Desvelando práticas bem sucedidas de uma professora de matemática

Abstract

The objectives of this dissertation are to identify the behavioral patterns associated with the interaction that occurs in the classroom of knowledge and feelings present in the very successful practices of a Mathematics teacher and to reflect on the changes that happened to me as I accompanied the practices of a Mathematics teacher. I analyzed and highlighted the actions developed by the teacher in her interactions with students and their relationship to math knowledge and the teaching of that subject. For this analysis I was a non-participant observer of the teachings of Professor Sara, in a state run public school, in a neighboring city of Belo Horizonte, MG, Brasil. The observations of the lessons were done with groups made up of three classrooms at the Elementary level in subsequent grades: one classroom of 6th grade and two classrooms of 5th grade. During the observations I did six interviews with the teacher and two interviews with the student groups, one of the sixth grade and the other of the fifth grade. The data from the second 5th grade classroom did not interfere with the results of the study. In the analysis of Saras teaching skills, two large categories were used: Development of a Plan and Development of Teaching. The highlight of the first category is the analysis of the teacher to student relationship with regards to the development and organization of classroom activities and the norms of conduct utilized by the teacher. To highlight the second category, the teachers mathematical knowledge in relation to her interaction with her students in the development of the learning activities was analyzed. During the development of this work three phases were identified related to changes that developed. In the first phase, called an outsiders view, I relate my awkwardness in light of teaching practices that did not develop with my expectations. In the second phase, called an insiders view, I change the way I view that skill, in that I verify that the theoretical reference in which I was working is not adequate to analyze her, thus I look into indications in the teachers own skills, in order for me to explain it. In the third phase, called eyeing into the inside, in which I look into the changes that occurred in me which led me to perceive different ways to be a mathematics teacher. The results of this research lead towards the defense of an equilibrium between the operational/procedural and the structural/conceptual perspectives in the teaching and learning of Mathematics and the defense of a complementation of one perspective in relation to the other, in the practices of the teachers in the classroom. In lieu of the results, a proposal is made to incorporate certain elements of knowledge already adopted in the literature as important for the teaching of Mathematics, an emphasis in the operational dimension that has not received adequate attention in the actualized teaching of Mathematics. Another result, more directly tied to research methodologies, showed that a less interactive contact, that is, without the direct interference of the researcher in the planning of the teachers lessons, can contribute to a reflective attitude not only from the teacher but also from the investigator in relation to these practices.