Construção de conceitos matemáticos pertencentes ao campo multiplicativo em uma turma do oitavo ano

Abstract

This research aimed to analyze the learning process of the multiplicative comparison axis by eighth grade students. In this dissertation, we had as a research question: How does the learning process related to the multiplicative comparison axis in students of an eighth grade class? To achieve the proposed objective, our research scenario was the Professor Hélio Ferreira da Silva Municipal School, located on the outskirts of Paracambi, which belongs to Baixada Fluminense. The 22 subjects involved belong to an 8th grade elementary school class, with an average age of 13 years. We sought theoretical contributions in the Theory of Conceptual Fields with the studies of Vergnaud (1981, 1983, 1990, 1991, 1996, 1999, 2009), which led us to the studies of Magina, Santos and Merlini (2011, 2016), who classified the Field of Multiplicative Structures, which was the subject of this research. The research had a qualitative approach based on the action research method, since we analyzed the resolutions of two evaluations - initial and final - and the schemes used during a teaching sequence, both formulated from the studies of Magina, Santos and Merlini (2011, 2016) and applied by the researcher in the class. As a result, we point out that the multiplicative conceptual field, in the ternary relations, multiplicative comparison axis, that the class referred to unknown is the one that students presented the highest number of correct answers, followed by the classes referring to unknown and unknown relation, in that order. However, after applying the teaching sequence, the unknown relationship class was the one that showed the greatest increase in the number of correct answers. The analysis of the concepts presented by the students points to the use of the multiplication and division algorithms, followed by the use of the addition of repeated plots or successive subtractions.