There's an almost dogmatic response by many to any of these shootings that gun control will be effective in curbing them. It's way more complicated than that. Imagine you have a raging MRSA infection and someone says "You should take a single dose of penicillin." That's honestly what most of the gun control arguments are like. A single dose of penicillin wont have any effect on a MRSA infection just like most gun control measures wont have any impact on school shootings.
Background checks? Guns in these school shootings would almost all have not been stopped by background checks. Bans on assault weapons? There are already enough assault weapons out there to fight a major war. Ammunition tax? People hell bent on killing a bunch of kids aren't going to worry about what would happen to their financial security if they buy a bunch of bullets.
I'm not against gun control. What I'm against is gun control that would only serve in making it harder for responsible gun owners to get and own guns while not actually stopping events like this.
If we're going to talk about gun control, it needs to be targeted at stopping the actual problem. If the problem is mass school shootings then background checks and taxes aren't going to be effective. So what would be?
I'd start with pushing for a minimum age to own and carry a gun to be 21 (though this might require a constitutional amendment). The top 6 deadliest k-12 school shootings have all been perpetrated by people under the age of 21. You have to go back to the 1700's to find an incident of k-12 violence with double digit deaths done by someone over 21 (and that was part of Pontiac's War). Keeping these kids from buying guns themselves would be the first step.
Second, I'd establish tort liability for people who give someone access to their guns and that person then goes and kills people and I'd make that tort liability non-dischargable in bankruptcy. If these kids can't buy guns themselves, they have to take someone else's guns, most commonly a parent's gun. So there needs to be strong incentive for people to limit the access of others to their guns. Basically make it clear that if you let your kid have access to your gun and your kid goes and shoots up a school, you'll lose everything and live in squalor the rest of your life.
But this isn't a problem you can come close to addressing with gun control measures alone. If we're going to curb this it needs to be a multi-prong effort.
I think the next thing you have to do is study the problem in depth. I don't care if it's allowing the CDC to do it, tasking the ATF to do it, or outsourcing it to research institutions but we need exhaustive research into all of the causes of these shootings. We can't fix a problem we don't fully understand. Why do other developed countries with high gun ownership, such as Canada, not have this problem? We need to find out.
Two areas I'd definitely address is mental health and school security. Access to mental healthcare is improving in this country but we still need to do more. We definitely need to try to overcome the stigmas associated with getting help or getting your kid help. Why people don't consider mental healthcare to be the same as physical healthcare is beyond me. Early intervention would prevent the vast majority of these shootings if we could just get to that point.
Second I'd address school security. Someone walking into an elementary school and shooting it up isn't doing it because they just really hate children. They're doing it to go out in a blaze of infamy. They're often suicidal and want to show the world how wrong it was to mistreat them. The harder you make it for them to achieve infamy by attacking a school, the more likely they are to choose other targets. Maybe the same number of people still die but at least it's not a group of almost exclusively children.
I want to see federal appropriations to make schools legitimately harder targets. I want to see bullet proof doors and glass installed, have at least two cops per school whenever kids are there with one being assigned to guard the main entrance, camera and buzzer systems, etc. The worst school shootings aren't done by the kid hiding a handgun in their backpack, they're done by someone walking into the school with a rifle and body armor. Make it extremely difficult for these people to gain access.
This isn't an easy problem and traditional gun control ideas aren't going to touch it. We need new ideas and a new approach. Sadly this wont happen. It'll just devolve into a debate about the same, old, ineffective gun control measures.
