You must be logged in as an Admin:
Site administration > Users > Browse list of users > Click his/her name > Edit profile > Type new password.
Another way is by direct access to the database:
update mdl_user set password = md5('New password') where username = 'his or her username';
If you don't want the hassles of being contacted by students, you can create a simple application to change passwords independently. On my system, I created a Telegram bot, where students can change their password from Telegram application. They don't need to have an email.