Error Analysis in Mathematical Modeling Practices

Abstract

From the perspective of Error Analysis, a mistake made by a student in a mathematical production can be transformed into a challenging question, where investigation and exploration contribute to deepening mathematical knowledge. In this sense, Borasi (1996) suggests inviting students to investigate the consequences of accepting an error as truth. This workshop aims to explore the potential of mathematical errors made by students in the development of an activity based on Mathematical Modeling as a teaching strategy. The activity will deal with the theme “insertion of women in the labor market” adapted from Senes, Braz and Barros (2022), in which it is proposed that participants, in groups, investigate the problem: How can we estimate the number of women currently in the labor market? Bearing in mind that Mathematical Modeling deals with approximations of reality, it is essential to check whether the resulting Mathematical Model is appropriate to the context analyzed. At this stage, it is common to identify errors in the formal mathematical development, and so we intend to provoke reflections on some errors that may arise and/or those that arise during the process. In particular, in this workshop, there will be a time to socialize the groups' answers, and then we intend to explore an error in the affine function, questioning the definition of the slope of the line, assuming by hypothesis that it can be defined in another way, based on an error made in solving this same Mathematical Modeling problem, when it was proposed to another group, as presented in Vidotti and Oliveira (2024). In this way, we hope to help ensure that mistakes are seen as a positive element in the learning process. This workshop is aimed at students or professionals in the field of Mathematics Education. It will last 4 hours and there will be 30 participants.