It is enouth to hidden the block.
After login with the administrator:
Site Administration > Modules > Blocks > Manage blocks > Recent Activity (hide)
Site Administration > Users > Premissions > Define roles > Edit(Student) > View reports = Prevent
The same for the teacher.
After the beginning of the semester, now we have about half of the traffic that we have in the first days, but is still considerable high comparing with the last year, so we cannot turn on neither the recent activity block nor the reports to professors.