Estudo sobre avaliação e validação em argumentação matemática em sala de aula

Abstract

This study investigates teachers’ conceptions regarding mathematical argumentation and proof. Everyday classroom situations, such as students’ tendency to seek only a final answer to proposed problems, were the initial motivations for developing this study. We took as guidelines the typologies proposed by Balacheff (1988) and Hanna (1990), in addition to the functions presented by De Villiers (1990), in order to verify how and if the research participants are aligned with what is proposed by these authors and how they understand mathematical proofs. We also considered data produced in research studies such as those by Caldato (2018), Mateus (2015) and Aguilar-Júnior (2012), which leads us to raise the hypothesis that teachers do not value informal or naive arguments presented by Basic Education students. The research was conducted with teachers who corrected an activity consisting of two questions, answered by 9th grade Elementary School students. In addition, the teachers answered a form about their conceptions about the proposed theme, in addition to a semi-structured interview conducted virtually. Finally, the two documents – the one containing the answers to the correction and the form about the teachers’ conceptions – and the transcript of the interview are analyzed together to verify the similarities between the conceptions of these teachers, their practices and the proposals presented by theorists in the area, in order to answer the research question: how do the teachers participating in the research understand, evaluate and validate mathematical argumentation in the classroom? We found that the teachers are well aligned with the proposals of the theoretical frameworks, including the official documents, despite the fact that few had had contact with argumentation studies in their undergraduate courses.