Semiotic Interpretation in Mathematical Modeling Activities

Abstract

In this article, we are interested in capturing students’ experiences when they develop mathematical modeling activities that allow us to describe mathematical modeling in semiotic terms from these experiences. Our results take into account an empirical research in which mathematical modeling activities are developed by students in a Mathematics Degree course. The semiotic interpretation allows us to infer that the students’ actions are based on the categories of Peirce characterized as firstness, secondness, and thirdness, understanding the phenomenological and ontological perspectives of these categories. In this sense, to mathematically model a situation meets the peculiarities of a phenomenon capable of producing knowledge in the Peircean perspective, according to which the identification of a continuum of the three categories is the indication of this construction. It is precisely in this sense that the experience emanating from thirdness makes the object, in this case, mathematical modeling, no longer for the interpreter, the student, as the thing it was, but as the thing that became after the experimentation process mediated by the interpretants signs. The semiotic interpretation of students’ experiences leads us to a description of mathematical modeling in semiotic terms which ensures that, in order for students who appropriate mathematical modeling to have experiences relating to the identification of mathematical modeling (to be mathematical modeling) at the same time when they develop modeling activities (to do mathematical modeling), the phenomenological and ontological perspectives of the Peircean categories are interdependent in the constitution of the mathematical modeling phenomenon.

Keywords:
Mathematical Modeling; Peircean Semiotics; Students’ Experiences