Tracing the change in discourse in a collaborative dynamic geometry environment: From visual to more mathematical

In this paper, we investigate what appears to be an intermediate developmental stage in geometrical thinking according to Sfard’s commognitive framework. More specifically, we examine the change in three middle-school students’ mathematical discourse as they worked on a geometry construction problem within a virtual collaborative dynamic-geometry environment. We trace how their word use, use of visual mediators, and routines changed character during an hour-long collaborative problem-solving session. Our findings indicate that students gradually moved from a visual towards a more formal discourse -one that is primarily characterized by a routine of constructing dependencies. We conclude that interacting with expert interlocutors may not be the only path towards advancing one’s mathematical discourse; this process may also take place within a computer-supported collaborative-learning setting. Thus, collaborative dynamic geometry can be viewed as an effective material condition for learning geometry.