Paul Heymont, a social studies teacher at Automotive High School, shows off the list of sports and clubs on offer at the Brooklyn school.

It’s hard to get students interested in your school when, according to the  city’s “turnaround” plan, it might not exist in the fall.

That’s what Deborah Elsenhout, a guidance counselor at Banana Kelly High School, reasoned when droves of families walked right past her booth at last weekend’s Round 2 High School Fair, toward the hallway reserved for new schools opening in the fall.

As one of 33 schools proposed for the “turnaround” school reform model, Banana Kelly is waiting to learn whether it will shut down this June, to reopen in the fall with the same students but a new name and a staffing overhaul. Students who apply to the 25 high schools on the turnaround list would automatically be transfered to the new schools that would replace them.

Elsenhout said she either glossed over the turnaround situation to families who did stop, or didn’t mention it at all. But it’s hard, she noted, to advertise a school without a name.

“We do have a rigorous academic curriculum and a strong connection with the community,” she said. “But there’s a sadness, knowing people will be losing their jobs.”

Teachers at many of the turnaround schools have expressed persistent confusion about the plan and its implication for their students. They also found it posed a dilemma at the fair, where 270 schools were given a weekend to pitch their programs, new and old, to hundreds of eighth-graders who were not accepted at their top-choice high schools during the city’s main admissions process. Some teachers reassured families their schools weren’t going anywhere, but others said the schools were already gone.

Marvin Siegfried, one of four teachers staffing the John Dewey High School booth on Sunday morning, said the specter of the turnaround plan and its accompanying uncertainty has toned down his pitch to families.

“Parents have come up to us saying, ‘we heard the school is going to close,’” he said. In response, he has been paraphrasing Mark Twain to them: “News of our death is greatly exaggerated. I think something will work out.”

Siegfried, a social studies teacher who has been at Dewey for 25 years, said he is telling families about the school’s Academy of Finance, a career-education program he oversees for juniors and seniors that has been offered at the school for several decades.

But most of the teachers from five of the turnaround high schools present at the fair told me they were struggling to keep a positive front for prospective students, knowing that turnaround could drastically change the school culture and academic offerings between now and September.

Lantigua Sime is an assistant principal at the High School of Graphic Communication Arts, another turnaround school. But next year, as he told families at the fair, his school might be called “the Clinton Hill School of Visual Arts,” or “Arts Varsity High School.”

The High School of Graphic Communication Arts gave prospective students mock ballots where they could propose a new name for the school.

Those were two of more than 100 suggestions floated by eighth-graders who were encouraged to help name the new school that would exist if Graphics is closed and reopened through the turnaround process. Sime said he was using the new school idea as a selling point, handing out mock ballot cards for students to submit suggestions at the fair, even though the city’s eleventh-hour plan to close his school has yet to be approved.

None of the families who bumped elbows in the crowded, third-floor corridor asked him what the turnaround plan was about, he said, but they did ask about the school’s statistics, such as its graduation rate (55.8 percent).

“We don’t really have data because we’re a brand new school,” he said he told the families, because the city’s plan for the school would involve replacing half its staff and renaming it — effectively turning it into another school entirely.

“Not many people have asked, but the people who do hear about it kind of automatically think of the school as bad,” said Javaughn Vassel, who has been teaching at William E. Grady Career and Technical Education High School for two years. “I am slightly worried. Whatever happens, I’m preparing a backup plan just in case,” he said, which involves applying to other teaching jobs.

“I think my students are very worried about it,” Vassel added. “I tell them that rallying a lot probably isn’t going to change anything, but putting more effort into the school to get their grades up could.”

Synclaire Pope, a senior at Dewey who was helping man its booth, said she has only positive things to tell families about her school.

“I’ve been volunteering a lot at the high school fairs, and I tell people the school is doing really well, in my opinion,” she said. “We have so many great programs here.”

Paul Heymont, a teacher from Automotive High School, stood alone at his booth on the fourth floor just after noon on Sunday. The morning had been “going slowly,” he said, despite the array of programs he was advertising, including the school’s college and career counseling center, internships that start in 11th grade, and industry-certified training programs in eight different areas of car repair. He said he had not mentioned the turnaround to passersby but thought it would do damage to the school community he was there to pitch to families.

“Nobody’s asked me about it. But I don’t want to use the word turnaround,” he said. “I’d say it’s a destabilization. Kids look for stability when things are changing in their own lives.”