Teorema de Tales: uma abordagem experimental de semelhança de triângulos com estudantes do 9º ano do ensino fundamental

Abstract

Mathematics Education currently faces significant challenges that must be overcome to foster meaningful learning. Prominent barriers include a lack of solid conceptual foundations, instructional methods disconnected from real-world contexts, and inadequate infrastructure. These factors constrain both teaching and learning, imposing concrete obstacles to the pedagogical practice. To address these issues, this study proposes an approach grounded in three theoretical pillars: (1) Mathematical Experimentation as an epistemological tool to contextualize concepts; (2) Problem-Solving Methodology (Polya, 1978), which stimulates active and autonomous thinking; and (3) Critical Meaningful Learning (Moreira, 2006), which emphasizes connections between prior knowledge and new understanding. The primary objective of this research was to investigate the impact of the workshop "The Mathematics of Thales: an experimental activity proposal for Middle School" on students' comprehension of Thales's Theorem and triangle similarity. This qualitative intervention study was conducted with 17 ninth-grade students from a public school, organized into four working groups. The methodology combined experimental activities based on historical problems with participant observation, analysis of written productions, and semi-structured interviews. As an educational product, a didactic workshop structured into four stages was developed, designed as a guide of experimental activities that can be replicated by Mathematics teachers in Basic Education. The results demonstrate an improvement in the learning of mathematical concepts, increased student engagement and motivation, alongside the development of logical reasoning skills applied to problem-solving. These findings align with contemporary trends in Mathematics Education, highlighting that mathematical experimentation, particularly when integrated with a historical perspective, is a promising pathway to overcome decontextualized, purely algorithmic teaching. By reconnecting Mathematics with its human and historical dimensions, this approach not only facilitated learning but also made the content more accessible and relevant, offering a real and innovative alternative to traditional methodologies.