MODELAGEM MATEMÁTICA: UM OLHAR A PARTIR DE TRIÂNGULOS EPISTEMOLÓGICOS

Abstract

In our previous study, we came to the conclusion that Mathematical Modeling can be described as a set of concepts and procedures that are necessary for the solution of a problem, and that in these procedures, the students use or produce signs. We had assumed that the signs – being instruments of communication – bear information relating to the knowledge of those who produce them about what the sign signifies. In addition, based on Heinz Steinbring’s presumptions, we regarded the signs in association with two other elements: object/context of reference and concept. In our investigations, we discuss this trinity under the name of epistemological triangle. With the goal of discussing Mathematical Modeling based on epistemological triangles, while taking into account the signs produced/manifested by the students as they performed Mathematical Modeling activities, we constructed epistemological triangles for three Mathematical Modeling assignments completed by undergraduates enrolled in the fourth term of a Mathematics Teaching Degree in a public university in the state of Paraná, Brazil, as part of a Mathematical Modeling class with a focus on Mathematics Education. We follow a qualitative approach for the methodological choices of our research. The conections that we establish between signs, concept and context of reference illustrate that, as the students progress with the Mathematical Modeling activities, the signs they produce cause the contexts of reference to be altered and modified, leading to the emergence of a variety of contexts. Such movement displayed in the epistomological triangles highlights the dynamic character of Mathematical Modeling. Furthermore, the act of observing the associations between the signs and the other two vertices of the epistomological triangle (context of reference and concept) suggests that the semiotic reading of a Mathematical Modeling activity comprises a junction of epistemological triangles. We speculate that the triangles show that mathematical concepts in mathematical modeling activities present themselves in unison with the phenomenon being studied; that the interaction between teachers and students aids them in producing more elaborate signs and as such expands how they see and treat the phenomenon; that it is possible to approach and discuss a variety of mathematical concepts throughout modeling activities; that Mathematical Modeling proves to be a valid medium for teaching and learning meaningful mathematics, once the mathematical concepts being elicited are connected to the phenomenon being studied.