It's well known that education majors in college have some of the lowest SAT / ACT scores of any major. The Education Realist blog points out, however, that a large fraction of those dumb ed majors fail to graduate, and that to become a public school teacher you not only have to have a college degree but then, usually, pass some kind of licensing exam, which can range from easy to rather hard for calculus teachers.
So, the people who make it through both college and then pass their subject area test tend to have higher SAT scores than the average Ed major. An ETS study of those who passed the licensing test in 20 states shows that, yes, gym teachers aren't all that intellectual, averaging about 960 on a 400 to 1600 scale. Elementary school teachers average a little over 500 on both Math and Verbal. High school teachers tend to be sharper, with math teachers averaging just under 600 on Math. Here's a graph from ETS of SAT scores for each subject area.
Overall, public school teachers are pretty average for college graduates, but then college graduates are above average. With the exception of high school math teachers, teachers tend to score higher on the Verbal / Critical Reading section than on the Math section. That's their job: to use words to explain stuff. But it also explains why they have trouble dealing with the flood of data that's been incoming in recent years: thinking about statistics isn't their strong suit.
My guess is that smarter teachers would probably be a good thing, so we ought to be thinking about ways to make the job of teaching more attractive to smart people. In general, smart people don't like dealing with knuckleheads, so forcing teachers to carry most of the burden of discipline, a growing trend in recent decades, is a good way to keep smart people out of the business. You can instead use some of those gym teachers to run after school detentions instead of delegating most of the disciplining down to the teachers as happens in so many public schools desperate to avoid disparate impact lawsuits by not generating a paper trail of discipline actions carried out by the administration.
Of course, the Obama Administration is actively working to make teaching a less attractive profession to people who like thinking about The Great Gatsby via their sweeping investigations into the mystery of why black students get suspended relatively more often than other races. Thinking statistically is not the Obama Admin ed experts' strong suit either, evidently.