A aprendizagem de polinômios através da resolução de problemas por meio de um ensino contextualizado

Abstract

The objective of this study was to verify how learning of polynomials took place using problem solving in a contextualized learning situation. Thus, the present research was developed in the context of polynomials, based on the construction of cardboard boxes, using students previous knowledge. Based on a bibliographic review of studies on the theme, we defined the categories of comprehension of the concepts: Contextualization, Previous knowledge, and Mathematics teaching-learning-evaluation through problem solving. Since the phenomenon of interest in the study is related to the school, specifically the study of polynomials, it constitutes an intervention of a qualitative nature in a specific situation: a long-term case study. Based on Problem Solving as a teaching-learning method in the classroom, we sought to give students the opportunity to do hands-on mathematics , i.e. develop the content of polynomial in a way that students could collect, experiment, and analyze, in a real-world context, subjacent mathematical patterns. All the work was developed in an interactive situation, with the students divided into groups. This research was carried out over the course of two projects: Project I, conducted with 6th graders in the context of constructing cardboard boxes Polynomials and the operations defined by them (2006); and Project II, conducted with same students one year later, in 8th grade Appropriation of concepts constructed in Project I, and the exploration, based on this work, of the important algebraic concept known as Function . Analyzing the work carried out, we found that the development of the concept polynomial , followed by the concept function , using the manipulation of concrete materials, resulted in more meaningful learning for the students. Starting with a concrete situation, followed by generalization and abstraction in a higher stage of learning, the students, as co-constructors of knowledge, were able to establish relations between the themes addressed throughout the work, within a broader system, where meanings and conventions were being established.