A exploração-investigação matemática: potencialidades na formação contínua de professores
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This thesis work evaluated the formative potentialities in mathematical explorationinvestigation for the professionals teaching mathematics for children from six to eleven years old pre-school teachers, teachers of the elementary school, and a professor of mathematics (student in pedagogy) focusing: (a) the development of exploratoryinvestigative activities in a group of teachers which periodically meet together for share new professional experiences, and (b) professional pedagogic practices developed with reference to the mathematical exploration-investigation. The main question was described: What are the formative potentialities of the mathematics exploration-investigation for teachers engagement in developing mathematics teaching? . The context of this work was to obtain the data collection of a continuous forming group involving the participants and the researcher, in order to investigate this thesis qualitatively in narrative style evaluating the life experiencing representation, valuing the perspectives of the group participants, producing a text based in a continuous movement for life, representing, evaluating, and representing again. The material analyzed was composed by: video recordings transcribed by the researcher; written and oral narratives from researcher and participants; researcher´s diary notes; written data of teacher and their students and pictures. According with the data of the authors who analyze the mathematics explorationinvestigation, the professional apprenticeship, and formation in their life we could conclude that the explorative-investigative activities were the responsible for the increasing teachers knowledge of geometrical contents in their substantive and syntactic structures, and reflections about didactic resources. Besides, it was possible to evidentiate elements that relate tasks in a sequence, and the activities developed as promoter of problematization of professionals practices of the teachers. In the classroom of the first years of the elementary school, the activities were transformed in opened problems and explorationinvestigativon, with encouraging the creation of an environment of negotiation of meaning and communication of ideas with the children. This has enabled teachers apprenticeship for improve their knowledge about their students and how they might arguing, questioning and establishing investigative positions in geometry class and in other contents and about way of teacher s intervention to enable such situations.