This question is very difficult to answer, because it is hard to make generalizations. Children act up in school and do violent things for many reasons and they do not always have the same characteristics. However, if we had to make a few generalizations, I would say that two characteristics are present with troubled children.
First, children who act up in school have a difficult time at home with their family life. Some are abused, others are neglected, and still others go through other untold difficulties. When these troubles are present, sometimes it translates into behaviors that are harmful. We can also broaden this to speak of their general environments as well. The way a child grows up make a big difference. If a child sees and experiences violence, there is a greater chance that this will manifest.
Second, some children have problems that are more internal, that is, they might be attention deficient and hyperactive. This can lead to various types of insecurities to the point where they act up.