Examining the role of examples in proving processes through a cognitive lens: the case of triangular numbers

Abstract

In this paper, we analyze the role of examples in the proving process. The context chosen for this study was finding a general rule for triangular numbers. The aim of this paper is to show that examples are effective for the construction of a proof when they allow cognitive unity and structural continuity between argumentation and proof. Continuity in the structure is possible if the inductive argumentation is based on process pattern generalization (PPG), but this is not the case if a generalization is made on the results. Moreover, the PPG favors the development of generic examples that support cognitive unity and structural continuity between the argumentation and proof. The cognitive analysis presented in this paper is performed through Toulmin’s model.