Reply #143: No, but they vary measurably across the population of students

[Recursion]

And their improvement over the course of a given year is modeled as a combination of development (zeta), previous attainment (lambda Y sub zero), the student's effort (beta X sub i), noise (epsilon -- was it too hot in the room that day? Did the kid's parents have a fight the night before? etc. -- maybe the epsilon should be much higher than it is), and a 3x3 linear system of the teacher, school, and school district.

Maybe students can't be objectively assessed on subject mastery. In that case tests should govern a lot less of the course of their lives than they end up doing.

If they can, some of their performance has to come from the teacher they had -- if not, why do we care who teaches?

This model sets up the 3x3 linear system to determine how much a students' performance comes from the district (by looking at how all the students in the district did), how much from the school (ditto), and how much from the teacher. And, again, if none of it actually comes from the teacher, why do we care who's teaching?