Um estudo sobre as intervenções de um professor em atividades de modelagem matemática

Abstract

In this dissertation, I present a qualitative research on the relation between teacher intervention and mathematical modelling as a pedagogical practice. The general objective of this study is to understand how the teacher's intervention process takes place in mathematical modelling activities. The specific objectives are: to identify which moments of a teacher's performance can be understood as an intervention during the development of a modelling activity in mathematics education; describe how a teacher's intervention happens during the development of a modelling activity in mathematics education; and to characterize the intervention of a teacher based on his performance during the development of a modelling activity in mathematics education. In general, it is possible to understand mathematical modelling, from the perspective of mathematical education, as a pedagogical practice in which students are invited to investigate real problems using mathematical tools. In investigative activities such as mathematical modelling, teachers act as advisers holding themselves off from the traditional practice of teaching mathematics. The focus of this research is on the study of this performance; specifically, in the teacher's intervention actions in the students' activities. For that, I used a qualitative research approach. Data collection was carried out in a classroom where a mathematics teacher developed a learning environment for mathematical modelling following his own criteria. For the data construction, I used participant observation and the data recording was done through video and audio recordings and through notes in a field notebook. The analysis of the empirical material produced showed three main research results: i) the interventions that aim to clarify and suggest are more frequent in the stages of choosing the theme and formulating the problem, respectively; ii) the teacher's intervention process does not follow a sequence of steps for the activity development as pointed out in some modelling schemes; and iii) the teacher's interventions can be divided into convergent (when it refers to the stage in which it was identified) or divergent (when it refers to a stage different than that which it was identified).