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Top law enforcement officers, administrators from a New Mexico school district where two students were shot and killed in December and some of the state’s most influential lawmakers grappled Thursday with the challenges of making public schools safer.

Officials gathered at the State Capitol for a hearing before the Legislative Finance Committee on school violence and what can be done to limit the risks.

Some lawmakers said at the start of the meeting that it’s the top issue for constituents in their districts and that simple efforts like ensuring locks on classroom doors work will help.

Lawmakers during the recent legislative session approved $46 million to be used for public school security projects over the next four years, but officials have acknowledged that it will take more than building upgrades and surveillance cameras to restore a sense of security for students and teachers.

According to a briefing prepared by legislative analysts, there is no one strategy or combination of strategies that can provide a guarantee against another school shooting.

Experts who study mass shootings, including those on school campuses, indicate school violence-related fatalities are not happening more frequently, but are more deadly than past attacks, according to the document.

The briefing also warns that mental health cannot be used as a single indicator for risk. The report cites other factors such as poverty, exposure to violence, child maltreatment and substance abuse as better predictors for a person’s potential for violence.

New Mexico Public Education Secretary Christopher Ruszkowski said in a recent interview with The Associated Press that some things can be done immediately like working more with law enforcement but that the long-term strategy needs to focus on prevention.

“Now is also the time for schools to be engaging parents and families in new ways,” he said. “We need as many eyes and ears and as many people being vigilant and compassionate for our kids as possible. Schools are going to have to embrace new forms of parent and family communications.”

New Mexico schools use various security measures, from cameras and locking exterior doors to school resource officers, but the analysis found that school officials don’t generally work with law enforcement or emergency responders on their security plans.

The briefing recommends more coordination with local police and sheriff’s departments when it comes to training, assessing risk, reviewing school floor plans and intelligence gathering.

Another recommendation calls for the state Public Education Department to consider collecting data on school bullying, discipline and other measures of student well-being.

The briefing also suggests that state education, public safety and human health departments work with federal agencies to develop an early warning system to identify students who pose a potential threat to themselves and others and to implement support and intervention programs.