Hi claireduignan -
Canvas Parent can "hang on" to past enrollments of your student(s) based on the way your child's districts closes terms. To give you a little more information: when the Canvas admin creates the courses for the term or school year, they also decide on which day the content becomes accessible and on which day the content becomes unavailable.
From the sounds of it, the district to which you are connected has chosen to make it so users can go back and reference past courses.
So, like @rmurchshafer suggested, you will need to log-in to the desktop version of Canvas and then customize your dashboard (How do I use the Dashboard?). That should allow you to click a small star to the left of the course name. The solid star designates that it will be displayed on your dashboard; the empty one will remove it.
If the "favoriting" of the courses doesn't copy over to the app, please reply! I'd be happy to do more troubleshooting and/or researching until you have an answer.
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