O ensino da proporcionalidade na perspectiva da teoria das situações didáticas: uma engenharia didática com estudantes do 9º ano do ensino fundamental

Abstract

Proportionality is a concept considered essential for understanding various topics in Mathematics, and is also fundamental for solving everyday problems. This concept has been applied in external assessments, such as those of the Basic Education Assessment System (SAEB), at national level, and the Ceará Permanent Basic Education Assessment System (SPAECE), at state level, whose results demonstrate the lack of appropriation of it. The objective of this work is to evaluate, from the perspective of TSD and ED, didactic situations that involve proportionality and that use the Modellus software, through applications with students in the 9th year of Elementary School. The software is used to make learning these concepts more meaningful, by enabling better visualization and dynamism of teaching situations. Didactic Engineering (DE) is used as a research methodology. From this perspective, this study is divided into the stages proposed by ED namely: prior analysis, a priori analysis, experimentation and a posteriori analysis and validation. In the first stage, Preliminary analyses, an epistemological, documentary and didactic analysis on proportionality was carried out. In the second stage, didactic situations were constructed using the Modellus software and the research investigation hypotheses were defined. The experimentation stage was embodied by the application of didactic situations with students in the last year of Elementary School at a municipal public school in Fortaleza. Finally, in the a posteriori analysis and validation phase, an analysis was made of the records from the previous stage during the dialectics of TSD, action, formulation, validation and institutionalization. Furthermore, at this stage, the hypotheses constructed in the second stage of DE were validated, evaluating the reproducibility of the didactic situations. As an Educational Product (EP), a website was created that provides four teaching situations, as well as reading suggestions and other materials that supported this research. The results of this study corroborate that the use of Modellus software to teach proportionality promotes an investigative and creative environment, which places the student as an active subject in the process of building their knowledge. Furthermore, it was proven that TSD structures didactic situations, giving the teacher the possibility to predict student actions, allowing the management of these actions, however, allowing the student to be active in their learning process. This study envisions the use of this methodological proposal by other teachers and researchers who wish to integrate digital technologies to teach proportionality, aiming for students to have a more informed learning about this concept.