A data science class he signed up for required several prerequisites he did not have, he said, so eventually, he dropped it and signed up for a social psychology class instead. That one, offered by Wesleyan University, he finished.

When it came time to fill out his college applications, he wrote about the data science class even though he did not finish the course, which he disclosed. That does not appear to have been a problem. Last week, he began freshman orientation at Lehigh University in Pennsylvania.

Seth Allen, dean of admissions at Pomona College, said his school had seen online courses on applications from both domestic applicants and those abroad. In other countries, Mr. Allen said, some young people use the classes as a way to augment fairly narrow curriculums — in India or the United Kingdom, for example, students specialize quite young, he said. And even in the United States, some students use them as a way to study subjects not offered in their high schools, not just during the summer but year-round.

Anthony Liu, 17, who will be a freshman at the Massachusetts Institute of Technology this fall, said he completed five MOOCs on topics like artificial intelligence. He estimates he tried out nearly 20 others that he did not finish.

“I come from a school that’s really humanities-focused, and I’m a math and science guy,” said Mr. Liu, who is from Daly City, Calif. When he signed up for the classes, he was not planning to put them on his college applications, he said, but then decided it could not hurt.

“They’re not going to view it badly,” he said.

Mr. Akim, the Stuyvesant High junior, said he took online courses because he was curious about the subjects and in fact, he was not sure whether he would include them on his college application because the classes were introductory. (He completed only one.)

“If I were to take something more high level,” he would be more inclined to include it, he said. “Whether they want to say it or not, everyone wants to put something overly impressive on their college application.”