Investigando geometria: aprendizagens de professoras da educação infantil
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The present work begins from the teaching experience of its researcher and in studies which identify the absence of geometry teaching in the education of children and youngsters; it is also based on data indicating the formation possibilities of mathematical investigation in the math teaching, and research specifically considering geometry as a privileged field for exploration and investigation. Its main objective was to investigate the teaching professional knowledge of four six-year-old pupil teachers and it chiefly focused on the moments when such teachers: got involved in geometry exploratory-investigative activities, discussed the teaching process in this math field, designed tasks to be implemented in the lessons, experienced the pedagogical process and meditated on it. Furthermore, it sought to investigate the formation possibilities of exploratory-investigative activities in the constitution and (re)significance of the teacher s knowledge and the possibilities for such activities to be in the lessons for six-year-olds through the actions developed by the participant teachers. This study counts on the qualitative approach and its theoretical fundamentals lie in the research on teacher s knowledge taking into consideration that learning to teach is a continuous process influenced by various aspects and in the works on exploratory-investigative activities in the math teaching. The empirical data stem from an in-service education course and consist of: researcher s diary notes, participant teachers notes, video recordings, and transcriptions of the recordings at the meetings in the course, where the researcher also acted as a trainer. The data analysis was then based on three facets: the importance geometry takes, exploratory-investigative activities and teacher s knowledge, the reconstruction of professional knowledge as to the reconsideration of the pedagogical praxis. The analysis confirmed that geometry is not a math field regularly present in the teachers school routine owing to their experience when at school as students and presently as teachers. During the participation of the teachers in the activities designed for them to learn geometry in the context of exploratory-investigative math, an initial feeling of estrangement arose towards open-ended tasks, progressed by a questioning and argumentative attitude. It also came to light some elements related to the importance of the tasks in the development of the activity. The reconsideration of the pedagogical practice as a result of the activities experienced and the moments of sharing reflections gave birth to the development of new viewpoints as to how geometry is conceived at the outset of primary school, being beyond geometric patterns and encompassing spatial notions and spatial representations. Moreover, such reconsideration resulted in new elaborations of the pedagogical content knowledge, which indicates possibilities for mathematical exploration-investigation in the math teaching for six-year-olds. It also showed changes in the teachers attitude when adopting a questioning and investigative posture, which would, in turn, take children to question and justify their hypothesis in an integrated activity with their teacher. The actions developed by the participant teachers in the classroom confirmed such possibilities, and brought new perspectives to understand the purpose in the children s writing and attitudes when playing in the room.