The Discourse Mapping Tree as a tool for mapping classroom discussions in linear algebra

Mathematical discussions, along with other learner-centered teaching practices, are becoming more prevalent in tertiary mathematical education, yet the mathematical content of these discussions and the learning involved remain less explored. We developed the Discourse Mapping Tree (DMT), a commognitive based tool for mapping mathematical content during discussions, which allowed us to examine learning of a class as a whole in linear algebra discussions. The DMT displays the objects on which a discussion focuses, the multiple types of realizations of these objects and the narratives authoring links between the realizations. The DMT showed that the division of labor between the instructor and the students in our study was not always symmetrical. This tool provides a succinct overall image of the publicly available mathematics during a classroom discussion and allows for the mapping of complex tertiary level mathematics which include multiple objects and realizations. • Introduces the Discourse Mapping Tree (DMT) tool for mapping discussions. • Shows instructors’ key role in linking sub-discourses in linear algebra discussions. • Provides a visual tool to summarize mathematical content in class discussions.