Average GRE is useless. Elementary teachers have far lower GRE scores than secondary school teachers, and are about average in verbal and below average in math. Secondary school content teachers are above average in verbal and average in math. However, close to half of all secondary school teachers get higher than 600 on the math section, which is more than the number of math and science teachers. While I suppose it's possible that math and science teachers have terrible math scores and the English/history teachers are scoring those 600+ scores, I'm figuring it's far more likely that math and science high school teachers have eminently respectable GRE scores in math, and that English/history teachers have higher than average verbal.

Anyone who claims that teachers are stupid is using propaganda instead of ETS data.

<A href="http://educationrealist.wordpress.com/2012/01/15/teacher-quality-pseudofacts-part-ii/">Cite for SAT scores</a> and for <a href="http://educationrealist.wordpress.com/2012/01/12/teacher-quality-pseudofacts/">GRE scores</a>