I recently found a Web site of teacher salaries by state, alongside other statistics. The Web site provides charts comparing teacher salaries to such things as median house price, median household income, and cents of benefit per dollar of salary, but expanding the data set a bit to include a representative standardized test result led to the following intriguing result:

The figure is sorted by math results, from lowest to highest, and the dotted red lines are trendlines for the respective measures. Notice that there appears to be a negative correlation between teachers’ total compensation (as a percentage of median household income) and math scores.
All sorts of considerations arise. There is a positive correlation between a state’s median household income and its students success on the math tests, and a (less significant) correlation between results and per-pupil spending. The obvious rebuttal to my chart, therefore, would be that as household income goes up (along with test scores), teachers earn less as a percentage thereof, thus creating that negative correlation. However, further examination shows that teacher compensation and NAEP math scores both go up with median household income, while the teacher compensation in absolute terms has almost no effect on test scores.
Put differently, wealthier populations see better results on the tests and pay their teachers better, but paying teachers more does not remedy demographic disadvantages. Not surprisingly, given all of this, Rhode Island is tenth highest in total teacher compensation and ninth highest in per-pupil spending, but thirty-sixth in NAEP math scores.
For your reference, each state’s data is available via these links: teacher salaries Alabama | teacher salaries Alaska | teacher salaries Arizona | teacher salaries Arkansas | teacher salaries California | teacher salaries Colorado | teacher salaries Connecticut | teacher salaries Delaware | teacher salaries District of Columbia | teacher salaries Florida | teacher salaries Georgia | teacher salaries Hawaii | teacher salaries Idaho | teacher salaries Illinois | teacher salaries Indiana | teacher salaries Iowa | teacher salaries Kansas | teacher salaries Kentucky | teacher salaries Louisiana | teacher salaries Maine | teacher salaries Maryland | teacher salaries Massachusetts | teacher salaries Michigan | teacher salaries Minnesota | teacher salaries Mississippi | teacher salaries Missouri | teacher salaries Montana | teacher salaries Nebraska | teacher salaries Nevada | teacher salaries New Hampshire | teacher salaries New Jersey | teacher salaries New Mexico | teacher salaries New York | teacher salaries North Carolina | teacher salaries North Dakota | teacher salaries Ohio | teacher salaries Oklahoma | teacher salaries Oregon | teacher salaries Pennsylvania | teacher salaries Rhode Island | teacher salaries South Carolina | teacher salaries South Dakota | teacher salaries Tennessee | teacher salaries Texas | teacher salaries Utah | teacher salaries Vermont | teacher salaries Virginia | teacher salaries Washington | teacher salaries West Virginia | teacher salaries Wisconsin | teacher salaries Wyoming