This page contains instructions for clearing the notification number that displays next to a user's name in the Global Navigation bar in Compass 2g.
Click on your name in the upper right corner of the screen, then click the clock icon:
Click the gear icon on the right:
Click the select/unselect checkbox so that all the check boxes are cleared, then click Save.
This will clear the number of all non-grade related notifications. To clear the grade notifications click on the icon with the check mark.
Visiting that page will automatically clear the number for grade notifications that displays in the Global Navigation.