Take the guns out or put more in - what is the answer?

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With yet another mass shooting reported from an educational establishment in the United States, the question arises yet again - what is to be done to stop this sort of thing happening? One thing is quite clear, which is that nothing seems to have been done in recent years that has made the slightest bit of difference. One obvious solution would be to take guns out of American society - repeal the 2nd Amendment and make the possession of firearms illegal. It would be the equivalent of what we did in the United Kingdom - our anti-gun laws have almost eliminated gun-related violence from our streets. However, another proposal is that the number of guns should be increased, including allowing them to be carried in schools and colleges. The thinking here is that as soon as somebody starts waving a gun they stand a very good chance of being shot by somebody else before a murderous rampage can take place. One problem with this latter scenario would surely be what would happen if person A draws a gun and is then challenged by person B? Suppose person C only sees person B and not person A, then draws a gun on person B? Meanwhile, person D ... You get my drift? So what is the answer - more or fewer guns in American educational establishments, and society in general?