23 June 2009

Teachers' Behavior Management Tax

"I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated."- Poul Anderson

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.


ThomasLB said...

I've never considered that before. This was an interesting post.

Big Al said...

I would guess the goal of a teacher is to reduce the student-to-student interactions during classroom instruction time while attempting to insure the teacher has a unique 1:1 relationship with each and every student.

Lifehiker said...

Big Al, you have hit the nail on the head! Ron explained a real problem that will be affecting our teachers and students, you came up with a solution - albeit one of great difficulty.

This "law of increasingly complex relationships" is something I've noticed with respect to non-profit boards of directors...it seems that the larger they get, the less effective. Seven to nine people seem to do well, but more than that often become disfunctional.

Big Al said...


I've always thought it odd when "non profit" organizations have a board of directors. To me, that's a conflict of ideals: if you're a non-profit, why do you need a board of directors? They are non-profit only in the sense they don't show a profit on their balance sheet. I have to chuckle whenever I see the look on faces when I break the news to the unfortunate uninformed that many non-profit groups have CEO's commanding high 6-figure salaries. Just the other day I explained this to one of my teenage sons. I watched as the revelation that sunk in turned to anger. He felt duped and he was TICKED!