Conceções e Práticas na Formação Inicial de Professores sobre Transformações Geométricas

Abstract

In this paper, I intend to present a set of ideas resulting from an approach to geometric transformations, on a flat surface, originating from the future teachers’ conceptions and practices, within the curricular unit of Geometric Transformations of the master’s degree in Teaching in the first cycle of basic education and teaching of mathematics and sciences in the second cycle of basic education, School of Education and Communication, University of Algarve, integrating examples of symmetries, in rosettes, friezes and patterns in nature and art. The methodology used in the collection and analysis of data takes an interpretative stance. The data was collected using the audio records of all classes, the mathematical tasks that were carried out, the teacher’s notes and the future teachers’ output, produced either in the context of the classroom, or as assignments carried out autonomously. Data show that these future teachers rediscovered the concept of symmetry, involving various types of symmetry, in rosettes, friezes and patterns, and were able to make an analysis of less common situations, such as segments of straight line, rosettes (other than those with a circular shape), friezes and patterns with hidden slid reflections. The consolidation of the mathematical knowledge resulted from a diversity of examples of symmetries, in rosettes, friezes and patterns from a new mathematical stance of nature and art, considering the work done in the classroom with students of the second cycle of basic education.