Hello, @lburnham. I assume you mean all of a student's discussion posts from an entire class and not just their posts within a discussion. For the entire class, there is an idea proposal to do that and it has been themed:
[Discussions] See all of a student's posts togethe... - Instructure Community
That same page has links to the process for how we as community members can vote on ideas to improve Canvas.
If instead you are interested in seeing all of a student's posts from a single discussion, there are two ways to do that. If it's a graded discussion, the SpeedGrader by default collects all of a student's posts shorn of context. You can achieve the same effect for any discussion by using the search box on the discussion page and type any portion of a student's name.
I hope this answer is helpful and that you participate in the theme voting once it becomes active.