Um estudo sobre ações mentais matemáticas, memória e atenção na resolução de inequações polinomiais do 1º e 2º graus

Abstract

This dissertation investigates the neurocognitive processes involved in solving first- and second-degree algebraic inequalities, including a product inequality and a quotient inequality, with an emphasis on identifying the mathematical mental actions, the memory contents evoked, and the attentional focuses required in different types of exercises. The research is based on the Theoretical Model of Mathematical Mental Actions, developed by Alvarenga and Domingos (2020), and on the contributions of contemporary cognitive neurosciences, especially those of Dehaene (2022), Lent (2019), Izquierdo (2018), Herculano-Houzel (2017), and Bear, Connors, and Paradiso (2017). This is a qualitative, descriptive, exploratory, and theoretical-analytical study that adopts an original method of analysis developed by the researcher himself, which integrates Alvarenga and Domingos’ model with the cognitive functions of memory and attention, as well as with brain regions involved in mathematical learning. The corpus consisted of exercises extracted from high school textbooks widely used in Brazilian education. The solutions were carried out by the author of this dissertation based on the methods proposed by the textbook authors, ensuring pedagogical coherence. Some of the problem statements were reformulated in order to stimulate new or different mathematical mental actions and to increase the cognitive complexity of the tasks. The analyses, systematized in charts, highlight the mobilized mental actions, the contents of long-term and working memory, the attentional demands, and the brain regions presumably involved. The results indicate that the articulation between mathematical mental actions, memory, and attention allows for a deeper understanding of mathematical thinking processes and reinforces the pedagogical potential of task reformulation from a neuroeducational perspective. This dissertation may contribute to the field of Mathematics Education by proposing a replicable analytical methodology grounded in scientific evidence and aligned with students’ cognitive functioning.