Teachers do have the right to strike just like any other workers. However, such a move would disrupt the educational process of the people served. Teachers have unions that watch out for the best interests of the workers. I agree that teachers are overworked and underpaid, but a strike may not leave the best impression on a public school system that relies on property taxes.
I believe teachers have the right to strike because in the end they are providing a service, and if not fairly compensated and or treated by the administration it is there constitutional right to strike and take a stand. They are just like any other worker, providing a service for which they get paid for and if they don't feel like they are being paid the subsequent figures for the service they provide they have the right to express their opinion by taking a strike.