“The sides of a polygon do not intersect” … Delving into the voice of the students

Abstract We characterized both discursive expressions of three sixth grade students on the phrase intersect each other and the effect they have on the construction of collective and shared meanings of intersection. Recording data, extracting information without losing the context where the interaction is framed, and selecting expressions to analyze were all done by using a classroom-based qualitative strategy. The analysis, following techniques typical of ethnomethodology, was done in terms of: (i) intelligibility and authenticity, (ii) features of the discourse proposed by Sfard and (iii) our conceptualization of collective voice and shared voice. We found a geometry classroom in which student voices are collectively constructed and generate shared meaning about intersection, which is reflected in a punctual discursive transition. The contribution of this paper resides in the use of the discursive features regarded in the analysis to focus the gaze to the discourse on mathematical content.