Evidence? Mostly personal experience of my own teaching along with my parents who both taught.
> (2) demands actual evidence, since the implication that male teachers will, what? allow things to escalate to physical violence? Hardly belies any real improvement in teaching outcomes.
There are two pieces to this. One is physical and one is social.
As for physical: if I'm managing a classroom, I have a lot of authority by virtue of being 6"+, 100bs+ bigger than most of the students. My voice alone is far more powerful than that of a woman. In addition, I can embarrass or insult a troublemaker without much fear of physical repercussion. This is really huge as it gives me a lot of graded options that a woman would have to think twice about. And, at bottom, the students have to wonder exactly how much damage I could do to them if they really push me into a corner.
As for social: my personal experience is that a lot of female teachers want compliance (personal control dynamic) while male teachers can function as long as there is no interference (group outcome dynamic). A good example of this was an exchange between my parents:
<female> "I want them to quit chewing tobacco in my class" (Note: personal control dynamic).
<male> "Well, you're not going to get that without throwing somebody out of class every day. Are you willing to disrupt your class for that?"
<female> "Not really."
<male> "Okay, so presumably you could ignore it if they don't spit in the back of the class (group outcome dynamic)?"
<female> "I guess, but ..."
<male> "Fine. That's achievable by telling them: "If you're man enough to chew, you're man enough to swallow it (Note: peer embarrassment). If I see any on the floor, all the people I see chewing are cleaning it." Now they'll police each other, and you'll only occasionally have to send one to the office."
> there are a LOT of female teachers that actively try to gain their student's approval.
Go teach at a school. There are always quite a few women who want to be "buds" with the students. I don't really see this among the men except in the genuinely dangerous cases.