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Public schools teach math and science much better when the teachers DON’T have a degree in education

Of course. A degree in education says, "I didn't have the brains or skill for a real degree."

I once looked into getting certified to teach. My Ph.D. in physics, bachelor's in math, and several years of teaching in college wouldn't save me from having to pay for classes like "Philosophy of Education" and "History of Education."

Of course. A degree in education says, “I didn’t have the brains or skill for a real degree.”
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exactly correct. as shown by this:

http://www.freerepublic.com/focus/f-bloggers/2932550/posts

IQ estimates by college major via SAT scores [average education major has 2-digit IQ]
blogspot.com ^ | March 25, 2009 | The Audacious Epigone

Posted on Monday, September 17, 2012 8:17:59 PM by grundle

IQ estimates by intended college major via SAT scores

Assuming the mean IQ of SAT test-takers included in a report by the College Board to be 103*, the estimated average IQ of students by intended college major follow. The estimates exclude writing results, which were added in 2005 and constitute what is generally considered the least objectively reliable part of the test**. The critical reading and mathematics (previously known as the quantitative section) portions are equally weighted:

Intended major IQ

Interdisciplinary studies 114.0
Physical sciences 111.2
Mathematics and statistics 110.7
English and literature 110.1
...
Education 99.3
Agriculture 99.2
Transportation 98.7
Other 97.8
Family and consumer sciences 97.5
Parks, recreation, leisure and fitness 97.5
Public administration and social services 96.6

Amazingly, you have the same experience and credentials that I have: BS Math, PhD Physics, two-time award winner as an outstanding Grad TA and one year post-Doc as a lecturer. I've been looking into teaching as a retirement option (I never used my PhD, and have been doing software development for 30+ years.)

I learned I would need to spend $30,000 at my 1970's Alma Mater, because, as I was told, "You might know math and physics, but you don't know how to teach math or physics." Well, yeah, I kinda do. And if results are any indication, you folks really don't.

At PSU, we had some (very limited -- 6 credits, I think) overlap in the sophomore level math courses with Math Ed majors. We loved 'em. They helped make for a great curve. But you shudder to think that those dumbasses are out there teaching kids math.

My daughter's math teacher in middle school actually sent a note home to me that said, "Your daughter says that you told her that 0/0 is not defined. That's only in algebra. In the rest of mathematics, 0 divided into anything is always zero."

WTF!?

The worst part is, the engineers and scientists I taught were often functional illiterates who went nuts when I corrected their grammar and spelling; but many of them actually spoke English more correctly than some of the things I've heard from putative "English teachers" at back-to-school nights over the last twenty years.