When a substitute teacher was accused last month of sexual misconduct, Jim Bartley and other parents at Cloverly Elementary School were stunned. It was not just that they found the allegation horrifying. It was also how often the same Maryland school had been rocked by an arrest.

“Three in 21 months,” said Bartley, a father of four. “We have had enough.”

Bartley spoke as he and a small group of other parents rallied near the Silver Spring school one recent morning in a near-freezing rain to highlight concerns the school has faced in the suburb just outside Washington. They gathered with posters and young children, hoping to get the attention and help of top school officials in Montgomery County.

Their efforts did not go unnoticed.

They have been promised a meeting with Montgomery County Schools Superintendent Jack R. Smith, who is expected to visit Cloverly on Tuesday night for a closed session with parents and staff members.

“It’s a solutions-focused event, to address the concerns they raised,” spokesman Derek Turner said.

Several parents said they hope Smith will consider measures to boost security, increase employee training, improve the screening of substitute teachers, expand adult presence in classrooms and add counseling at the school of about 500 students.

“They need to have a better system,” said Genevla Zani, who has two daughters at the school. “Whatever they have isn’t working.”

School district officials said Monday that they are concerned about the three arrests, two of which involved students at the school and one involving alleged possession of child pornography. But they also said that the cases may partly reflect the vigilance of the Cloverly community.

“They are very thoughtful about recognizing and reporting this,” Turner said.

The concern about Cloverly goes back to 2016, when one of the school’s most beloved teachers, John Vigna, was charged with sexual abuse. His case went to trial last year, and he was sentenced in August to 48 years in prison for sexually abusing four female students over the course of 15 years.

The case came to light after Cloverly staff members noticed a student’s troubled reaction to a “body safety” class that included information about good, bad and confusing touches. The girl later disclosed Vigna’s conduct.

Testimony and court documents revealed that school officials had warned Vigna about inappropriate behavior but left him in direct contact with children. It was one of several such cases in the county.

Parents such as Bartley, whose youngest child still attends Cloverly, said the 2017-2018 school year began with little communication about the Vigna case and no visible changes in school procedures. That frustrated some families, and their concerns grew when a lunch aide, Sean Kelley, 30, was arrested on child pornography charges in January.

Alex Foster, an attorney for Kelley, said it was too early to provide a detailed comment. “It’s important to let the case play out in court and see where it goes before we make any prejudgments about it,” he said.

Kelley’s child pornography charges did not involve students at the school, officials said — he allegedly downloaded explicit images from the Internet — but parents were disturbed. And they were troubled anew in March, when substitute teacher Steven Katz, 59, was alleged to have touched a male student’s buttocks during science class. He was charged with sexual abuse of a minor and a fourth-degree sex offense.

Katz denies the allegations, his attorney said. “Mr. Katz is adamant that he’s done nothing wrong and intends to fully contest the allegations against him,” Robert Bonsib said.

The arrests left some families reeling.

Sonia Livingston, a mother of three, said that after the third arrest, “you’re just saying: ‘How can this happen? How can it happen in one place?’ ”

Livingston said she is hoping for results from the Tuesday meeting with Smith. She noted she has had three conversations in three years with her 9-year-old about alleged offenders linked to the school — one when her son was in second grade, one when he was in third grade and again during fourth grade.

Children get confused, she said, and their trust gets eroded. “They don’t understand,” she said. “They ask: ‘Why again? Why in our school?’ ”

Many parents praise teachers at the school, which was deeply divided by the Vigna case, with some families standing by the longtime educator and others asking how he was kept in place so long.

Principal Melissa Brunson declined to comment through a district spokesman.

The meeting Tuesday night will not be open to reporters. District officials said parents asked that the meeting be closed. At least one parent involved said both sides sought the closed format.

School officials have pointed to improvements dating to 2015, when they launched an effort to increase abuse-related staff training, create an employee conduct code, expand background checks, clarify reporting procedures and emphasize the need to report suspicious conduct.

Turner said officials are open to doing more. “There’s always going to be room for improvement,” he said.

Sheryl Wisniewski, a mother of two Cloverly students, said she was horrified by the three arrests. What is needed, she said, is better communication to parents and more support for students and the staff. “And no tolerance for this kind of behavior,” she said. “We really want to make Montgomery County and Cloverly in particular a place where people wouldn’t even think to try it.”

She and others suggest the school system use Cloverly as a test case for new approaches to make schools safer. “If we find things that work, let’s roll them out everywhere,” Wisniewski said. She said the goal is to improve safety for all county schools.

Jennifer Alvaro, a longtime clinician and advocate on sex abuse issues who served on a school system advisory panel, said that best practices should be used at all schools immediately and that it would be unethical to add safety measures at just one school in a 205-school system.

She called for an outside investigation of all cases of sexual abuse in Montgomery County schools and urged the school system to do more to step up background checks, body safety classes and sexual harassment reporting. School culture needs to change, she said.

“I understand Cloverly’s pain and frustration,” she said. “But this is about more than one school.”

Dan Morse contributed to this report.