The analysis of transplantability between discourses: the case of scales and equations

This paper aims to report on a theoretical analysis, framed within Commognition. In particular, we elaborate on the definition of discourse isomorphism (Sfard, 2008, p. 122) to study, as a specific example, the relationship between algebraic discourse on equations and discourse on two-pan scales. We analyze the extent to which this inter-discursive relation is defined, preserving intra-discursive relations, and the limits of this correspondence. In our elaboration, developed in a design-based research project on students’ participation in algebraic discourse, we present the notion of transplantable discursive elements and the analysis of transplantability, a tool useful to describe correspondences and limits in relationships between two discourses that could guide design and a-priori analysis of didactical activities.