“No to privatization,” read signs at a protest in San Juan in May. “No to school closures.”

Puerto Rico officials say the existing schools are failing. Only about 49 percent of students achieved proficiency in Spanish last year, and just 33 percent in math. Political leaders say that more educational options — and fewer, better staffed schools — will help raise academic standards and establish a consistent rate of spending per student.

“The number of schools doesn’t determine the quality of your education system,” Gov. Ricardo A. Rosselló said at a recent news conference.

Puerto Rico’s finances have been controlled by a federal oversight board since 2016, when the island essentially declared bankruptcy. Advocates for the teachers have asked Congress to assure that new charter schools are barred from receiving any of the $589 million in federal hurricane aid set aside to restore the public schools. More than 30 Democrats in Congress have asked the governor to declare a moratorium on school closings.

Julia Keleher, a former Washington-based education consultant appointed by Mr. Rosselló to take the reins of Puerto Rico’s school system in 2017, said the school choice bill, in the works since before the hurricane, would allow the sort of flexibility adopted by some mainland school districts more than a decade ago. It would also give teachers a $1,500 raise, their first in 10 years.

“It’s incredibly important that this transformation happens,” Ms. Keleher said in an interview.

The protests echoed demonstrations by teachers across the country who have pushed, with some degree of success, for higher salaries and more funding for public schools. That’s no coincidence, said Randi Weingarten, the president of the American Federation of Teachers, who attended a protest organized by the union’s Puerto Rico affiliate outside the island’s Capitol this spring.

“It all comes down to choices, and the island has made a choice — just like the state government in Oklahoma or the state government in Arizona — that children are not a high priority,” she said.