Secondary mathematics teachers' use of students' incorrect answers in supporting collective argumentation

This study illustrates how two secondary mathematics teachers used students' incorrect answers as they supported students' engagement in collective argumentation. Three ways of supporting argumentation when students contributed incorrect answers are exemplified, and the structures of these arguments are investigated. Then, by focusing on the correctness of argument components as represented by the diagrams, we developed a potential model of levels of validity in classroom-based argumentation. The model may help the field to identify fine-grained conditions of validity within episodes of collective argumentation. The findings of this study provide insight into how teachers can manage or capitalize on incorrect parts of an argument when they attempt to support classroom-based argumentation as part of a long-term teaching intervention.