Avaliação para a aprendizagem em Modelagem Matemática na Educação Matemática: elementos para uma teorização

Abstract

In this thesis, we present the Mathematical Modelling in Mathematics Education such as a didactic methodology that aims is to prepare the students to be an active citizen in society, able to use Mathematics like a tool to understand social situation. Even some researchers arguing about to use Modelling in the classroom, there are some obstacles that hinder this. Among these obstacles is assessment because no one present parameters, suggestions or ways of how teachers can make an assessment during a modelling activity in the Basic School. Considering the inexpressive number of articles on assessment in Mathematical Modelling in Mathematics Education, in this work we discuss elements that allow us to begin a theorization about this. The elements brought to discussion were collected during classes which the teacher used Mathematical Modeling. Twenty-seven students from a public school in Porto Vitória (PR) and the teacher from this class participated in this study. The question of our study was: What is revealed in the assessment practice when the teacher uses Mathematical Modeling as a didactic methodology in the Basic School? To answer this question we did a qualitative collaborative research. The collected data, which we call episode, were analyzed according to Grounded Theory. This investigation is supported on renamed researchers who discuss about assessment conception, such as Franco (1990), Rodrigues (1994), Hadji (1994), Fernandes (2004, 2006, 2008, 2009), Guba e Lincoln (2011), Luckesi (2011) e Lopes e Silva (2012). The perspective of Mathematical Modeling we adopted is that of Burak (1992, 1994, 2010), discussed in the light of Mathematical Education as presented by Higginson (1980), Rius (1989), Burak e Klüber (2008) e Burak (2010). The analyses show an integration of different assessment conceptions. However, some episodes reveal peculiarities considered intrinsic to Mathematical Modeling, such as the subject studied is chosen by the interest of the students, the subject chosen imply interdisciplinarity, and the students can develop curiosity. These episodes indicate new relation between teaching and learning in Mathematical Modeling, thus we need to (re)think about how to contemplate these relations. Therefore, in this thesis, we begin a theorization of assessment for learning. The elements discussed allowed us to theorize by a systemic-critical assessment. This theorization is sustained by Dialogical-Critical paradigm, integrating teaching and learning processes and whose goal is to assess the students in a continuous and whole way. We argue that a systemic-critical assessment is a deliberate and systematic process of searching for information that allows us to identify what students already know and what is still in the process of maturation. The inexpressive number of papers concerning assessment in Mathematical Modeling in Mathematics Education makes this thesis a landmark for the advancement of discussion about this subject. Keywords: Mathematical Modeling in Mathematics Education. Assessment. Mathematics. Theorization.