I've never fully understood the mind of the Providence Teachers Union, and I especially don't know anything about the state of the leadership and politics post-Steve Smith. I will simply point out that in the 1,900 member union, the vote a new proposed contract was 182 yes, 611 no.
That's for an in-person vote held in Providence Monday evening, so low turnout isn't that surprising, but less than 10% voting yes is pretty weak. One would suspect that new teachers in particular didn't show up, and probably a lot of people who might have held their noses and voted yes if pressed just didn't feel like hanging around until the meeting or driving back into town.
I suspect that a not very different contract will eventually be passed with better marketing and perhaps a few veiled threats, or maybe just waiting for Taveras to leave.