Among the latest states hit by the protests is Arizona, where teacher pay is more than $10,000 below the national average of $59,000 per year. The Pendergast Elementary School District, where Mr. Soberano works, has recruited more than 50 teachers from the Philippines since 2015. They hold J-1 visas, which allow them to work temporarily in the United States, like au pairs or camp counselors, but offer no path to citizenship. More than 2,800 foreign teachers arrived on American soil last year through the J-1, according to the State Department, up from about 1,200 in 2010.

“In these times, you have to be innovative and creative in recruiting,” said Patricia Davis-Tussey, Pendergast’s head of human resources. “We embrace diversity and really gain a lot from the cultural exchange experience. Our students do as well.”…

“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.”