And here’s one example of the way people in this country tend to view education, and one reason that teaching is held in such low esteem here - it’s not a real subject.
Speaking as a teacher of 25+ years…it isn’t. 
My grad school started off in 1899 as The Watauga Academy with the specific purpose of training teachers. In 1903 it became the Appalachian Training School for Teachers until 1925 when it became the Appalachian State Normal School. Four years after that it was the Appalachian State Teachers College. It finally became Appalachian State University in 1967. So it was only a “normal” school for four years even though it was specifically training teachers for around 68 years.
Normal schools in the UK went two ways. Some were absorbed into universities (like the Normal School of Science, where HG Wells briefly taught, which is now part of Imperial College London). A few others diversified and became universities in their own right, like Edge Hill.
I imagine the impetus behind it is that normal schools were mostly women-only, and since single-sex education is now mostly dead, there wasn’t much point in retaining them.
And there’s an important distinction. In my OP, I was considering “Normal Schools” to be defined by their curriculum, program length, and credentials awarded rather than their name. I think the Appalachian Training School for Teachers was probably a “Normal School” in all but name, and that the Beijing Normal University is a regular university awarding bachelor’s and possibly master’s degrees that just happens to specialize in teacher education or that has a history in teacher education. After all, anyone can buy a plot of land in Arizona and build a shack on it and call it “Fizzbin Imperial University and Institute of Advanced Hyperbolic Topological Studies and Advanced Normal And Industrial School of The Desert Under Three Cacti Rising”. It doesn’t mean that you can award real degrees or even teach anything meaningful.
One think I could do is contact one of the ex-Normal schools and ask when the last 1 or 2 year non-degree teacher training class graduated. It’s almost certainly the case that James Madison University no longer offers a 2 year non-degree teacher training program for high school graduates and that wannabe primary school teachers have been steered into bachelor’s degree programs for a long time.
Although Gallows Fodder didn’t identify his location, this is more or less the norm (heh) for the former New York State normal schools. There were ipwards of a dozen scattered around the state, over and above what New York City did for teacher training (which I’m not sure about). The name change to State Teachers College(s) was followed by a formal consolidation (each remaining a standalone college physically) into the State University of New York in 1948. I’m not clear on when they started granting degrees (B.S.Ed.) rather than certificates. In addition to the teachers’ colleges, SUNY folded into itself the (originally two-year) Agricultural and Technical Schools > Colleges, a College of Forestry (now the College of Environmental Science and Forestry), severfal specialized schools located at and affiliated wuth Cornell University, and a College of Ceramics at Hornell.
The SUNY State Teachers College at, e.g., Oswego, became the SUNY College at Oswego, then the SUNY College of Arts and Sciences at Oswego. Originally there were three University Centers with graduate and specialized schools, at Albany, Stony Brook, and Buffalo, the last-named being a previously-existing university that became part of the SUNY complex. A University Center at Binghamton soon followed, and I gather several of the colleges grew into univerrsites over the years. The community colleges became additional two-year colleges within SUNY as well. A final element was Empire State College, combining distance-learning independent study courses with seminars conducted at cities around the state that did not have SUNY institutions.
Huh? My friend never left the university. She did a bachelor’s, then started doing a master’s, contemplated the PhD, decided she wasn’t interested in that, and would rather teach younger kids or at a community college, got the MS, and then did extra work to get her teaching credentials. Never once entered “the workforce” until she started work as a teacher. She didn’t know that’s what she really wanted though, until after her undergraduate degree.
If anything, I’d say those are even more stringent and prepared than straight undergrad in education, especially if they are teaching older kids (middle and high schoolers).
I have another acquaintance who is an education major, but is minoring in theater and history, since those are the areas she would like to teach.
Or the National Taiwan Normal University, it’s known wordwide for it’s Mandarin Training Center (Kevin Rudd, the ex-PM of Australia, is an alumnus).
Just out of curiosity, does your university share a nickname with a large naval vessel? Because if it does, I’m a two-time alumna.
What a wonderful and esoteric question. 
I doubt that 1 in 10,000 people would ask about “Normal” schools today.
They still exist in New Zealand but in name only. For example George Street Normal in Dunedin which certainly used to be a place nascent teachers trained.
Peru still has a few normal schools with such a name and Pedagogic Institutes whic are the same.
Do they have Númenórean students?
I think it’s next to Invernesse.
We still have them in Finland. The “normaalilyseot” or “norssit” are under university administration in contrast to most other Finnish schools which are administered by the municipality (and a few private schools). Teacher students have compulsory training periods which are supervised by a senior teacher.
As an aside, at least in Helsinki the normal high schools are pretty consistently in the top 10 when comparing baccalaureate exam results nation-wide.
Hey, let’s not forget about the California State Normal School and its Los Angeles branch.
How did the word “Normal” come to mean “a place that teaches pedagogy” or whatever it means here?
The first such school was intended to serve as a model, or “norm”, for future institutions devoted to the purpose.
Of course; why do you think Peter Jackson filmed LOTR there. anyway? (While down there, check out the Mines of Maoria! :D)
Furthermore, the first normal schools were in France, where they were called “écoles normales”. The idea was that they would be model schools, where the teachers would be taught in classrooms next to the ones where the students were taught. The teachers could then use the knowledge they had gained from their classes when they got a chance to teach in the classrooms for students next door. It was thus what is now sometimes called a laboratory school, where new teaching ideas could be tried out: