A Matemática na Modelagem Matemática na Educação Matemática: um olhar fenomenológico

Abstract

Mathematical Modeling in Mathematics Education is a topic that has gained prominence in academic research over the past 40 years. However, the Mathematics in Modeling is not clearly spelled out. Guided by the question "What is this, the Mathematics in Mathematical Modeling in Mathematics Education?" we conducted a phenomenological research with a hermeneutic perspective on the data produced. The interest in the interrogated phenomenon is linked to the perceived gaps in reflection on the topic, as the author encountered a lack of reflection on it. This interest solidified as we delved into readings dedicated to Mathematics, revealing the absence of reflections in other research focused on Mathematics teachers' conceptions. Supported by Phenomenology, we suspended pre-existing beliefs and expectations, positioning ourselves to listen to the phenomenon to see what it reveals. With the interrogation and the assumed stance, we present the articulated understandings, developed and presented in three distinct articles, as the thesis is being written in a multipaper format. In the first article, we present reflections on Mathematics in the Platonic, Aristotelian, and Kantian philosophies. This movement became relevant to understand the tradition influencing our culture and howthese philosophies permeate Mathematics. The second article emerged from concerns that arose from the stance taken to conduct the thesis and the research for the first article, especially regarding Mathematics in the phenomenological approach. In it, we question, "What understandings of Mathematics emerge from Husserlian phenomenological philosophy?" Through this investigation, we understand that the constitution of mathematical knowledge begins in the mathematician's subjectivity, founded in the lifeworld, which, through acts of consciousness, articulates various knowledge about the targeted phenomenon. In the third article, we question, "What is this, the Mathematics in Mathematical Modeling in Mathematics Education for Higher Education students?" By interviewing 13 students, with the aid of the qualitative analysis software ATLAS.ti for data organization, we articulated six categories that indicated understandings of Mathematics. Among them, the understanding that Mathematics is in things and, therefore, a discovery, and that it represents the empirical world stands out. Additionally, although Mathematics facilitates more reflective thinking about reality, the nature of Mathematics itself is not reflected upon.