Unidade de ensino potencialmente significativa com modelagem matemática para a aprendizagem do conceito de volume em uma escola militar do RS ; Potentially meaningful teaching unit with mathematical modeling for the learning of volume concept in a military school of the state of RS

The motivation of this study arises from the perception of the author, who perceives that teaching and learning of the concept of volume in high school happen, as standard, focused on applications of formulas and with little emphasis on contextualized situations. This fact characterizes, in the context of Theory of Meaningful Learning, which is called mechanical learning. Therefore, the problem that guides this research is: "How does the Meaningful Learning process of the concept of volume by students from a class of a Military School of the state of Rio Grande do Sul perform when they undergo a Potentially Meaningful Teaching Unit (PMTU) mediated by activities of Mathematical Modeling? In order to answer this question, a PMTU is proposed and implemented, subsidized by activities of Mathematical Modeling to approach the concept of volume of geometric solids in high school. The didactic sequence presented was structured in such a way that, initially, it was possible to identify the students' previous knowledge regarding the concepts of Plane Geometry and its transition to Space Geometry. The following activities start from more general and inclusive concepts and are progressively differentiated into more specific concepts seeking to favor integrative reconciliation. It can be seen, in the probing phase of students' prior knowledge, a certain fragility of subsumer concepts of Plane Geometry, necessary for anchoring the concepts of Space Geometry. However, with the modeling activity, it was possible to retrieve some necessary prior knowledge and prepare them for future learning that are part of the proposed PMTU, especially with regard to the volume of geometric solids. As the sequential aspects of the teaching unit move forward, we identify the students' ability to make use of the concepts learned in different situations, while demonstrating progress in the exchange and externalization of meanings. However, the summative evaluation allowed us to identify that the greatest obstacle to learning remains prior ...