"If we have evidence that current teachers are ineffective (and don't international math test scores provide this evidence?), then why not let the non-educators take a shot?"
In reading through the comments, this particular point focused my attention because I suspect its primary sentiment runs deep within the larger discussion about the state of U.S. math education. I.e., our international math ranking is poor; teachers must not be doing such a good job; so why not let somebody else take the wheel?
On the surface, this doesn't seem a particularly unreasonable argument. It does, however, make some tacit assumptions that are questionable, and even downright strange. Namely:
Teacher training is a negative-value-added process.
Any meaningful discourse about education has to address teacher preparation programs. If teachers are truly failing en masse, then clearly something important and fundamental is lacking in their initial training. Now of course these programs aren't perfect. They might not even be world-class. But to suggest that non-educators would be better classroom teachers is to imply that I'm somehow a worse math teacher after year-long stint in grad school and months of practicum work and student teaching than I was the day I left the Marine Corps in search of a new career. Which is ridiculous. How can exposure to current research in pedagogical content knowledge, educational psychology, and legal/policy decisions make me worse? How can active observation time in great, good, bad, and awful classrooms make me worse? Hands-on experience with real students? Regardless of the level of helpfulness of any of those things, I know that it's strictly non-negative. And please let me know if you can prove otherwise, because I'd like to sue for my $25,000 back.
The countries with better outcomes are being taught by non-educators.
If international math test scores suffice as proof of U.S. teachers' ineffectiveness, then those countries with higher scores, one supposes, must provide some sort of evidence about effective practices. Is Finland spanking us because it got its teachers out of the picture somehow? Not quite. Over there "teacher" routinely rates as the most admired profession among high school graduates; after a rigorous screening process, the most qualified teaching candidates are educated at government expense; all teachers are required to hold, at a minimum, a master's degree (source for all the above). Finland isn't great in spite of its teachers; it just does a much better job of screening and training them. Which all sounds easy and practical, but in order to replicate that in the U.S., our society's view of the teaching profession would have to change dramatically. You must believe your tax dollars are well spent paying pre-service teachers' tuition. You must believe teaching is an important and prestigious position. You must believe that teachers shouldn't have to take a vow of poverty to educate our children. In short, the answer seems not to be getting non-educators into the game, but forcing über-educators into the game.
People who devote all their professional time, energy, and resources to teaching can be called "non-educators."
Like any other profession, education is vulnerable to a certain level of entrenchment. Change can be slow and difficult, and new blood can't hurt. But if someone leaves a career in, say, mechanical engineering to spend all her working (and a whole lot of her non-working) life thinking, studying, worrying about, and practicing teaching math to high school students, then she has officially become an educator. Because that's what educators do. But again, if the profession hopes to attract any of the best and brightest from other fields, then there is going to have to be a societal sea change that makes teaching a viable option for people who have gone to a whole lot of intellectual and financial trouble to become the best and brightest in the first place. Those of us who have made those sacrifices in spite of the trouble/prestige ratio welcome you.