The first mass school shooting was in San Diego by a 16 year old girl, armed with a .22 rifle. However, you're not wrong... it seems to be disproportionately men.
This is going to probably shock you, but I actually really really agree with you here. I, too, work in education at the district/admin level. My take on this is probably a little different, even though some of my co-workers believe certain teachers should be trained and conceal a weapon.
No offense to your wife or any other teachers, but they have way too much else to pay attention to than to worry about a weapon in their coat/bag/purse/locker/safe etc. That, and some of my teachers are small or even tiny. Lastly, as an IT person, I constantly have to deal with teachers and their lack of respect for security. If the had a tiny gun safe in their classroom, some teacher is going to put a sticky note with the combination to it on the side, I promise you.
That being said, I think the signs on the door of ever school stating that it's a gun free zone ends up with a shooter knowing he's not going to encounter resistance, and thus makes the school a "soft target." Which sucks.
My plan would to be train and conceal carry only certain support staff that are typically not in a classroom or at least aren't classroom based. This prevents introducing a weapon into a classroom that is just sitting all the time. Plus, to be honest, if something were to go down, the select few should only be backing up the school resource officer if they can. I feel teachers would not understand that working as a team mentality. First responders do not tend to victims... they are to stop the shooter, and I don't see teachers being able to step over a bleeding student in time of crisis, personally. That is not a knock, it's because their hearts are bigger than mine.
Lastly, we had a retired police chief give a wonderful talk to our staff yesterday. He is trained and has many certifications on dealing with school shooters, and now what they are calling "open air shooters." He went through statistics and helped myself staff realize just how rare this happens per capita, but that we should have a plan. He also told us that our lockdown plan was going to get people killed, which I've felt personally all along. The best part was when he encouraged a plan to fight in addition to locking down, and seeing the look on administrator's faces. The biggest thing he proposed to our staff, I felt, was building their confidence.
I'm not saying we should expect everyone to fight, because the reality of many people I've trained with in boxing and muay thai is that the natural reaction to getting hit in the face is that you don't want to do that anymore. My suspicion is that the same likely exists here. However, seeing the teachers feel confident, I bet the students would see that too and feel confident in day to day life as well.
Apologies for coming back to this thread. :)