O conceito de escala em situações cotidianas: uma experiência de ensino remoto da Matemática

Abstract

The study of the concept of scale is foreseen in the Base Nacional Comum Curricular (BNCC) from the 6th year of Elementary Education, in the thematic unit of quantities and measures, but the mobilization of knowledge linked to this concept begins in the initial years, when they are studied length measurements, flat geometric figures, fractional representations, among others. The present work contemplates a qualitative research-intervention research that aimed to investigate the contributions of a short course offered remotely to the understanding of the concept of numerical scale by students of Basic Education. The research-intervention methodology is based on the studies of Magda Damiani and the discussions about the results are based on the Theory of Conceptual Fields, by Gérard Vergnaud. The intervention research took place in a thirty-hour mini-course for students and teachers of Basic Education carried out in remote mode. Fifty places were offered in the mini-course, but despite the 21 enrolled, 11 of them did participate. The mini-course was structured in five synchronous meetings via Google Meet and four sequences of activities in the asynchronous modality available in a virtual environment (Classroom). In the first stage of the research, a survey of works on the concept of scale, reason and proportion was carried out in the annals of the Encontro Nacional de Educação Matemática (ENEM), from its first edition (1987) to the last (2019) through the analysis of the titles and the body of the text. The analysis of the works showed that the concepts of reason and proportion are related to those of scale, since one of the applications of the idea of ratio between two quantities is found in the reduction scale and in the enlargement scale, known simply as scale, and the concept of proportion establishes an equality between two reasons. The results of the intervention-research show that the short course offered remotely contributed to the students' understanding of the concept of numerical scale and its daily use. They also show that, in order to learn the meaning and applications of the concept of scale, it is necessary to understand other concepts, which makes the mastery of a concept somewhat complex. It was found that the study of a certain concept may require a longer time, which depends on the knowledge that the subjects have or that need to be acquired when solving situations associated with the same concept.