Because the structure and content of first-year writing varies so much depending on institutional philosophy and “ambition” of outcome, this question is fairly difficult to conceptualize as a generality. In my experience of undergraduate first-year writing, I found inspiration via discovery and promotion of scholarly research. Though that was something I was aware of before entering college, the specific applications that were shown to me, as well as involving myself in a research process that led to university-wide collaboration, were the most immediately beneficial outlet for my own writing aspirations. I know, as well, that this was not the case for many people in my class, and that many of them felt that this outlet wasn’t useful to their specific majors.
With our first-year writing course, I think that sort of impact is more readily demonstrable. This is very much a class that emphasizes the open-endedness of different interests, and that’s important for any general ed classroom. Especially during conferences, several of my students have expressed uncertainty as to what they really want to study during their time at Western, and that they appreciate the potential for exploration (though, they never say it quite like this) in the different projects I assign them. So if I’m able to at the very least offer them an explorative outlet that they make use of, I think this class will have been worth it for them.
Taken to the most idealistic extent, I’d probably offer the fantasy of a student discovering an inherent love for something we explored during class, and after the quarter continuing on to further cultivate that interest. This is vague, but purposefully so; I don’t necessarily want a student to realize that they love writing, and that they were born to be writers, or anything like that. But perhaps they will particularly enjoy collaging, and find something valuable in that process, which ultimately leads them to seek out other collages online, research the history of the medium, etc. Realistically, if I can in any way cement the concepts of medium and genre into the everyday routine thoughts of a student who previously never considered the distinction, that will in itself be a major impact.