a problem that was peculiar to one particular school. As far as I can tell, it is pretty much standard practice to use rubrics this way.
So my point here is that a teacher not understanding math has more implications for students than just poor math instruction.
