Sadly, I think that schools don't teach meditation because of the religious baggage that it has picked up over the past 2500 years. It's really a shame too, because what we are taught today as children is the exact opposite of introspection. Instead of looking at our sensations and seeing them for what they are, we are taught to ignore our feelings and to be tough.
But of course, it is even tougher to look directly at those feelings without judgement. The sensations need to be examined closely. If they are not recognized, they can and will most certainly hang around for years generating a lot of suffering while one attempts to pretend that they don't exist; until the person finally decides to acknowledge them.
I was absolutely blown away when I realized how much of my own misery was caused by blind reactions to my sensations, and the insane stories that I had built up around these sensations. I was also equally amazed by just how simple it is to retrain the brain. Well, the technique is simple but applying it does take some effort. But the payoff for this effort is immeasurable!