To tell a story, you need a protagonist: how dynamic interactive mediators can fulfil this role and foster explorative participation to mathematical discourse

This paper focuses on students’ mathematical discourse emerging from interactions in the digital environment GeoGebra, in which one can construct virtual objects that realize mathematical signifiers, and then interact with them. These virtual object realizations can become dynamic interactive mediators (DIMs) that influence the development of the learners’ mathematical discourse. In this case study, I analyze in fine detail the discourse developed by two dyads of students in response to an unfamiliar interview question. One dyad came from a class in which GeoGebra was not part of classroom practice and included students who, according to the teacher's evaluation, were standard-to-high achieving. The other dyad was from a generally demotivated and low-achieving class in which GeoGebra had become part of classroom practice. The analyses, focused especially on the low-achieving dyad, are guided by the question of how DIMs shaped these students’ discourse. According to the analysis, these students ended up succeeding where standard-to-high-achieving peers did not. Moreover, the detailed analysis of the ways in which the DIMs supported this dyad's learning showed mechanisms that may be general rather than specific to this one case. This suggests that appropriate integration of DIMs into the teaching and learning of high school algebra can be beneficial for low-achieving students.