I think this constitutes bullying, but the only response we're getting from the school is that he's doing it for attention and she needs to ignore him (she has talked with her teacher about it daily and I have talked with the teacher once).
Although the children are being mean, I don't expect the school to use staff to prevent children from killing insects at recess. They could tell certain children not to talk to your daughter.
The act of killing insects is not the bullying behavior, it is the psychological intent behind it.
Your DD is being targeted by another child, who has found a way to hurt her psychologically, and is doing so on a regular basis. In my opinion, that is bullying. Doing a certain behavior repeatedly, with the sole purpose of hurting another person, is not something that should be ignored by the school.
