The completion block relates to individual courses and whether or not they have been completed, and the stage at which students are at. See Course completion satus block so the reason it won't go into My home is because My home is not connected to courses as such. If within a course you have deadlines for assignments and newly posted forum posts etc then you can see those on the My home page. And also on each course if you have Activity completion settings against each activity then the student can see at a glance (from the ticks) what they have done and not done.
Teaching with Moodle
How can the student know what to do?
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