Establishing links between conceptions, argumentation and proof through the ck¢-enriched Toulmin model

Abstract In this article we analyze students’ conceptions in geometrical problem-solving and their relations to proving. The main purpose of this paper is to show how students’ conceptions strongly impact the argumentation activity and the construction of a proof. This is illustrated by analyzing two pairs of students’ argumentations and proofs taken from a set of data collected from a teaching experiment. Through the use of Toulmin's model enriched with the ck¢ model, we show the complexity of a cognitive analysis of argumentation and proof that accounts for the students’ knowledge system. Toulmin's model is useful to select those elements in the argumentation that are part of students’ conceptions while ck¢ allows us to see the role they have inside the argumentation.