The media sensationalizes everything, especially school violence. If one were to actually look at the data on violence in schools you would easily see that there just isn't a ton of violence in schools that occurs. As they say in journalism: if it bleeds it leads. The media wants to promote the gore because that's whats sells.
Yes, it is safe to send your children to public schools. Incidents such as the stabbings in the Pennsylvania high school are not limited to public schools, they can and do happen at private schools as well. What we (as a country) need is to provide more and better access to mental health professional to deal with causes and not wait to deal with the aftermath.
No, it is not safe to send a child to a public school, or any other school for that matter, because you do not know what mental issues the other children have. There are so many children at school at any time that a small number of adults cannot police all of them at once. Any day, a child may become a victim of a crime.
Overall I would say it is not safe to send children to public schools. These schools tend to be understaffed and they don't really provide a sound education, as can be seen with the current common core debates. Children are essentially dangerous too, especially when you group them together. The chance of violence is always high with children, especially in the tween and teenage years. The only downfall is the fact that sheltering them, causes even more problems.