Teach defensive action in all areas
First of all, it's pretty obvious to me that we don't do a good enough job as a society of recognizing and treating (or restraining) people who are at risk of going off the deep end and causing chaos among the rest of us.
However, what we also don't do well enough is to protect ourselves, and especially our loved ones, from violence, whether it is caused by criminals or by people who are mentally ill. And one of the main reasons that we don't is not because of a lack of gun control, but more because of too much restriction on where we can have guns. Do we let teachers keep guns in schools? We should do extensive background checks, make sure teachers are mentally stable and have no felony convictions or domestic violence backgrounds, and then encourage them to train in all forms of self defense, including keeping a gun and knowing how to use it.
In fact, we should be taking this approach in all walks of life. Regulating and otherwise discouraging honest people from owning and using firearms is not helping, it is making the situation worse. That's what I believe most Americans know deep down, that we can only become victims if we let it happen.