(AP) - Lily Rosell anxiously weighed whether to take her 7-year-old daughter to school Monday morning, the first day of classes since the Connecticut elementary school massacre that left 20 children around her child's age dead.

"I was dreading it," Rosell said outside her daughter's Miami elementary school. "I'm panicking here to be honest."

Rosell said she was looking at vans and any signs of something suspicious.

"Ultimately, if this is going to happen like it is nowadays, it could happen in a movie theater, at the mall, anywhere," she said. "It's now about being in the prayer closet a little more often."

Teachers and parents across the country were wrestling with how best to quell children's fears about returning to school for the first time since the killings at Sandy Hook Elementary School in Newtown, Conn.

Around the country, there were scattered reports of school lockdowns in response to threatening incidents Monday.

Schools in Ridgefield, Conn., were locked down after what police there called a "suspicious incident." Police swarmed a high school outside Philadelphia after school security mistook a student's umbrella for a gun. In Florida, three Tampa-area schools were locked down after officials found a bullet on the floor of a school bus.

Chicago resident Melissa Tucker dropped her 9-year-old child off at Jahn Elementary School on Monday morning. She also has two older children.

"I really was worried about sending them to school," Tucker said. "I actually was going to keep them home today and make further calls to the school to make sure what the school is doing to protect people from coming in and out of the school and making sure the doors are locked at all times."

She said she did make those calls and learned the school would be taking extra precautions to make sure all students entering and leaving the building were where they were supposed to be and safe. She said she plans to make another stop later Monday to speak to school staff.

"Now I see why parents want to home school their children," Tucker said.

A western Pennsylvania school district, whose board had voted to eventually arm its school police, instead, got a court order over the weekend so it could arm officers in each of its schools Monday. The court order, first reported by the Pittsburgh Tribune-Review, affected the Butler Area School District and the South Butler County School District, both about 30 miles north of Pittsburgh.

Butler Area Superintendent Michael Strutt told The Associated Press his 7,500-student district had an armed officer in each of its 11 elementary and three secondary schools Monday - and likely will going forward.

In Fairfax County, Va., just outside the nation's capital, schools deployed extra police as a precaution. In the elementary schools, teachers were told to acknowledge the shootings if students brought it up, but to direct discussion of the shootings to home rather than the classroom.

By the time Richard Cantlupe received the news of the Connecticut school shooting that left 20 children dead, his students about 50 miles north of Miami had already gone home for the weekend.

And so the American history teacher at Westglades Middle School in Parkland, Fla., was bracing himself for an onslaught of painful, often unanswerable questions when they returned to class Monday.

"It's going to be a tough day," he said. "This was like our 9/11 for school teachers."

School administrators have pledged to add police patrols, review security plans and make guidance counselors available.

And yet, it was pretty near impossible to eliminate the anxiety and apprehension many were feeling.

"For them, you need to pretend that you're OK," said Jessica Kornfeld, the mother of 10-year-old twins in Pinecrest, Fla., a suburb of Miami. "But it's scary."

Connecticut Education Commissioner Stefan Pryor said his agency was sending a letter to school superintendents across the state Sunday evening, providing a list of written prompts for classroom teachers to help them address the shooting in Newtown with their students.

"In many instances, teachers will want to discuss the events because they are so recent and so significant, but they won't necessarily know how to go about it," he said.

Cantlupe said he will tell his students that his No. 1 job is to keep them safe, and that like the teachers in Connecticut, he would do anything to make sure they stay out of harm's way. He is also beginning to teach about the Constitution and expects to take questions on the Second Amendment.

In an effort to ensure their students' safety and calm parents' nerves, school districts across the United States have asked police departments to increase patrols and have sent messages to parents outlining safety plans that they assured them are regularly reviewed and rehearsed.

Some officials refused to discuss plans publicly in detail, but it was clear that vigilance will be high this week at schools everywhere in the aftermath of one of the worst mass shootings in U.S. history: Twenty-six people were killed at Sandy Hook Elementary School, most children ages 6 and 7. The gunman then shot and killed himself.

Dennis Carlson, superintendent of Anoka-Hennepin School District in Minnesota, said a mental health consultant would meet with school officials Monday, and there will be three associates - one to work with the elementary, middle and high schools, respectively. As the day goes on, officials will be on the lookout for any issues that arise, and extra help will go where needed.

"We are concerned for everybody - our staff and student body and parents," Carlson said. "It's going to be a day where we are all going to be hypervigilant, I know that."

In Tucson, Ariz., where a gunman in January 2011 killed six and wounded 12 others, including U.S. Rep. Gabrielle Giffords, the largest school district in the state increased security after Friday's shooting. Planning was under way at the Tucson Unified School District to help teachers and students with grief and fear, and the district was working with Tucson police on security, district spokeswoman Cara Rene said.

Many schools planned to hold a moment of silence Monday and fly flags at half-staff.

Meanwhile, at home, many parents were trying their best to allay their children's fears while coping with their own. Kornfeld said her town is a lot like Newtown: a place where people generally feel safe being at home without the doors locked and playing outside after school.

"Why would that happen there?" she said. "It kind of rocks everything."

She sat down with her son and daughter after school Friday and explained to them what had happened. She reminded her children that they were with her, and safe.

"But it could have been us," her son replied.

Hoping to reassure them, she drove the children to their elementary school over the weekend. She wanted them to know it was still a safe place.

"Our school is the same as it was when you left," she told them. "It's going to be fine."

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CHRISTINE ARMARIO

AP Education Writer

Contributing to this report were Associated Press writers Matthew Barakat in Falls Church, Va.; Carla K. Johnson in Chicago; Joe Mandak in Pittsburgh; Jay Reeves in Birmingham, Ala.; Brett Zongker in Washington; Bob Christie in Phoenix; Holbrook Mohr in Jackson, Miss.; Amy Forliti in Minneapolis; Michelle Nealy in Chicago; Susan Haigh in Norwich, Conn.; and Jeffrey Collins in Columbia, S.C.

(Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.)