"We are going to be safe, and we will be open to educate our children," Adams said.
The previous mayor, Bill de Blasio, announced a plan last week to reopen schools with extra precautions including increased surveillance, COVID-19 testing, and at-home COVID-19 tests sent home with students who have an infected classmate.
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New Schools Chancellor David Banks said all was going according to plan.
"All indications are we are in a pretty good place right now," he said.
Mayor Adams said he wants all public school students tested.
"I'm a believer in mandating testing, but we want to do it right," he said.
Public schools are doubling the amount of weekly testing, and both vaccinated and unvaccinated students will now be tested. Previously, just 10% of unvaccinated students were tested.
The city is also changing its rules to limit quarantine. Instead of an entire classroom shifting to remote learning when one or more students test positive, all students in the class will be given rapid at-home tests.
Those who test negative and are asymptomatic will be allowed to return the day after their first negative test. Students will then be given be given a second at-home test within seven days of their exposure.
The state will give the school districts two million tests to support the changes.
"The test kits, I've certainly done them myself," Health + Hospitals President Dr. Mitchell Katz said. "They are not super easy, but with the instructions, they are entirely doable. You have to read the instructions. but if you read the instructions, you will get it right. New Yorkers are a smart and savvy group, and I believe in them."
Esther Farran said she felt fine about taking her 4-year-old daughter to her public preschool in Manhattan on Monday.
"I'm not very apprehensive, and really, we don't have any other options," Farran said, noting that she and her husband work. "And I see that this particular school takes good precautions."
Trisha White said in-person school was far better for her 9-year-old son than remote learning was.
"He could get the virus outside of school, so what can you do?" she said. "I wouldn't blame the school system. They're trying their best."
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PS 58 in Carroll Gardens, however, is closed on Monday. The school's principal sent a letter to parents that the closure is due to staffing shortages caused by COVID.
The DOE tells Eyewitness News it was not authorized, and there are substitutes that could have worked.
The United Federation of Teachers had asked Adams to postpone in-person learning for a week to assess potential staffing shortages given the spike in COVID-19 cases. UFT President Michael Mulgrew said Monday that the union remains concerned about staffing.
"This is going to be a very, very challenging week," he said at a news conference.
Mulgrew said the feasibility of using administrative staff members to fill in for absent teachers depends on factors such as how many teachers are out.
"There's no one-size-fits-all answer," he said.
New COVID-19 cases more than doubled in the city over the school break. In the seven-day period that ended Saturday, the city averaged about 36,900 new cases per day, compared to 17,180 per day in the seven days before schools closed for the holidays.
New York City's public school system is by far the nation's largest with about a million students. The city Department of Education website listed eight schools that were closed because of the virus, out of about 1,700.
School was canceled Monday in upstate Syracuse because of the increasing number of COVID-19 cases and a lack of substitutes to cover absences. The district said take-at-home tests would still be given out at city schools.
(The Associated Press contributed to this report)
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