there's strong evidence that smaller classroom size really does help a lot with performance across a wide variety of subjects.
A smaller classroom contributes to better results, but how exactly?
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)? I think both these effects are helpful, but what proportion do they have in the outcome?
In my opinion, the difficulty of explaining is not that different. It's not like 2× more students will ask 2× more questions; many questions will be the same. And having more questions asked and answered could help better understanding. There is always a chance another student will come with an unexpected question and make an original mistake, but on the other hand, you can make a Khan Academy video for the whole planet and many people will get it.
The critical part is maintaining the order in the classroom. If there is too much noise, students can't learn. If you have one disruptive student, that's bad, but if you have two of them, that's ten times worse because they will encourage each other. So with a larger classroom there is more noise and a higher chance of disruptive students.
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. Unless your population already contains too many disruptive students, in which case pretty much your only chance is to separate the other students in special classrooms and teach only them.
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 o...
Post by fellow LW reader Razib Khan, who many here probably know from the gnxp site or perhaps from his debate with Eliezer.