Hey Dave,
I'm assuming that a Discussion doesn't meet your needs, correct?
That particular text area function (the one mentioned in the original post) requires admin access to the Canvas theme. Also, it just uses browser storage. BUT. We have also found that embedding Padlets on the page works quite well when we want to have a quick Q&A without the students leaving the page. I believe you can make a certain number of Padlet boards for free, and then you simply grab the embed code and paste it into the HTML view on the Canvas Page. Don't forget to empty out the board or clone it when you start a new term!
Padlets are great for things like getting students to list pros/cons, argue for/against, or using the Timeline function to get students to upload pictures of themselves or slides of a project, etc.
As the instructor, you can see everything the students post, place restrictions on profanity, delete posts if needed, etc. It's all in one place.
It's good for collaborative work, but not great for individual reflective work - there's just the one board for everyone.
For individual reflection: H5P might have some options you're looking for, if your institution has the H5P plug-in enabled. I find it a bit fiddly to go in and see everyone's responses, though. It would be great if Canvas had, as you said, a way to embed the "assignment" functionality in a page (just without marks).
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