The best statement that explains how the Supreme Court interpreted the Fourth Amendment's protection from search and seizure in schools is:
They said that school officials only need reasonable suspicion.
In various rulings, the Court has recognized that students do have Fourth Amendment rights but that these rights are balanced against the need for maintaining a safe school environment, which allows for a lower standard of "reasonable suspicion" instead of the higher standard of "probable cause" that is typically required for searches outside of the school context.