Argumentação em atividades investigativas na sala de aula de matemática

Abstract

We tried, through this research, to understand how students' mathematical argumentation triggers and develops in a mathematical investigative activity. In order to achieve this goal a sequence of four investigative activities was performed in three classes in the 9th grade in elementary education at a school in the Municipality of Belo Horizonte. During the development of these activities, operations supported on theoretical arguments (BOAVIDA, 2005), investigations in mathematics class (PONTE; BROCARDO; OLIVEIRA, 2009), and as a mathematics teacher myself the experiences with this type of activity were carried out. The methodological approach adopted is qualitative and the instruments of data collection were participant observation (FLICK, 2009), notes, audio and video, and reports produced by the students. Data analysis was performed inductively and it is presented in three parts. To show that it is possible to identify students' arguments in investigative activities, in the first part situations are described and analyzed in which there was argument. In the second the interventions made by the teacher and researcher and its consequences which contributed to the development of students' arguments are reported and analyzed. In the third part the obstacles experienced in carrying out investigative activities, which disrupted the development of the argument are described and analyzed. The results indicate that the basic school students are able to argue about mathematics in several ways: by refuting counter example, to prove with the use of a non discursive resource, among others. You can initiate and develop students' mathematical reasoning through the use of interventions, for example, present to them the forms of argument. The lack of time, other priorities, lack of knowledge of the algebraic language, among others were obstacles to students' arguments, but they can be circumvented. It is important to the teacher understand what is argument, in addition to its meaning in common sense, and what are the forms of argument, which encourages students to develop and justify reasoning abilities. Therefore, it is necessary for the teacher to change the types of activities, as well as the manner of their class form, not just staying in the exercise paradigm, and that students accept the invitation to participate in these activities (SKOVSMOSE, 2000).