From the socio-critical perspective of mathematical modeling, reflexive discussions about the nature, criteria, and consequences of mathematical models are not a natural consequence of modeling in school. This report is part of a larger study focused on stimulating reflexive discussions in practice employing constructivist grounded theory as a research method. Twenty-seven college algebra students engaged in a 3-week modeling project at a community college in the USA. Audio-recorded group discussions and written reflections were collected to determine how reflexive discussions were taking place. Analysis of students' actions and reflexive discussions during the modeling project produced four concepts: "voicing mathematics," "personalizing mathematics," "challenging mathematics," and "negotiating mathematics." These concepts are integrated into an overall process for stimulating reflexive discussions and are conceptualized as "unboxing mathematics." The overarching concept of unboxing mathematics represents one interpretation of how reflexive discussions may be constituted during modeling activities and identifies classroom mathematical practices specific to the socio-critical modeling context of this study.