The math of relationships is one big reason that teachers dread large classrooms. While the number of students might rise gradually, the number of relationships in a classroom rises exponentially. This means that as classes get larger, teachers pay a higher "behavior management" tax and lose time they could otherwise use teaching.
If you have 15 children in a class, you have 105 relationships, any one of which could become an issue as simple as too much whispering and talking to something as complex as inappropriate affection or violence.
If you increase the number of children from 15 to 25 in the class (an increase of only 66%), the number of relationships triples. The math behind this is one reason that policy makers do so poorly with any kind of complex system: they tend to count the nodes (in this case, dynamic children) and ignore the connections (in this case the relationships).
This odd dynamic is true because when you add one child to a classroom of 15, you are not just adding 1/15th. You are adding 15 new relationships to the 105 already there. Each new child has a relationship to all the others.
The math looks like this
Adding another student is not just a matter of adding ONE more student. It is a matter of throwing the dice on, say, 20-some new relationships hoping that even one of these does not become a problem that adds to the behavior management tax. And if you throw the dice enough times, you are nearly guaranteed to have problems.
