I wouldn't say we have, in my country, the respect for seniority and discipline the japanese are known for, and which I think alpha0 is refering to in his comment. I apologize if I'm misreading his words. Nevertheless, my high school class was very crowded: we had 60 students in each class in my final year of high school. However, the picture she paints at the beginning of the piece isn't the one I knew: mine was a private school. As such, there wasn't as much social diversity. (We didn't have, for example, wheelchair access.) But the chaotic aspect of her classroom, in which each student is bringing his own little world to the class, is one I know all too well. So I'm very familiar with the "high-energy routines and structured group activities" Ms. Herman talks about in her op-ed. She's talking about what I've come to know as "classroom control": basically, the teacher's primary job isn't to teach, but to keep us little monsters seated and relatively quiet, while trying to explain why we need to know about the role of prepositions in phrase structuring, and then teaching us about it.
I, personally, always felt that smaller classes, like the special ones that prepared us to our version of the SATs, were much more productive than the normal, super-sized, ones. So, yes, make'em smaller.
Dan Meyer, a math teacher, in his TEDtalk (http://tinyurl.com/323wup9), said this about his teaching subject: "I sell a product to a market that doesn't want it, but it's forced, by law, to buy it. It's just a losing proposition." So, in addition to make'em smaller, make'em interesting. In other words, allow the teacher to make the subjects as interesting as he can. I have a feeling that it's much more important to make the student care about a particular topic than to make him learn it. If he wants to learn, he will; the opposite is also true. As Roland Barthes wrote: "no power, a little knowledge, a little wisdom, and as much flavor as possible."
I don't think there's an easy answer to education problems. I also don't think they are anyone's specific fault. The system is broken, or maybe it just seems too screwed to fix. The difficulties are numerous: the teacher's low salary and appreciation, the schools poor infra-structure, the questionable effectiveness of the assembly-line model of education -- or, as thenewgreen put it, the "post industrial model of curriculum". These are hardships I know exist in my country and I think also exist in other parts of the world.
Anyway, here are some good examples of alternative schools. Maybe they're doing better than the rest of us.