Conhecimento didático-matemático: um estudo centrado em áreas e perímetros de polígonos no contexto da Educação Básica

Abstract

The research aimed to analyze the didactic-mathematical knowledge (DMK) mobilized/developed by teachers who teaches Mathematics in the context of Basic Education, specifically concerning the calculation of area and perimeter of polygons. The specific objectives were: (i) to unveil and map the teaching and learning processes in geometry related to the calculation of areas and perimeters of polygons, based on academic Productions undertaken within national postgraduate programs, and (ii) to analyze the didactic mathematical knowledge (DMK) demonstrated by Mathematics teachers in relation to the teaching and learning process of geometry in Basic Education context. This study is justified by the topicality of the matter, the discussions it generates, and the potential contributions to Mathematics didactics, as well as offering new perspectives on research focusing on the DMK of Mathematics teachers. The study object was the calculation of area and perimeter of polygons and the teaching experience of a group of Mathematics teachers in the final years of elementary school and in high school. This work consisted of qualitative research, developed through field research with an exploratory, descriptive, and interpretative approach. The methodological procedures were based on a bibliographic review, stemming from a mapping of national research, and a field study using semi-structured interviews. The theoretical foundation was based on the application of theoretical constructs from the Onto-Semiotic Approach to Mathematical Knowledge and Cognition (OSA), particularly concerning the model of the teacher's didactic-mathematical knowledge (DMK). The research’s main findings, through the mapping technique, included a bibliographic review focused on since the formation of Mathematics teachers until the related theories and practices, as well as the dialogue between higher education institutions and schools. Additionally, it was possible to identify the connections between the experiences of Mathematics teachers, through narratives organized and analyzed using the model of didactic-mathematical knowledge (DMK), encompassing the dimensions of mathematical and didactic knowledge. The study also examined the subdimensions or facets of DMK epistemic, cognitive, affective, interactional, mediational, and ecological highlighting the connections between plane geometry, the calculation of area and perimeter of polygons, and the narratives of Mathematics teachers in the final years of elementary and high school education