This Linda Borg article in the Providence Journal covers familiar ground:

The demand for high school math and science teachers, especially in chemistry and physics, is so intense that districts often resort to “poaching” from one another, superintendents say. But the biggest competition comes from private industry, which offers higher pay and a better career trajectory.

In contrast, however:

In North Smithfield, Supt. Michael St. Jean said he had 260 applications for four elementary education openings last year.

Oddly, over the course of around 40 paragraphs, nobody expresses the obvious observation from economics.  We should change the way we structure employment in public schools so the system could rise to market price of the technical professionals who are in demand while reducing the pay offered to teachers in areas that have such a surplus.

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That’s how the market would function in the private sector.  If one job seems impossible to fill while another generates sixty-five times more applicants than there are positions, employers will try to get a qualified person to fill the second job at lower pay so that he or she can increase the offer for the first job.  This will go on across the industry until the pay being offered for the second job can’t attract any qualified applicants.