Creating Groups
If you are creating a course, you can add specific content to your course home page.
You do this by selecting the correct view in the "Highlighted Content" section:

Select one, or several, of the highlighted views. You can select as many or as few as you like. At the risk of stating the obvious, the "group_assignments" view will show all assignments for a specific group; "group_wiki" will show all the wiki pages for a different group, etc. The one view that bears a little further explanation is the "group_blog_question" view; we set this up to show some of the potential for different uses here. If any user in the group creates a blog post that they tag with the term question, it will appear in "Highlighted Content" section. To see an example of this, go to the English 11 course and look at the "Questions" section.
We have prefaced all the names of the group-specific views with the word "group"; however, we recognize that this is no substitute for a UI that only presents the relevant choices. We're working on it, but, obviously, it's not done yet.
And there's one last step. Just below highlighted content, you will see a field named "arguments."

To make this work, first click the link below the argument field to disable the rich-text editor. Then, enter in the text %nid --
This final step ensures that only group-specific content will appear on the home page.
Obviously, these instructions are daunting/offputting to non-technical users, or people new to Drupal. Ideally, this type of course creation screen will only be seen by users who have been trained in how to use it, or who are willing to experiment. As people experiment with a site, and become more familiar with the functionality, they will (hopefully) start to experiment with different types of functionality.