Ações mentais matemáticas na resolução de problemas de limites sob a perspectiva das neurociências cognitivas

Abstract

This study aims to investigate the relationship between Mathematical Mental Actions (MMA) and Executive Functions (EF) in the resolution of a Limit problem by students enrolled in the Differential Calculus course of the Mathematics Teacher Education program at the Federal University of Goiás. The study adopts a mixed-methods approach, in line with the framework proposed by Creswell (2014) and is grounded in the Theoretical Model of Mathematical Mental Actions (MTAMM) developed by Alvarenga and Domingos (2020), as well as in Cognitive Neuroscience, specifically Executive Functions (EF). The corpus consists of 41 written solutions produced by students in an assessment task and semi-structured interviews conducted with three of them. Quantitative analysis involved descriptive statistics and the nonparametric Mann–Whitney U test, comparing the number of MMA mobilized by students who solved the problem correctly and those who did not. Qualitative analysis was based on key principles of Content Analysis, as proposed by Bardin (2016), and incorporated elements of Discursive Textual Analysis, following Moraes and Galiazzi (2016), allowing for greater flexibility in examining the cognitive strategies employed by students in their solutions. The results indicate that success in the task is associated with greater coordination among representations and metacognitive monitoring, suggesting that performance in this type of Limit problem is influenced by the integration of conceptual reasoning and executive function regulation. Accordingly, the study proposes the implementation of pedagogical practices that promote multiple representations, reflection on errors, and cognitive self-regulation, with the aim of enhancing the development of MMA and EF in the teaching and learning of Calculus.