A lot of studies have shown the underpaid teacher belief is a myth. Yes, teachers salaries look small. But when one looks payment per hour, even when including grading homework and class planning done at home, teachers, on average, make more than bio chemists with much more advanced degrees. This doesn't even account for benefits, for which teachers are second to only one profession in the percentage of their pay they also receive in benefits - on average over 20%. The problem is not underfunded schools. Certain schools have been sued for being under funded and had, literally, millions of dollars poured into them and test scores continued to decline. Whereas St. Louis cut its budget in half and hired a private company to run the school district and scores skyrocketed.
The problem is that public schools, and their teachers, generally have no incentive to do well. If a voucher system was implemented, where tax dollars follow the student to whichever school their parents see as best, be it public or private, schools would have to improve their programs to keep students and their funding. This would cause them to get rid of poor teachers and reward those who do well.
John Stossel did an excellent report on this called "Stupid in America".