I think the motivation behind the behavior has to be looked at.
If a child mismanages emotions, such as anger, by pushing another or verbally attacking another, then the school can recognize this and help the child by setting limits and modeling appropriate ways of responding (this is a teaching opportunity, not just for the classroom or that child, but for life and all the children).
On the other hand, if a child shoves or ridicules to demean and make themselves look special, then modeling would be of no help. The schools needs to take all reports seriously, and guide the child who perpetrated appropriately. The parents regardless, should be notified and encouraged with specific ideas of ways to intervene.