I looked through that list, and once you filter out the non-school deaths, it seem to line up with the article.
For example, Rancho Tehama Reserve, California is listed as six deaths, but that was a shooter who killed five adults at other locations, then fired at a locked down school, injuring one student, before killing himself. So zero students killed. There are quite a few like that in the list.
First I'm not sure that is a good source. We have no idea if this list is vetted. Second, just because there is an increase in volume doesn't necessarily mean an increase in rate.
For example, Rancho Tehama Reserve, California is listed as six deaths, but that was a shooter who killed five adults at other locations, then fired at a locked down school, injuring one student, before killing himself. So zero students killed. There are quite a few like that in the list.