The fundamental role of proof in the development of students' mathematical competence has generated a growing interest in understanding how students themselves understand proof and what difficulties they face in their learning. With this interest, different authors have adopted Toulmin’s model (2003) to analyze the arguments proposed by various groups of students in situations involving proof, and to document their difficulties (Arce & Conejo, 2019; Molina et al., 2019; Soler-Álvarez & Manrique, 2014). On the other hand, recent research has used the theoretical tools of the Ontosemiotic Approach (Godino et al., 2015; Godino et al., 2019), in particular, the typology of objects and processes (Molina et al., 2019; Morales-Ramírez et al., 2021) or the model of levels of algebraic reasoning (Burgos et al., 2024; Larios-Osorio et al., 2021) to analyze the argumentative practices of students.

In this work, we describe part of the results of a training intervention with first-year physics and mathematics students at an Argentine university focused on the proof of mathematical properties in an arithmetic context. We articulate Toulmin’s model (2003) and the theoretical tools of the Ontosemiotic Approach to analyze what types of argumentations they develop, what difficulties they encounter, and what levels of algebraic reasoning they achieve.

Keywords: Undergraduate students, mathematical proof, Toulmin’s model, algebraic reasoning, Ontosemiotic Approach.