TAMPA — With the horror of Sandy Hook Elementary School fresh in mind, parents at Hillsborough County schools were grateful Monday to see squad cars in the parking lots and police greeting their children.It should not matter, they said, that the extra patrols will cost taxpayers close to $2 million in unincorporated Hillsborough."How do you put a price on life?" asked Cannella Elementary School parent Ann Adams.One by one, parents agreed as they dropped off their children at schools for the first time since winter break.So did crossing guard Tony Dorta. "An officer's presence is a good thing, especially in the times we're living in," he said.Tampa police and Hillsborough deputies reported a warm reception and no incidents."Just the way we hope it will go," said police spokeswoman Laura McElroy.Schools around the country have struggled with issues of security since the fatal shooting in December of 20 children and six adults in Newtown, Conn."I was crying for a week," said Pam Glasser, a parent at Gorrie Elementary School in South Tampa. "It's just unbelievable that somebody would take the lives of innocent children."But how to lessen the risk of attacks is a point of disagreement between gun control advocates and the National Rifle Association, which has called for armed guards at schools.A Rasmussen poll found that among parents of school-age children, 62 percent would feel safer with an armed security guard at the school, while 22 percent would feel safer if their child attended a gun-free school.In the Tampa Bay area, Pasco and Pinellas county school districts have opted against the extra elementary school presence, while Hernando County will provide enhanced security when children return today. .In Hillsborough, which already has school resource officers at its middle and high schools, the Sheriff's Office and Police Department have agreed to send patrols in the morning and at dismissal time to all 142 elementary schools. Some will be there during the school day as well. While the Police Department is redirecting existing patrols with no added cost, the Sheriff's Office is paying overtime.In a recorded telephone message, schools superintendent MaryEllen Elia told parents she is grateful to both agencies. "We believe this will make our schools more safe and secure," she said.Opinions on the School Board, though, were mixed.While sensitive to parents' concerns, members Cindy Stuart and Susan Valdes said they doubt a lone officer could stop someone who was heavily armed and intent on doing damage."When these tragedies occur, we come into a reactive mode," Valdes said. She's asking for information about security systems — including locked gates and buzzers — at the schools in her election district.Stuart, who has three children in the schools, said, "I completely understand where parents are coming from. It's something the public has asked for. But where is the money going to come from?"Member Stacy White said he appreciates the good-faith gesture, but, "I'm not sure that's necessarily the appropriate long-term solution." He and Valdes suggested there might be ways to combine the jobs of guards and resource officers, who function largely as community police.But, White added, "At the end of the day, we have to be extremely responsive to the community."Judging by the comments from parents at Cannella and Gorrie, the school community wants as much security as it can get."We need more officers at the schools," said Jennifer Hellman at Gorrie. "You can't control the guns."At Cannella, Jonathan Berrios said that he would also like to see more training given to teachers in how to respond if the school were under attack."If I'm home, I can hear the bullets, but I won't know what's happening in the school," he said.Teresa Penaherrera suggested each school have two officers. "One in a uniform and the other in plainclothes," she said.Michelle Venegas said she is grateful for any improvement. "Sometimes they leave the gate open during the day, and I've complained about it," she said.Like the others, she said she is not concerned about cost. "It's to protect the kids," she said.Nor were parents bothered by the suggestion that the patrols are largely for appearance."It can't hurt," said Jim Hernandez at Cannella. "I'd rather they be there than not be there."Times staff writer Jessica Vander Velde contributed to this report.