Unboxing mathematics: creating a culture of modeling as critic.

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.