Modelo de barras como estratégia para educação algébrica : um estudo com professores de matemática do ensino fundamental

Abstract

This research was developed in the Post-Graduate Program in Natural Sciences and Mathematics Teaching (PPGECM), of the Federal University of Mato Grosso (UFMT), Sinop University Campus, in the line of research of Mathematics Teaching, involving algebra of the final years of elementary school, specifically in the transition from aritmetic to algebra. It’s main objective was to analyze, with a group of eleven teachers who teach mathematics in the Final Years of Elementary School, the contributions of the Bar Model in the process of teaching and learning algebra. The Bar Model is part of one of the heuristics of Singapore's mathematics curriculum. That rectangular bars are drawn to represent the problem data, identifying known and unknown quantities. This is qualitative research, whose theoretical, methodological and analysis development, happened based on Semantic Fields Model (MCS), proposed by Lins (1999, 2012). And, also, supported by the proposal of algebraic education of Lins and Gimenez (1997), in the Resolution of Problems of Pólya (2006), in the Working Group of Santos (2016), Silva (2015), Ovando, (2017), Santana (2017), Viola dos Santos (2018) and based on the Bar Model cited by Cintra (2017), Dotti (2016), Gois (2014), Holetz (2019), Porto (2015) and Queiroz (2014), among others. For the data production, a formative action was designed, organized and performed a Formative Action, divided into two phases, with different and articulated functions, including: Formative Meetings and the Working Group (GT). The Formative Meetings, which took place remotely mediated by Google Meet, had the purpose of presenting the strategy "Bar Model", guided by the four (04) steps of Resolution of Problems of Pólya (2006), in this phase different approaches of algebra were worked, such as algebra as generalized aritmetic, algebra as equation and algebra as function. The Working Group, on the other hand, was dedicated to present the preliminary version of the Educational Product, to build together the final version, occurred in a hybrid (remote and face-to-face), with the participation of 03 teachers. The process of evaluation of the experience was systematized in two complementary papers, dissertation and an Educational Product. The Educational Product consists of a Book for the teacher and a notebook for the student. The book contains a collection of problems in which various resolution strategies are presented, and the student notebook contains one problem per page, as well as a script with the stepsby-step below to resolve each problem.