There are various different ideas about how to organize schools. In particular, people disagree about:
I doubt that there are any right or wrong answers to these questions. Each method will be good for some children in some situations and bad for others in other situations, and the best system is to ensure that parents have a choice.
Between the ages of 9 and 17, I attended traditional British single-sex boarding schools. These are somewhat controversial and people tend to oppose or support them rather strongly. I think they have some advantages and some disadvantages.
I went to those schools because my parents travelled from country to country, generally in Africa, and (reasonably enough) didn't think I'd get a good education if I moved around with them. This illustrates that boarding schools do make sense in certain circumstances:
Otherwise, if a normal family lives near a good school and doesn't plan to move, it seems a little eccentric of the parents to pay good money to lose sight of their children for two-thirds of each year.
Boarding schools have always been flexible enough to accommodate non-resident pupils as well. Now some of them will allow non-resident pupils to stay overnight on an occasional basis, when it suits their parents. This seems a useful facility that most children and parents would welcome.
Single-sex or mixed?
Mixed education is a more obvious choice because it's a better preparation for real life. However, educating teenage boys and girls together has some genuine disadvantages: they're likely to be distracted from their education by each other's presence, and there's also a risk of unwanted pregnancies. Totally mixed boarding schools, with boys and girls living in the same house as well as being taught together, are unlikely until foolproof contraception is invented.
Some people argue that mixed education tends to channel boys and girls respectively into stereotypical male and female interests and activities, and also that girls underperform academically in the presence of boys.
Thus, there are arguments on both sides, and parents can reasonably choose one or the other.
Teaching children of significantly mixed abilities together just doesn't work. Material suitable for one ability group is boring and useless to a different ability group.
However, children don't have the same ability at all subjects, and I think it would make sense to recognize this and to divide them into ability groups separately for each subject.
There is an argument that really stupid children are unlikely to be found in the same ability group as really intelligent children, in any subject, and that therefore it makes sense to have different schools for stupid children and intelligent children respectively.
I disagree with this in principle because it inevitably penalizes some children — not just those who have particular ability in one subject, but also those who are on the borderline between one type of school and the other. Furthermore, it's unkind and arguably unwise to stick a permanent label of "STUPID" on half the population.
However, the practical difficulty in catering for the ability range of the whole population in one school may perhaps justify this kind of segregation — especially if the school is small. As usual, I think the best system is to permit all kinds of schools, and let the parents choose.
How to discourage children from behaving badly is an experimental question that can best be answered by experiment: find out what works in practice, and use it. Perhaps there is good experimental evidence on this subject, but I haven't come across it.
I believe that people in general (not just children) shouldn't be punished violently for non-violent crimes. However, in principle I have no objection to violent punishments for violent crimes. If a child uses violence himself, I have no moral objection to hitting him in punishment. I don't know whether that's the most effective way to control his behaviour; it's an experimental question.
However, if someone (child or adult) is persistently and intolerably aggressive, I don't see how to deal with him without using force of some kind.
I don't think ordinary schools can reasonably be expected to cope with extraordinarily difficult children, unless they can be given a method of dealing with such children that is known to work. Failing that, I think such children should be segregated at special schools.
Certainly a school should have the right to exclude or expel particular children if it feels that it can't cope with them or that they're likely to be harmful to other children.