I think this move by Hamas will have a slightly unintended effect. What may happen is that a serious educational chaasm will grow between the educational levels of very poor Palestinians in the area, and those with parents who will obtain extra-curricular lessons from teachers in more practical subjects.
Palestinians aren't stupid, particularly if they have worked in the PA civil service, and they will ask the teacher Ammar next door to give geography lessons in return for mending his car, and also teach kids at home.
What you could end up with is two classes of Palestinians with dramatically different educational attainment: one with no more than indoctrination; the other with significant levels of knowledge, skills and ability. It happened to some extent in Iran post-revolution (amongst both religious and more secular families) and it could happen in this scenerio.
And bang. You've generated a a significant educational underclass in a community where the boundary is too high to jump, already pressurised by external and civil forces. More fuel for the tinder box.
I really don't feel Hamas can run the area. I just don't think they can do it. I think they think it is largely about security, and it's not.