Watts says arming teachers is exactly the opposite of what should be happening, and that her organization plans to go "toe-to-toe" with the gun lobby to prevent expanding easy access to firearms.
She says schools and lawmakers should instead focus on measures that will prevent guns from falling into the wrong hands in the first place.
"It is never an accident when a child gets an adult's gun," she says. "It is always criminal negligence on the part of the adult who owns the gun."
Pushing for more stringent background checks, banning high-capacity magazines and making basic safe-storage information more widely available for gun owners could help reduce gun violence not just in schools, but in all public places, Watts says.
"If you look at all the developed nations, this is only happening in America, and the question is, 'Why?'" Watts says. "We know it's not that we have more mental illness or that we have more 'bad people.' We know this is about easy access to guns in our country and not enough laws in place to regulate them."
But school shootings are not "just a gun issue," said Stephanie Ly, president of the New Mexico chapter of the American Federation of Teachers.
"We must do more to provide greater access to mental health services, bullying prevention and other programs that will help create the safe and supportive learning environments our children deserve," she said in a statement.
Although expanding mental health services and hiring more school counselors would be ideal, Gentzel says, it's not necessarily a realistic option. Schools are now so often strapped for cash, counselor positions have been on the chopping block.
However, other seemingly small moves to ensure proper safety policies are being followed could have a strong impact, Gentzel says.
Making sure law enforcement officials and first responders have diagrams of school buildings is critical, he says, as are regularly participating in safety drills and locking doors.
"It wasn't uncommon a generation or so ago for the doors in school buildings to all be open, and anybody could enter from almost anywhere," Gentzel says. "There have been efforts to try to control the entry to buildings and make sure visitors are known and what their reason for being in the building is."
But many times, there are gaps between what schools should be doing to enhance school safety and what they actually practice, says Ken Trump, president of National School Safety and Security Services.
"What we're finding in our assessments with schools ... is, ironically, that they're actually not doing those proven, tested fundamentals that they believe they're doing or that they should be doing," Trump says.
When it comes to lockdown drills, for example, many schools only practice in the mornings and afternoons. But in order to be more prepared, Trump says schools should vary these drills both in time and location – running them while kids are in the cafeteria for lunch, for example.
The idea that teachers, school staff and law enforcement officials should see shootings as a call to take up arms is an emotional response, stemming from a frustration that despite best efforts, shootings still occur and are happening more frequently, Trump says.
"People believe they have done everything, they believe the lessons have been learned and that they've done everything that they're supposed to be doing, and these things are still occurring," Trump says. "So there's this pressure that we have to do something else, because obviously all the things we're doing are not working."
School responses to recent events like Sandy Hook have differed from those that followed other school shootings – such as the Columbine High School massacre in 1999 – because certain stresses are triggering "more emotionally and politically driven" responses, Trump says.
"Unlike after Columbine, where resources were made available to do something about it, today tighter budgets, federal and state cutbacks in school safety programs and tight local budgets leave administrators knowing they need to do something, but with very limited resources," Trump says.