Conhecimentos Mobilizados por alunos sobre a Noção Integral no contexto das Concepções Operacionais e Estruturais - Vidigal, Luciana Fajardo (2007)
The aim of this research was to investigate the knowledge mobilized by those students who have studied Integral, a subject that permeates a major part of the Integral and Differential Calculus (IDC) course and is a source of difficulties for the students. The goal was to analyze the explicit knowledge of those who have studied this concept in a regular IDC course in terms of the integration techniques as well as the meaning and the concept utilization. It has also been researched whether this knowledge reflected operational and structural conceptions in the sense applied by Anna Sfard (1991), whose theory this paper is based on. In her studies, the author postulates that abstract notions are conceivable in two completely different ways: structurally (as objects) and operationally (as processes). As an investigation means, it has been used a questionnaire containing nine questions and applied to two groups of a private school s math course in São Paulo city. One of the groups was constituted by students who have recently studied the notion of Integral, and the other group by students who went through the same studies one year before. In terms of the first group, the conclusion drawn up was that the students have incurred in several kinds of operational calculus mistakes, also the processes involving integral notion showed up but only sometimes, indicating a clear structural conception failure. These characteristics were not observed in the second group. It has been noticed that all researched students apparently had mobilized the structural concept considering they have applied the mathematical object to determine the area of even spaces in the function graph, but when facing those circumstances in which they had to reason to be able to apply the concept as an object they did not have enough assurance in terms of structural conception, and tried to take refuge in the algebra processes