From my perspective, there are multiple steps that can be taken and ought to be taken to counter the problem especially of school shootings. I see three steps that should be taken, in the following order, based on enforceability and immediate impact that are primarily focused on gun violence in schools as we have a premier duty to protect the ones that cannot protect themselves accordingly.
1) Regulation on gun storage: Every gun has to be stored accordingly if it is not carried by the owner. With stored accordingly I mean some kind of safe or locker. You have to limit accessibility to guns for prospective school shooters and since they can't buy the guns by themselves for the most part, family stocks are a main weapon source. Further, you have to penalize failures to comply with this regulation pretty seriously. Similar laws are already in place in other countries and are for my point of the view the best short-term action that also has a chance of making it through the legislative process.
2) Intensify mental health screenings: From my point of view, guns are not the main problem. School shootings are foremost a symptom of deeper problems, but access to guns is what creates a deadly combination. But for every school shooting, there is also a kid that has been lost along the way and that feels the urge to go out on a killing spree and eventually kill himself. For the poster that asked what the number of mentally ill school shooters is, I'd argue 100%, but not all of them have been diagnosed beforehand and that's where we have to get better. Most of those kids have a history of being outsiders, being bullied, or being loners, and we as a society have to make a better job of helping kids before they get fantasies of shooting up their school.
3) Gun control: Lastly, and this is by far the hardest point, which I do not feel like happening anytime soon, is that we enact stricter gun control. I don't think it is the premier measure that should be done, as there are already too many guns in circulation and you can either get guns illegally or use some other weapon (think knifes, explosives, cars, etc.). What I would like to see though, is tighter regulation on who is able to buy guns with a focus on a mental health screening/ psychological background checks. While I do not want to take the guns away from the rightful citizens, I fail to understand while we wouldn't want to check who might be unfit for a weapon of lethal force. You wouldn't hire some lunatic to be your pilot or physician or whatever, why would you give them a deadly weapon. That's something I cannot really comprehend.