I am a user of JAWS and also other screen readers. I am creating my first course as an "instructor". I'm actually a staffer, not an official instructor at my college. But I've taken about thirty online courses using JAWS.
The problems are not really a JAWS or a Canvas issue. Instructors need to think carefully about how they structure a discussion. For example if there is more than one topic to discuss, each needs to be a separate discussion. Many instructors are kind of lazy; instead of creating a new discussion, they just create a new thread in the same discussion, making it unwieldy. Even more than blind users, this is very hard on students with learning disabilities or attention issues.
I even took a course from a guy who created one discussion for everything, gave it the topic of "class discussion" and we were supposed to post everything in there. It ended up with thousands of posts. We were each -- thirty of us supposed to post at least four times a week. Some teachers have no common sense!
JAWS has five different reading cursors and three different modes for reading on the web. If a user is a beginner, they can often get super frustrated trying to figure out which cursor and which mode to use. For example, when completing assignments you have to be in "forms" mode to check boxes, select radio buttons and edit text. But you have to be in "virtual cursor" mode, in other words out of forms mode to actually read the page. I know that sounds awkward, but believe me it's an improvement over screen reading two decades ago!
If you are working in a discussion, you will stay out of forms mode to read everything, but when you reply, you have to enter "application mode" to interact with the rich content editor.
This is necessary, these different modes, because a screen reader user needs to do two things with their keyboard, read the screen and interact with the screen. Visually, your eyes read the screen and you use your mouse and/or keyboard to interact. The JAWS user has to use the keyboard to do everything, thus the multiple modes!
JAWS can enter and exit some of these modes on its own if it gets enough context, and beginners often set it to do just that.
But if it gets the context wrong, then it's in the wrong mode for the operation you need to perform.
For example, as I'm typing this, application mode should have turned on, but it has not. I'm in the rich content editor for this forum, but JAWS somehow didn't get the message -- this happens unfortunately more often than one would like.
I am working in "forms mode" which isn't ideal for editing my post but lets me type, and I am typing carefully so I won't make too many mistakes I'll have to edit later. In "forms" mode, JAWS is set up for me to edit in single-line edit boxes and to use the space bar and arrows to check check boxes, choose radio buttons, drop down combo boxes. But to really function in the RCE I need to be in application mode, which tells JAWS that this is a web-based application and the keystrokes I issue are intended for the web app and not for it, the screen reader!
JAWS finally just decided to go in to application mode now, making it possible for example for me to use the Canvas shortcuts to go to the toolbar.
More advanced users tend to try to override that automatic behavior and manually engage some of these modes when they can. But like breathing, where the brainstem can keep the lungs working even when we are unaware, the user only has partial control over what the screen reader decides to do especially on the web, where the environment is complex and often without many standards.
If a real JAWS user is reading this, you'll notice I've oversimplified a bit for purposes of clarity.