Emergent Collective Argumentation Types in a Socio-critical Mathematical Modeling Activity

Socio-critical mathematical modeling encourages students to employ mathematics as a tool for social inquiry and action, promoting critical thinking and social awareness. While research on collective argumentation in mathematical modeling exists, its connection to socio-critical modeling remains underexplored. This study addresses this gap by examining the types of collective argumentation that emerge during small-group and whole-group discussions as students navigate different phases of the modeling process. Using an adapted version of Toulmin’s argumentation model and a framework for socio-critical modeling phases, this study analyzes classroom discussions in which high school students engage in a modeling task focused on fair raise distribution. The findings reveal three types of collective argumentation—mathematical, socio-critical, and hybrid—each characterized by unique aspects of student reasoning as they formulate and justify their claims. These argumentation types are linked to specific modeling process phases, illustrating dynamic interplay between student mathematical reasoning and their consideration of social and ethical issues. Our findings show that mathematical argumentation predominates in the model development phase, socio-critical argumentation in the model presentation phase, and hybrid argumentation in the model revision phase. Our work offers implications for how collective argumentation can promote equity-focused mathematical discussions in socio-critical modeling tasks.