While the culture of many mathematics departments inflects strongly towards STEM, most mathematics departments also offer a significant number of introductory courses intended for both STEM and non-STEM majors. We are a group of mathematicians who, in this work, examine the intent and goals of a university mathematics education for the non-STEM student. We engage in a community of inquiry to discuss how better to address the interests and experiences of our students, and conclude that centring the students' point of view and decentring the professional mathematician's point of view is potentially transformative in building resiliency and community. We propose a coordinate system to describe mathematical tasks, with a "contrived-authentic" axis, and a "clean-messy" axis. Finally, we elaborate on the value of the community of inquiry itself in developing our own philosophy and practice of teaching.