In theory, public elementary schools were open Tuesday. In reality, Carly Maready's three children were learning from home.

"Since November 18, I believe, my kids have been in school for five days. So this open school is not open,” she said.

Her children attend Dos Puentes Elementary School in Washington Heights, one of 344 elementary, District 75 or pre-K school buildings that were closed Tuesday. Each had multiple coronavirus cases - and when that happens, a school closes for at least 24 hours for an investigation. That investigation can result in a school closure of up to 10 days. Parents are often informed late in the evening of a shutdown the next day.

"Trying to do my job with three kids in school, not knowing what tomorrow looks like, not knowing if I'm taking them to school, not knowing the school is even open, the principal doesn't even know until 7 o'clock, 8 o'clock at night, it is just so hard," Maready said.

Some parents have questioned the city's policy of closing schools for so long following two unlinked cases in one building. At the same time, some teachers question whether schools should be open at all.

"My school was in one of the highest zip codes in Manhattan, so coming out of Christmas break, I definitely did not feel great about coming back to work," said David Love, a music teacher at I.S. 278 in Inwood.

Love sees about 50 students a week in person and often teaches them during their “instructional lunch” period.

"I'm in a classroom with kids without their masks on every day, sometimes multiple classes, and I keep my distance the best I can," he said. "But for example, today, a kindergartner asked me to come open his juicebox. And what am I going to do, say, 'No, figure it out, you can't have your juice today?' That’s not an option for us."

The increase in cases and fears of new faster-spread strains of the virus have left many teachers worried, he said.

"I'm hearing people talking about just waking up with horrible anxiety every single day because we're worried this is going to be the day we get sick," he said.

Since schools reopened after Christmas break, the number of positive cases, and school closures, have only risen. A total of 3,645 staff and students have reported positive coronavirus test results since January 3. Still, Mayor Bill de Blasio maintains schools are the safest place in the city.

"The vast majority of our schools are open right now and have been since we came back in December. As someone who was a public-school parent, I certainly feel for all parents and all kids when there has to be a closure," de Blasio said Tuesday.

Actually, it's not a majority. All middle and high schools have been closed since mid-November. 

Only 850 elementary and District 75 schools, for students with special needs, are eligible to be open. Most of the 344 buildings that were closed Tuesday are such schools, although a few are smaller sites with only pre-K or child care programs.

"When the mayor comes out and says stuff like that and just says, 'No, everything's open, we're doing great, everybody's going to five days, we're on the right path,' I think he wants to believe that and think that, but that's not reality," Maready said.

The Education Department updates its numbers of how many schools will be closed at 6 p.m. each day. Data added Tuesday night show it's continuing to increase: on Wednesday, 373 schools will be closed.