Here we are in a physics lab at Western High School, founded 1844, the oldest public all-girls school remaining in the United States. Elyathamby Vignarajah, slight and soft-spoken and wearing a tie, always wearing a tie, is leading a class in a discussion of phase changes. “How can you change a solid into a liquid?” he asks. “Let us think of ice.”

“Heat,” one of the young women in the front of the room says, not very loudly.

“Who said that?” She raises her hand. “Thank you. Ice to water, water to what? Steam. Thank you.” Any observer would notice the unwaveringly polite, even courtly manner. Ladies, he calls his students. Ladies, may I have your attention. Ladies, please write this down. Ladies, this is not writing practice. When you are writing your notes please think about what they mean and what you are doing. Thank you, ladies.

None of them, naturally, call him by his full name. Mr. V., he is called at Western, and was called at the other four Baltimore schools where he also taught over nearly four decades. Mr. V. rises early, teaches all day, goes home, takes a nap, rises again to grade papers and prepare for the next day, and all this at the age of 81. “Preparation is very important always,” he says in the melodic accents common to his part of the world.

The students he taught when he was right out of college, in a Catholic school in his home country, were different than the ones he sees today. They stood when he entered the classroom at Good Shepherd. “Good morning, sir,” they said. “Thank you, sir.” When he first arrived in Baltimore he was asked, do you think you can teach American children? The culture is different here.

“Let me try,” he recalled saying.

There were adjustments, but his entire life has been a series of adjustments, even dislocations. His father died when he was young and there was little money. No electricity: “finish your work before the sun goes down,” said his mother, who was the one who taught the alphabet with a hand in the sand and math with the tamarind seeds, since she could not afford to buy her son paper. What she could do was push him forward. High school, university. He started teaching as soon as his finals were done.

In 1974 relatives found a mate for him after comparing horoscopes. “She’s a very fashionable girl,” said someone sent to check her out. And so he and Sothy, both teachers, were married. But they were Tamil people, and after Ceylon became Sri Lanka Tamils were less and less welcome. “Things were getting worse and worse and we were on the brink of civil war,” Mr. V. recalls, sitting in his living room with his family. “Tamils had a hard time getting jobs and going to school.” His brother-in-law had come to New York, and in 1980 their papers to follow him finally came through. Sothy had been in Baltimore ten years before, as a young teacher ambassador at Poly, then the all-boys brother school of Western, and she persuaded her husband that that was where they should settle. They had come halfway around the world with a toddler, a baby, and $200 in seed money.

“They were a very friendly group of people,” Sothy recalled of her colleagues at Poly. “I kept in touch with them.”

“Everyone was so helpful,” her husband said. “They helped us find an apartment, open a bank account.”

It all led finally to this, this comfortable house, walls hung with art from their native region, and the two children, grown now, as conspicuous a reflection of the American dream as anyone could possibly imagine. Thiru and Krishanti both graduated from the Baltimore public schools and both went on to Yale. Thiru went to Harvard Law School, where he was president of the Law Review, and clerked for Justice Stephen Breyer on the U.S. Supreme Court before becoming deputy attorney general in Maryland. Krishanti received a master’s degree from Oxford as a Marshall scholar, then went to Yale Law School and later on to a job in the White House as policy director for Michelle Obama.

“He used to say, I teach my students like I teach my kids,” says Thiru. “I grade my students like I grade my kids.”

“He had high expectations for us and he has high expectations for his students,” says Krishanti.

So many students, all over the city. “There are nurses, engineers—they say, oh Mr. V., do you remember me?” he says. “Some of the students I have now, when they take their progress reports home, their parents say, Vignarajah is your teacher? He taught me. Sometimes a student will come and say, you know my mom? She says she remembers you.” Thiru recalls his father coming to observe when he was trying a murder case and one of the guards saying, “Mr. Vignarajah, is this your son?”

“I didn’t remember his name,” Mr. V. says of the guard, “but I began to remember his face.”

Most students at Western High School go on to college, and many will be the first in their family to do so, as Mr. V. was. But they have issues besides homework assignments and test results. Some are being raised by grandparents, others are in foster care. There are those who live in parts of the city where crime and violence are overwhelming. As he collects their worksheets at the end of class, they have no idea that their teacher has faced his own demanding challenges, that he and his wife almost fled to Nigeria to escape war in Sri Lanka, that when he first arrived in America, in New York City, he worked for a time in a factory testing lighting control parts and made some extra money by assembling them at home in the evenings.

His teaching career has spanned more than half a century, and there are some things about progress that annoy him. Calculators, for example: “I say, how did you reach this conclusion. The students say, I used my calculator. I tell them, you must show your work. I don’t want to know how the calculator works, I want to know how your brain works!” He says that if he were secretary of education he would keep smartphones out of the classroom. “They are very distracting,” he says.

In some ways this is a story without an ending, because the work of a teacher resonates for years after the teacher has left the classroom. But in one way it has finally arrived at a close. Mr. V. has two grandchildren now, and his son and daughter had wondered if that would be a powerful lure to finally lead him to leave his work. “At the beginning of every year,” Krishanti says, “he says, maybe this year will be the final year. Then at the end of the year he always says, maybe just one more year.” But in the autumn of 2017, on the first day of school, Mr. V. was not in the classroom. It was time to retire.

“If I’d wanted life to be easier I would have taken some other job,” he had once said. “Other places you work, you deal with files, folders. But you are talking about a child’s life here, and if you miss the chance their life is just blasted. How can anyone say that is not an important job?”