The Pedogogy doesn't matter as much as you think it does, because you learn it from your kid what works pretty fast. Most of the pedogogy is crap and outdated and you have to choose one and stick with it for the class where with homeschooling you can try many different teaching methods without having to get approval from the school board, and even then you have the pick the one that works for most students but leaves out others.

People put a lot of stock in the intelligence of teachers, but consider it this way, most teachers choose a career that requires a 4 year degree plus certification that won't make enough to live comfortably or earn them over what a standard retail job makes much less pay their loans, this is something they think long and hard on (which is probably not much more than "I really like working with children") and make their decision on. It attracts the kind of people who think that's a good idea. Anyone more intelligent that wants to teach runs the numbers and decides against it except in rare cases. Any pedogogy those kinds of people learn isn't that advanced and can be picked up by most by reading a book on it over a month. These "professional" educators isn't exactly an advanced profession like that of a medical professional or a scientist, most of those people would struggle or fail out of such programs. The alternatives for most teachers is a communications degree, or sports/massage therapy. Altruism doesn't equate to being good at something, the proof is in the quality of education offered today.

Edit: They don't deserve contempt, but I'm saying if you increased teacher's salaries, the competition would be such the people that go for it now would simply unable to compete with the sudden competition based the altruistic motives plus pay. Altrustism only motivates you so much, doesn't last long when you're over worked and under paid and dealing with 30+ class sizes. Pedogogy be damned, you'd get people who would be able to actually teach kids on an individual level and demand more from administrators or have the conviction to walk out and move on to something else if they didn't.

> Any teacher must be familiar with both the subject matter and basic pedagogy, regardless of whether they're teaching one student or many

I think you are imagining a homeschool from the 1980s. My kids learn many aspects of the subject matter from sources like Khan Academy and Outschooling. The idea that the teacher needs to know the subject matter deeply in order to manage the child's education is obsolete.

I taught kindergarten for five years and teach small groups and individuals at various levels now. Basic pedagogy is really, incredibly basic and the kind of stuff you pick up by experience relatively quickly even without formal instruction in it. More generally the economics of education literature shows that the only reliable determinants of teacher quality are subject matter expertise and teaching experience. Subject matter expertise is specifically not expertise in pedagogy because teaching qualifications have no discernible effect on students’ education whereas a Math teacher with a Math Master’s gets better results, or a Chemistry teacher with a Chemistry Master’s etc.

Seriously, consider what you’re saying. You’re saying that people without an education in pedagogy are unable to teach. Most of the parents reading this probably taught their children how to read before they got to school. The overwhelming majority of college faculty never have any training in teaching. Many, many people tutor without ever getting an M.Ed.

idk what it's like where you live, but in my state all you need to be a teacher is a bachelors degree and a teaching certificate. the degree doesn't need to be related to the subject you teach and you don't need the certification either if you want to teach at a private school.