I would suggest removing the "login" link and the message saying you are not logged in on the "/login/" page.
Clicking that link only brings you back to the same page.
Not only is there no need for the link, but it may cause confusion with some students.
How I Did It
This is how I made the changes on my site.
Near line 300 in the /login/index.php file.
// I'm sure there's a better way to do it, but to save time, I just did this.
// I changed $loginsite, to $loginsite2, to eliminate the Login link on the login page.
// NOTE the 2nd one is now loginsite2
print_header("$site->fullname: $loginsite", $site->fullname, $loginsite2, $focus,
'', true, '<div class="langmenu">'.$langmenu.'</div>');
// I also thought that there is no need for the standard FOOTER on the login page, so I did this.
// Commented this out, so no footer on the login page.
// Added this: