Abstract:

The processes of teaching and learning mathematical proof pose a challenging issue in the field of Mathematics Education. Given that mathematical proof is an inherent process within the discipline itself and takes on different forms in classrooms at various educational levels, several authors have explored less abstract approaches to mathematical proof. To analyze and document the difficulties that students encounter with these forms of proof, multiple authors have relied on Toulmin's model. However, there is a lack of research that examines the complexity of the transition from informal argument to rigorous proof based on the practices, objects, and processes involved in mathematical proof, especially those of an algebraic nature.

In this regard, within the Ontosemiotic Approach, some research has been conducted on mathematical proof with the intention of clarifying the meanings attributed to it, how they interrelate, and how they should be considered in instructional processes. Continuing in this line of research, the objective of this research is to demonstrate, through a case study, how students who have just entered university programs in mathematics and physics solve tasks that require justifying elementary arithmetic properties. The aim is to identify their personal meanings regarding proof, by articulating the analysis using Toulmin's model, along with the analysis of their practices and the level of emerging algebraic reasoning.

Keywords:

Undergraduate students, mathematical proof, algebraic reasoning levels, Ontosemiotic Approach.