There are a lot of people with problems these days. Some problems lend themselves to bullying. It’s an issue that does not get solved by less shmoozing.
Recess is a lesson in life. Life does not always have teachers and rebbes. Of course, a school needs to be watchful and act if something occurs. But it’s never going to be perfect, just as life.
The main issue is to instill in the non-bullies the evil that is making someone feel bad, hurt. If a child saw another be embarrassed and had even somewhat internalized the Chazal that embarrassing a person is an aspect of killing someone (to the extent that the din is [disregarding the details] yareg v’al yaver if faced with the option of being killed or enabling an embarrassment of someone) – then would it be such a problem.
Now, this is mainly with somewhat older children. Young children (to throw out a number, up to ten) need very close (but at a distance) supervision of their social skills. This is as an importance job to a teacher or rebbe to help instill in children proper bein adom l’chaveiro. Just as a teacher cannot answer a lengthy call in the middle of class, they can’t when supervising. Note: a school should be set up that every teacher gets real breaks not supervising recess breaks. But older kids, need to learn to fix things for themselves. And that just does not mean with them themself but their surroundings and others as well. They need to stand up (after asking their parents or a rebbe how to proceed) and fix bullying dynamics. Just as if they saw that one of their classmates was being beaten or was starving, one would hope that all fair-minded classmates would speak up, so to with the matter of bullying.
I’d like to also say a potential thing to parents that children that are being bullied. This needs to be discussed with their rabbi. As stated, the din is that one makes someone’s face white from shame, it is as if they killed them. Now, if someone was actually chas v’shalom trying to kill your son or daughter, there would be no qualms. The person has a din rodef. Any means that are necessary (though not more). Extreme means are not out of the question. Digging up dirt on the bully. Extreme pressure on the parents of the bully. Of course, one must seek counsel. But the matter is of life and death, and those who can stop the matter, must. PLEASE READ THE NEXT PARAGRAPH THOUGH.
Note: as stated, a lot of times the bullying is due to issues at home etc. Try to see if you can help the bully figure those things out (or the parents of the bully). Your daughter is being harassed by a girl from an unstable home. Contact a chesed organization (or make one) and try to help the bully. Get her a mentor. Get her babysitting jobs or something to build her self-confidence. Do what you got to do. Don’t hide behind that why should I do someone a favor, when I am the one that has been wronged. No, your kid’s (spiritual and emotional) life is in danger. No excuses. And no blame games.