I heard Beshem a mechanech that a child who is bullied can or perhaps should resist or retaliate in a physical manner in order to prevent future bullying. Speaking to the teacher and speaking to the bully sometimes- simply isn’t effective (or the teacher doesn’t do anything about it), especially when the victim has a reputation of being weak and has more than one perpetrator and the bullying continues outside of the school setting. Is this a valid approach in halachah as well as hashkufah?
It seems obvious from your question that we are only discussing a theoretical question, as it is impossible to give a correct answer to such a question without knowing all the details of the specific situation.
In theory though, it is true that there is such an idea. The Sefer Hachinuch mitzvah 338 regarding onoas devorim,says, that when a person starts up with us we may defend ourselves and answer him back even in a hurtful manner. (Of course it is better not to answer him sharply, however if there is a need it is permitted). The reason is, because the torah did not mean that a person should be like an emotionless stone, and that he should let people hurt him and take advantage of him. It is the same on other levels too. If someone comes to kill us, we should kill him first. We also find this regarding hitting someone who is hitting you see Machaneh Yisroel ( R’ Y. Grossman) 23 that it is permitted and he wouldn’t even have to pay him for the damages. See CH:M 421-13,
After this is said, we have to be very careful, when to use this idea and when not to. He surely doesn’t mean to say that that we can bully and insult people at the slightest provocation, and when this idea can be avoided, it is surely better. We all know of the lofty pious level of “shomim cherposom v’einom mesivim” (not answering when someone insults us). At times that we can do this, depending on the situation that is terrific. However the idea the idea of answering back when needed does exist.
In the case that you are presenting, things are even stickier, because this idea is very subtle, it can be confusing, especially to small children, and this is not the general chinuch that we want to give our children. But again, each situation has to be evaluated on an individual basis.
Another point, is that there is a difference between resisting or retaliating at the time that he is being bullied, and taking revenge afterwards, which would not be allowed.