Characterising Pre-Service Primary School Teachers' Discursive Activity when Defining

This paper studies how pre-service primary school teachers construct and select mathematical definitions through the analysis of their discursive activity. Specifically, the theory of commognition (Sfard, 2008) is employed to determine whether the existence of different meta-rules always leads to the existence of a commognitive conflict. Moreover, we study the reasons that give rise to the commognitive conflicts found and whether they are resolved. To this end, we studied the discourse of 45 pre-service primary school teachers while they answered several questions on defining geometric solids. The data in this study consisted of audio recordings of their discussions and their written answers. In this paper, three vignettes showing different meta-rules are presented. In the first, discussions regarding the characteristics of a definition promoted the appearance of different meta-rules that existed in incommensurable discourses, which meant the existence of a commognitive conflict. This conflict highlights the fact that certain pre-service teachers confuse the processes of describing and defining. Both the second and third vignettes featured the appearance of two different meta-rules. However, in both cases, those meta-rules could coexist in the same discourse, and therefore a commognitive conflict could not be inferred.