The Massachusetts Senate on Thursday unanimously approved a bill that would allow school systems to bring back bilingual education, potentially upending a 15-year-old voter referendum that widely banned school systems from teaching students academic courses in their native language.

Senator Sonia Chang-Diaz, a Boston Democrat, called the practice of delivering instruction only in English to students with language barriers “a failed experiment.’’

“It’s a one-size-fits-all system that is failing too many students,’’ Chang-Diaz said before the vote.

But bringing back bilingual education is far from a done deal. The Senate vote followed passage of a similar bill last month by the House. Now, those two bills are headed to a conference committee to iron out differences.

It also remains unclear whether Governor Charlie Baker will support any resulting compromise.

Voters swept bilingual education out of most Massachusetts schools 15 years ago, outraged that students were languishing in the programs for years without gaining fluency in English while their academic performance suffered.

The thinking at the time was that students would learn English faster if they were fully immersed in the language in all their classes. Teachers are only allowed to use a student’s native language sparingly to check for understanding. The law does allow for some limited use of bilingual education, such as programs that allow English-speaking students and non-native speakers to learn each other’s languages.

But many students lacking English fluency continue to flounder. Students who are classified as “English-language learners’’ collectively have among the lowest standardized test scores and graduation rates in the state.

There are more than 90,000 English-language learners in the state, representing about 10 percent of the state’s public-school enrollment.

“We are thrilled by today’s unanimous Senate vote, and grateful for the strong leadership that made it possible,’’ Amy Grunder, director of legislative affairs for the Massachusetts Immigrant and Refugee Advocacy Coalition, said in a statement. “Today’s vote sends a powerful message that Massachusetts is ready to put students’ needs above politics, and give all young people a chance to learn in the setting that works best for them.’’

The major differences between the House and Senate bills center on how much flexibility school systems should have in choosing programs to teach students the English language.

The House measure would loosen current requirements for school systems to seek waivers to the English-only rule, while the Senate bill would abolish the waivers and instead give school systems a choice of specific programs, including English immersion and bilingual education.

Sal DiDomenico, an Everett Democrat, said the bill in many ways is about returning local control to the school systems by empowering them to choose the right programs for their students.

“They know their students better than we do,’’ DiDomenico said.

James Vaznis can be reached at james.vaznis@globe.com. Follow him on Twitter @globevaznis.