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Honestly, when I was a student going through HS, I could care less how smart the teacher was. What I cared was whether the teacher could teach ME the material. I had plenty of teachers who were smart, including one with a PhD, who I found were horrible teachers. They understood the concepts themselves, but couldn't explain it. And if a math teacher ACTUALLY failed Math 12, and was able to pull themselves together, work their ass off and go to teaching school to teach math, I think they'd probably be a better teacher than most.
The same goes for a driving instructor. I could care less if he's gotten a speeding ticket a few years back. There are laws that prevent dangerous drivers from teaching, and that's all I really care.
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