Atividade orientadora de ensino de geometrias na perspectiva lógico-histórica : unidade entre ensino e aprendizagem na formação inicial de professores de matemática

Abstract

The manner Teaching Activities (TAs) of different types of Geometry may be presented as a unity between teaching and learning, or rather, as Teaching Guiding Activity (TGA) in the initial formation of teachers, is discussed. It has thus been presumed that the logical and historical perspective may become a didactic factor in teachers´ initial formation when TAs are developed as from the subject-group-class-narrative dynamics. Current qualitative research was developed based on the following questions: Did teaching activities developed in the disciplines ‘Geometry’ and ‘Euclidian Geometry and Topic for Non-Euclidian Geometries’ generate aims and motives to teach and learn to teach Geometries? Did the activities experienced by the subject-group-class dynamics and posting of narratives become a TGA? Which are the productions of meanings, aims and motives explicit in the narratives prepared by undergraduates of the Math course during their experience in TAs of Geometries within the logical and historical perspective as from the subject-group-class dynamics? Data were retrieved from questionnaires, TAs, field diaries and narratives posted on the Internet. The empirical material was analyzed by four descriptive and analytic categories emerging from three-fold data, namely, From the isolated to the collective; The New; From Learning to Learning to Teach; Contradictions. Results show that Geometry TAs within the logical-historical perspective as from the subject-group-class-narrative dynamics trigger information related to the appropriation of theoretical knowledge, teaching of theoretical knowledge, organization of teaching, pedagogical activities and research in most people involved in the teaching-learning process.