My original point was that if you want better teachers, you need to pay them commensurate with the value they create. The private sector will generally reward professionals if their service is needed and valuable. If you grant that education is a public good, then it makes sense to pay for good workers. That means taking care of your people while disempowering the union. If you're hostile to the workers they're going to rally around that union, no matter what. You can accomplish more with effective management than with a blanket opposition to teachers being taken care of.
As for why I quote this study, the ATUS is the standard source for data of this nature. Feel free to post better data if you have it.