Actually, it doesn't matter whether it's true or not, does it? I mean this doesn't really have anything to do with the original question - which was "Does it make sense if someone with a Doctorate in Mathematics isn't allow to teach math b\c no teaching degree/licence" (just as a reminder in case somebody can't remember after 50+ responses - I often have that problem
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I think most of us (maybe even all?) can agree on some things:
There can be bad licensed teachers, as well as bad un-licensed teachers. Likewise, there can be good licensed, as well as good un-licensed teachers.
Maybe most of us can also agree that different people will learn better in different environments and with or without other people around them. Some children will do great in a class, some children won't and will have a better experience if they're taught at home by their parents, by a private tutor.
There are many things that play into this. E.g. learning in a class doesn't just have to do with the student-teacher relationship but also with student-student relationships. I could imagine that a student that is continually bullied by their classmates will have a very hard time keeping up with their studies regardless of how excellent the teacher is (or whether they have a license or not).
I'd also like to add that people normally don't just learn from teachers. We can learn from any random dude passing by because everybody has things they will know better than others. Some of these people are great at teaching others, some people are just better at learning things from other people even if the average person would say they're very bad at explaining things. This is a matter of interest, intelligence (sorry, not trying to be mean here), time ... - you name it. Many factors play into it.
So, in a nutshell, I think that the whole situation of education is much more complicated than having/not having a license.
In regards to this discussion: I think people have given good reasons and examples for why they prefer teachers to have a license. Just off the top of my hat: That can be everything from being able to trust the person more, to making sure the person knows their stuff in regards to education, to legal reasons ...
In other words, you've actually gotten your answer already. People have told you why they think licenses do make sense in their opinion. Whether you agree with these things or not is an entirely different matter and you're the only one who can judge that. I also don't think that there is any need to 'convince' (since I think I saw this come up somewhere) anybody here. We don't need to have the same opinion on this at all.