The payment covered Mr. Soberano’s airfare and rent for his first few months in Arizona, as well as a $2,500 fee for Ms. Avenida and a fee of several thousand dollars to Alliance Abroad Group, a Texas-based company that is an official State Department sponsor for J-1 visa holders. The J-1 lasts three years, with the option for two one-year extensions. For each year he works in the United States, Mr. Soberano will owe Alliance Abroad an additional $1,000 visa renewal fee.

“You have to make some sacrifices to leave your family way back home,” Mr. Soberano said. Every night, he prepares lessons for his seventh- and eighth-grade science students, and every morning, he wakes up at 4 a.m. to video chat with his wife and two teenage daughters, who are ending their day in Manila. Despite their separation, he said the experience has been rewarding, “teaching in a different culture, but also, financially.”

The school districts that recruit teachers like Mr. Soberano say that they have few other options, because they can’t find enough American educators willing to work for the pay that’s offered. They say that the foreign teachers are being given valuable opportunities, and that American students are enriched by learning from them. But critics argue the teachers are being taken advantage of in a practice that helps keep wages low and perpetuates yearslong austerity policies.

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Though J-1 teachers account for only a tiny share of Arizona’s 60,000 public schoolteachers, international recruitment has spread quickly in recent years, as sponsor companies market themselves to districts facing shortages and word spreads among administrators. According to the State Department, 183 Arizona teachers were granted new J-1 visas last year, up from 17 in 2010.

“Rather than increase salaries, districts may once again resort to recruiting internationally as a way to solve the teacher shortage,” Randi Weingarten, president of the American Federation of Teachers, a national teachers’ union, said in a statement. She added that while her union “will fight for everyone working in our communities and educating our kids to have fair wages, rights and workplace protections regardless of where they’re from, the use of the J-1 visa program to fill long-term shortages is an abuse of an exchange program.”