A Cornell University survey of its faculty found that about one-third were “not interested in teaching classes in person,” one-third were “open to doing it if conditions were deemed to be safe,” and about one-third were “willing and anxious to teach in person,” said Michael Kotlikoff, Cornell’s provost.

Faculty members at institutions including Penn State, the University of Illinois, Notre Dame and the State University of New York have signed petitions complaining that they are not being consulted and are being pushed back into classrooms too fast.

At Penn State, an open letter signed by more than 1,000 faculty members demands that the university “affirm the autonomy of instructors in deciding whether to teach classes, attend meetings and hold office hours remotely, in person or in some hybrid mode.” The letter also asks for faculty members to be able to change their mode of teaching at any time, and not to be obligated to disclose personal health information as a condition of teaching online.

Kellermann, 62, an English professor at Penn State, in an essay for Esquire magazine, proclaiming that “1,000 of my colleagues agree.” Those colleagues have demanded that the university give them a choice of doing their jobs online or in person.

Rachel Pell, a spokeswoman for Penn State, said the petition signers there represented only about 12 percent of the 9,000-member full- and part-time faculty.

Anna Curtis, an associate professor of criminology at the State University of New York, Cortland, asked to be allowed to teach remotely from home so she could care for her 4-year-old son.

Joseph Brennan, a spokesman for Montclair State, said that another group was looking at pedagogical issues, and that the university was making getting back to in-person classes a high priority.

Instructors at Georgia Tech said they were told last week that they would either have to be 65 or older or have one of seven specific health conditions, like diabetes or chronic lung disease, to qualify to teach remotely.

“Due to these extraordinary circumstances, the university is temporarily suspending the normal requirement that teaching be done in person,” the University of Chicago said in a message to instructors on June 26.

Yale said on Wednesday that it would bring only a portion of its students back to campus for each semester: freshmen, juniors and seniors in the fall, and sophomores, juniors and seniors in the spring.

“Nearly all” college courses will be taught remotely, the university said, so that all students can enroll in them.

He said the university environment would be safer than the outside world because students would be tested even when they did not have symptoms.

Hundreds of cases have been linked to universities in Southern states in recent days, including clusters among the football teams at Clemson, Auburn and Texas Tech, and outbreaks tied to fraternity rush parties in Mississippi and to the Tigerland nightlife district near the Louisiana State campus.

Joshua Wede, 40, a psychology professor at Penn State, argued that it was not possible to maintain a meaningful level of human interaction when students are wearing masks, sitting at least six feet apart and facing straight ahead.

He is not scheduled to teach until spring, he said, but he expects to sit out that course for health reasons and on principle, because he does not think it is fair to promise students something they will not get