Discovering key interactions. How student interactions relate to progress in mathematical generalization

Abstract

This article presents a study of 8th grade students working in groups to solve a task about generalizing patterns. The study aimed to openly explore how progress in mathematical thinking might relate to the discourse. To do this, we first studied both separately. The progress in mathematical thinking was studied by inspecting how the groups progressed through different levels of generalization. The discourse was studied by characterizing each student interaction. When combining these, we realized that some specific types of interactions were related to students progressing to a higher level of generalization. We call these key interactions, and they were mainly of the types of advocating, locating, and reformulating. These seem clearly important for identifying evidence of progress during the discourses, but might also be helpful for understanding how specific types of interactions relates to sharing and growing mathematical thinking.