CONTRIBUIÇÕES DA TEORIA DOS CAMPOS CONCEITUAIS PARA O DESENVOLVIMENTO DO CONCEITO DE VOLUME DO CILINDRO

The present work aims to analyze the operational invariants mobilized by 3rd grade high school students in problem situations involving the concept of volume of the solid geometric cylinder. This is research with a qualitative and participatory approach. Data collection was carried out in a state school, in the city of Manaus in Amazonas, in the second half of 2023. The didactic event, proposed by Vergnaud and adopted by researchers at the field school to study the research object, was organized in three meetings, in which a problem situation was presented in each, on the concept of solid cylinder volume so that participants could explore and present their solutions. In this study, an excerpt from the research referring to the first meeting developed with the participants is presented. For this purpose, observation, the logbook, the recording of the dialogues carried out by the participants and the photographic record of the resolutions presented were adopted as instruments. Among the results, a constant need for the participant to resort to the use of algorithms was observed (leaving the conceptualization process in the background), the difficulty of expressing thoughts was made explicit in questions that asked for an organization of the steps adopted, implying the operational form of the thought. We point out that there are true and false operational invariants, however, what draws attention is the number of pertinent concepts in action that show obstacles in the consolidation of the concept of volume and other concepts of plane geometry.