A construção do conceito de simetria: contribuições da matemática e cultura e das atividades didáticas

Abstract

Mathematics is a science full of meanings, also in everyday life. Cultural practices can and should be used in the teaching of this discipline. However, the mathematical interrelationship and culture is not a reality in public schools, because in most cases the main pedagogical resource is the textbook and the presentation of content is given in a hierarchical way, teaching first the easiest contents which will be a prerequisite for learning more complex content. The purpose of this study was to analyze the learning process of a class of students from the 9th grade of elementary school in the final years, especially on the mathematical concepts involving symmetry and isometry from Didactic Activities (AD) that relate bobbin lace and the cultural mathematics elaborated by Santos (2012). The study is qualitative, of the inductive type, with exploratory purposes, aiming at the approximation of the mathematical learning with the culture. We outlined the work based on the participant observation, the subjects were 30 students of the 9th grade of elementary school final years of a school in the municipal public school of Caucaia - Ceará. As a source of data collection we adopted the record from photographs and the field diary, for annotations of the responses produced by the students in the Didactic Activities (AD), as well as comments of facts occurred during the investigative process during the Didactic Session (SD), based in the methodological assumptions of the Fedathi Sequence (SF). Our results allowed to identify conceptual gaps of the students with respect to the geometric transformations, mainly in relation to the concept of reflection. We also observed the students' primary difficulties regarding the concept of laterality. From the analysis we verified that the AD proposed by Santos (2012) corroborate the learning of the concepts of geometric transformation, specifically, rotation, translation and reflection, mainly for evidencing the visualization and representation skills, fundamental for learning these concepts.