Parents are always going to be the biggest influence on younger children, so it would make sense to implement teaching the social perceptiveness by helping parents understand the above.
That said, some schools are incredibly adept at teaching things like this. Before getting her doctorate, my mother (licensed psychologist) worked for a local school district with a program called "
Second Step" where a trained, licensed psychologist is hired on via grant to work with young children at a school or district to help them develop conflict resolution, impulse control, and empathy training (along with recognizing emotional states through nonverbal cues, which ties directly into the article I posted before). By my understanding, it was a massive success until they ran out of funding. Programs like this pop up all over the US. I get the feeling if they were nationalized, we'd see a massive drop off in bullying.