Desvendando o Raciocínio Proporcional: um estudo sobre os conhecimentos necessários para ensinar a comparação por relações

Abstract

This study investigated the professional knowledge of teachers who teach mathematics in the initial years, especially with regard to Proportional Reasoning (PR) especially when comparing relationships between quantities. Using a qualitative approach, four teachers from a private school in São Paulo participated in a group study session. During this session, they resolved a situation involving relational thinking, analyzed responses from fictitious students and discussed a real situation related to the topic. The results revealed a limited initial understanding of RP, with an emphasis on additive approaches and a lack of consideration of proportional relationships between quantities. However, the proposed activity allowed a reflection on the teachers' practices, leading to an expansion of the understanding of RP, especially after analyzing the students' problem-solving strategies. Furthermore, reflection on the graphs presented highlighted the importance of considering different perspectives when interpreting quantitative information. It is concluded that the teaching of RP requires an integration between mathematical and pedagogical knowledge. This study highlights the importance of more in-depth and contextualized approaches to PR both in initial and continuing teacher training.