Does it make easier to explain (to answer every student's questions and check every student's mistakes), or does it make easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)?

Your disjunction isn't complete there: it could be something else, like how many questions are asked. We LWers are of course familiar with the testing effect, but not so familiar with Bloom's 2 Sigma problem. Alas, I cannot seem to find the reference now, but I recall reading that in tutoring, students are asked 2 or 3 orders of magnitude more questions than in ordinary classrooms.

If this analysis is correct, there seems to be an easy fix -- just throw the disruptive students out of the classroom, and you can have rather good results with large classrooms too.

The reason this isn't implemented is that children are forced to attend school. If they could get out of classes without consequent punishment, not just one or two 'disruptives' but many students might opt out. A school doesn't have anywhere to keep such a group; classes are in large part make-work to occupy students.

On the other hand, if you punished disruptive students but did so outside of class, the habitual disruptives would spend a lot of time in punishment sessions, and would definitely not learn their lessons / pass end of year exams / etc. Schools in the US* prefer to have everyone barely pass exams, to 80% passing with high scores and 20% failing irretrievably. The failing students' parents have too much political power over the schools.

• I'm not from the US, but have seen enough people complaining about US schools on the 'net. The Israeli public schools I went to in the 90s were the same. Every time teachers tried to set up separate classes for non-disruptive students who could be taught instead of disciplined, the non-eligible students' parents complained.

easier to maintain discipline (to keep the class quiet and make sure everyone is really doing the exercises)? I think both these effects are helpful

I realize and confess that my sentiments are unusual, that my thinking on this subject is grossly distorted by ideology and therefore not to be trusted, and that I don't myself know how to set up a learning environment that will actually work for actual children, but I must beg the community's forgiveness, because I want to say this anyway: I think this ideal of "discipline" causes tremendous harm (which of course I understand is not to say that it doesn't also have benefits, but those benefits are not the subject of this comment). I consider it a monstrous tragedy that so many millions of people grow up (as I grew up) without any conceptual distinction between learning important things and being enrolled in a school and obeying the commands of the designated "teacher", with no idea of there being a difference between morality and obedience.

Personally, I've mostly recovered from this phenomenon to my satisfaction. I now have an explicit notion that it is morally righteous to learn great ideas and train useful skills, and some experience of the pleasures and satisfactions to be had from these endeavors---which is not to boast that I'm doing well; I would never be so delusionally arrogant as to think that I'm doing well---but I think I'm doing far better than I was before I learned these ideas. It certainly seems so when I contrast myself to my fellow undergraduate students. Last semester at community college, I witnessed a student passionately arguing with an instructor that surely his paper deserved an A- rather than a B+. (I'm given to understand this is not an uncommon occurrence.) I imagine there are many who would take such incidents as evidence that there's not nearly enough discipline in "our" schools: how insolent of a mere student to argue with an instructor! I, however, draw a different moral. I wanted to cry out to the student: Don't you see how silly this is? Your work, your creation is already good or already bad, no matter what letter the instructor writes on it afterwards! But perhaps it was I who was being silly. The student, of course, didn't care about good writing; he just wanted to get into the University of California at Berkeley. That was the highest goal he had been trained to aspire to, from the days when his elementary-school caretakers rewarded him for being quiet and doing what all the other children were doing. Again, I do not claim that I know how society should be organized; any particular reform or revolution I might propose could very well just make things worse. But can I at least say that it's sad to see entire generations of human minds systematically crippled in this way?---because it's sad.

[Slightly edited from original version]