Genovese isn't saying anything new, or anything particularly smart. Statisticians and econometricians have been investigating value-added models for quite some time. If you want to read an actual worthwhile take on the effects of non-random assignment you can read this:
and note, it's a 5 year old paper. Genovese didn't say anything insightful.
Or think of it this way, which is more likely?
- Genovese is right and thousands of Ph.D. statisticians and econometricians engage in statistically bankrupt methodologies.
- Genovese doesn't fully understand the problem, nor the methodologies people use to try to mitigate the known issues.
The actual models use tons of controls, try very hard to account for all observable characteristics, as well as try to figure out the bias caused by what's unobserved. They also track both teachers and students over the course of many years to help sort things out. They take into account a child's past level of educational growth as well as the teacher's history. They worry about whether effects are additive, cumulative, (or both) over time. It's an immensely complex problem and many incredibly smart people have spent years trying to disentangle all the moving parts.
Unfortunately, people in fields like Genovese tend to only have a cursory knowledge of statistics. That's all you need when you can actually do clean, simple, random experiments. They're usually pretty much in the dark when it comes to understanding what people do in fields where the problems are much more complex.
None of this is to say that there aren't real critiques of Value-Added measures. There are! It's just that Genovese's take on it is pretty dumb.
Here's a RAND paper that has some models in it:
Tell me if they look anything like what Genovese is assuming value-added models are like.