People are paid what they’re “worth” in terms of economic exchange, not what they’re “worth” to society. Sometimes, the two match up nicely. Brain surgeons, for example, make a lot of money in exchange for providing incredibly valuable services. Schoolteachers, on the other hand, make relatively little money despite being in an occupation whose services are quite needed.

There is a crucial aspect left out here. Brain surgeons make lots of money because they are very good at what they do. Teachers earn mediocre wages irrespective of how poorly they may perform their job. In terms teachers are well aware of, brain surgeons, a subset of doctors, occupy the far right of a bell curve.

Teachers, on the other hand, are the population that makes the bell curve. There are a good number of teachers that are by far under compensated for the services they provide, but there is an equal amount that are by far, overcompensated.

Here in Chicago teachers with entry level qualifications start at significantly more than entry level pay.

Teachers are actually generally well paid given the low barriers to entry and working conditions. The latter can be abysmal in urban and/or incredibly poor areas but, generally, it's a nice job.

Still, "education" is so highly prized that people argue that the purveyors of same should be much more highly paid. The economics mitigate against that, though, given the numbers and the source of funding (taxpayers).

Schoolteachers, on the other hand, make relatively little money despite being in an occupation

Depends on where you are. Here in Chicago teachers with entry level qualifications start at significantly more than entry level pay.