Teachers salary(subject they teach)=Better schools

Ed Glaeser wrote today the key to better schools is hiring better teachers. Because, as evidence by my last post, the education field is not getting the best and the brightest. Since Dr. Glaeser has already begun giving advice to President-Elect Obama, I decided to throw in my two cents.
The problem is so simple to solve, yet I know it never will be. It became apparent to me when my cousin's wife said,

You know there is a problem with our system when I had to fight to get a job paying $27,000 a year, when Matt (my cousin) had no trouble finding a job paying $60,000 right after graduation.

Lisa was right. There is a problem. The problem is not that her husband was making so much more than her, but that she expected to be paid the same. Matt studied Economics, one of the highest paying majors right out of college, and took a job in DC, one of the most expensive cities in the country. She on the other hand took a job in Utah teaching English. It was no secret she would be getting paid less. Starting salaries for teachers is public information, there is no reason her salary should have been a surprise. Had she wanted more money, she should have switched majors.
But, she gives us the root of the problem when she said she had to "fight to get a job". Fact is in Utah anytime there is a teaching position in English, History, Physical Ed., or Art there are hundreds of applicants. However when my sister, Natasha, applied for a position teaching math she had several schools knocking on her door. This same problem occurs with science teachers. School districts in Utah are constantly pleading for teachers. The solution is so simple, it has already been applied at all of the universities, yet somehow it has eluded public schools: Pay math teachers more, and PE teachers less. If the math and physics majors really are the best and brightest students coming out of our universities, then you are going to have to offer them something better than an History teachers salary to get them in front of a bunch of whining 10th graders.