Desenvolvendo uma Mentalidade Matemática por meio de uma Abordagem Problematizada no ensino de Áreas Geométricas

Abstract

The motivation for the development of this work arises from the teacher-researcher's experience within the public school network of the municipality of São Gonçalo. Faced with the difficulties observed in students’ learning and through conversations with fellow educators – where the idea that "it's very hard to teach someone who doesn't want to learn" was frequently echoed – and after coming into contact with the book Mathematical Mindsets by Professor Jo Boaler, which emphasizes that the best learning opportunities arise when students believe in themselves, the teacher-researcher began to reflect: do students truly not want to learn, or does a lack of self-confidence result in a seemingly disinterested attitude? From this reflection, the central objective of this research was defined: to observe how students develop a mathematical growth mindset, with a focus on geometry. The adopted methodology is qualitative, drawing inspiration from action research, case study, and investigation of one's own teaching practice. Data production took place through exploratory and investigative mathematical activities, using manipulatives and a dialogical approach. Data were collected through an activity notebook – one for each student group – and through audio recordings of the sessions. The data analysis was guided by the concepts of Mathematical Mindsets, Mathematical Exploration and Investigation, as well as Problem-Based Mathematics. As a result, it was possible to observe significant changes in the way students engaged with mathematics, including how they began to reinterpret concepts, formulate and test hypotheses, and expand their mathematical understanding by working with concepts across different domains. Additionally, a transformation in interpersonal relationships within the learning environment was observed, along with an improvement in students’ self-esteem. It is worth noting that this research resulted in an educational product: a didactic sequence titled Problematizing the Teaching of Area – Creating Meaning and Connections between Arithmetic, Algebra, and Geometry. This material presents the activities developed during our intervention and also suggests other problematizations that could have been proposed to students. The didactic sequence aims to serve as a starting point for other teachers to plan and implement mathematics lessons focused on the development of a growth mindset and the active engagement of students in the learning process.