Analyzing proof using two frameworks: Toulmin's model and the Onto-Semiotic configuration - Milanesio, Bettina (2025)
In mathematics education research, there has been a growing interest in analyzing how students understand proof as they progress in their studies. This analysis requires specific theoretical tools that guide both the design of concrete tasks and the recognition and management of students' knowledge. [Objective] The objective of this paper is to exemplify the articulated use of two frameworks for studying proof: the extended Toulmin’s model and the Onto-Semiotic configuration of the Onto-Semiotic approach. [Methodology] A qualitative, descriptive study is conducted, based on a case study with first-year university students as they prove arithmetic properties. The study was implemented three different times during the Discrete Mathematics course at an Argentinian university in 2023. [Results] At the beginning of the course, the analysis tool revealed the limitations in the arguments proposed by the students to validate the given propositions. Using inductive and abductive arguments, students formulated conjectures, demonstrating conviction in their truth. As their studies advanced, results improved, since they resorted to deductive arguments in their proofs. Nevertheless, the analysis revealed difficulties in the processes faced when developing proofs. [Conclusions] This research highlights the synergy between the tools used to characterize the argumentative structures in the students’ proof process and underscores the importance of recognizing its complexity as an explanatory factor for the difficulties encountered.