on teacher pay...
From the persistent and nearly-universal shortages, we know that math, science and special ed teachers are typically underpaid. The chief cause is obvious: unions bargain with govt to keep pay the same between fields-- when equilibrium wages differ markedly between fields.
Of course, many people (subjectively) claim/imagine that they're "underpaid". One frequent oversight is to look at wages, but to ignore benefits, deferred comp, and job characteristics. Teachers have it [really] good on all three of these. Beyond that, the easiest answer is: go to a job that pays you what you're "worth" in the labor market. If teachers are generally underpaid, the chief cause would be what economists call "monopsony"-- monopoly power of the employer. (Note that this stems from govt's failure to enforce anti-trust laws against itself!) There would be reason to sympathy here-- except teacher unions forcefully lobby for this arrangement, wanting monopoly power over parents/children in the provision of K-12 services.So, we have what we have now: expensive schools ($15,000 per child; $375K per classroom of 25) and claims about being underpaid.