The simplest way, without custom development, is to change the'View Block' permissions for certain roles, for the blocks you want to display or hide.
In other words, this with the Teacher role would see some blocks but not others, and those with the Student role would see some blocks but not others. See https://moodle.org/mod/forum/discuss.php?d=318747#p1278630 for more information.
You can do this with any block in Moodle, but from v2.8 onwards, it appears that the 'Assign Roles' link has gone for blocks on the Dashboard page - but if you have access to the backend database, you can trick Moodle if you know the contextid number of the block. See https://moodle.org/mod/forum/discuss.php?d=318747#p1294163 for more information and instructions.