VALIDAÇÕES MATEMÁTICAS PRODUZIDAS POR ALUNOS DO NONO ANO DO ENSINO FUNDAMENTAL: desafios e possibilidades.

Abstract

In this research, we had the general objective of investigating mathematical validation processes developed by students from a 9th grade class of Elementary School of a state public school in Mato Grosso, during the academic year of 2020. Specifically, we sought to identify how the students analyzed formulated and presented mathematical validations for their statements and/or conjectures, classifying mathematical proofs that were produced by them, as well as to identify elements related to the activities developed by the students that could favor the production of validations. Therefore, we developed a qualitative research, of the case study type, whose experimental part was implemented in a public school in the state of Mato Grosso and was divided into three phases, namely: Phase I, which occurred when the analyzed students were still they were in eighth grade. On this occasion, we developed and applied face-to-face mathematical validation activities related to numerical sets and algebraic expressions. This experience served as a pre – experimentation and supported the (re)elaboration of the proposal to be applied in phases II and III. Phase II refers to the months of May, June and July of the year 2020, when state schools were with school activities paralyzed due to the pandemic caused by the new coronavirus. In this way, the contact took place in a non-face-to-face manner, in which we developed and applied activities related to potential and root themes. Phase III, in turn, took place during the teaching period of non-face-to-face classes of the aforementioned public school, in the months of September, October, November and December, in which we discussed mathematical validations related to the themes potential and roots, quadratic equations, functions and ratio and proportion. In these last two Phases, our interaction with students took place individually, considering their particularities and possibilities, as well as the pandemic scenario, so that data were obtained through WhatsApp and printed material. Therefore, we analyzed the interaction we had with two students, considering our dialogues, speeches, writings and the resolutions presented by them for each activity, seeking to meet our research objectives. For the elaboration, application and analysis of situations, we rely mainly on Balacheff's Proof Typology Model, on Brousseau's Theory of Didactic Situations, possible functions of the mathematical proof signaled by De Villiers and other authors, as well as on research that dealt with the theme. At the end of this process, it was possible to identify that the students started to consider performing several tests and generalization elements in their tests. Despite the interactions, one of the students seemed to remain in a pragmatic perspective, presenting and being satisfied with tests of this level, which may indicate that, even in the face of different validation situations, part of the action of producing tests concerns the student and his understanding of this particular way of justifying claims. Another student, whose data we analyzed, started to present more frequently tests of intellectual level.