Teachers unions scored political victories in several states Tuesday, beating back proposals that ranged from merit pay to school vouchers and unseating a Republican school superintendent with a national reputation for aggressively changing the way teachers are evaluated and compensated.

But the unions also lost several battles, including an attempt to enshrine bargaining rights in the Michigan constitution and to quash proposals to create public charter schools in Washington state and Georgia.

The mixed election results reflect the complexity of a larger national debate about how to improve public education.

“Uncertain — it’s an uncertain mandate on education,” said Andrew J. Rotherham, a former Clinton administration education adviser and co-founder of Bellwether Education Partners, a nonprofit organization that supports school reform. “Anyone who thinks the unions are irrelevant hasn’t been paying attention. On the state level, they can still make a big difference.”

One of the clearest victories for the unions was the surprise ouster of Tony Bennett, the Republican school superintendent of Indiana, who was completing his first term.

Bennett, along with a Republican legislature and Gov. Mitch Daniels (R), pushed through one of the toughest teacher evaluation plans in the country, a new school voucher program, an expansion of charter schools, a third-grade reading requirement and the first-ever state takeovers of troubled schools. Bennett also championed new academic standards that have been adopted in 44 other states and the District.

He had become a darling of the segment of the school reform movement that emphasizes accountability and a target of unions who said he jammed through changes without their input.

Democrat Glenda Ritz, a public school teacher, beat Bennett by a margin of 52 percent to 48 percent. Bennett raised more than $1 million for his campaign, while Ritz had just $200,000.

“Tony Bennett had all kinds of money, but we did a massive phone-call program and just told people who Glenda was,” said Dennis Van Roekel, president of the National Education Association, the country’s largest teachers union. “And we turned it around. People really care about education and are tired of this overreaching.”

In South Dakota, a Republican-leaning state, the union overwhelmingly defeated a new law that would have created merit pay for teachers, weakened tenure and evaluated teachers based on student test scores. In another red state, Idaho, the union worked to kill three measures that would have instituted merit pay for teachers, limited collective bargaining and required students to take online courses and use laptops.

In Florida, unions knocked down a ballot measure that would have changed the state’s constitution to allow public dollars to go to religious institutions, which would have cleared the way for school vouchers.

Those defeats suggest not only union strength but that Republicans are divided about many of these policy changes, said Frederick Hess of the American Enterprise Institute.

“For huge swaths of the GOP base — conservative, suburban homeowners — these reforms don’t do anything for them,” Hess said. “They bought their houses because they like their schools. They’re okay with giving more choice to the urban centers, like vouchers and other things. But when their teachers are saying to them at back-to-school night, ‘Hey, this stuff is not good for our community,’ they listen.”

But in Washington state and Georgia, the unions were unable to block initiatives to allow the states to create charter schools, which are funded with public dollars but are privately run.

Voters in Washington had turned down the measure in three previous elections. But after a campaign in which supporters raised nearly $11 million from billionaires Bill Gates, Paul Allen and Alice Walton, daughter of Walmart founder Sam Walton, voters approved the measure, 51 percent to 49 percent. Opponents raised just $30,000.

This election “was a split decision between the teacher unions and the ‘reformers,’ ” Hess said. “It was a good night for teacher unions and a good night for charter schools. And I think we’ll see a lot of recalibration going forward, as people try to figure out where the fault line is.”