Estudo e ensino de frações : aprendizagens e dificuldades docentes no processo de formação continuada - Siebert, Vani Teresinha (2015)
This research aims to answer “Which are the difficulties and the learning, of teachers of 4th and 5th year of Elementary School, manifested during the formative process in relation to the specific, pedagogical and curricular knowledge about fractions?”. For its development, we counted with the collaboration of three teachers: one of the 4th year and two of the 5th year of Elementary School in two schools in the city of Cuiabá-MT. As theoretical foundation, we based ourselves in the Cultural-Historical Theory (Vigotsky, 2003; Leontiev, 1972; Moura, 2001, 2004, 2008, 2010; Kopnim, 1978), with methodological foundation in the qualitative research (Bogdan & Biklen, 1994) of the action research (Thiollent, 2003; Ghedin; Franco, 2008). It was in the context of Observatory Project of Education with focus in Mathematics and initiative to Sciences (OBEDUC) that the interest for this research began. Acting as a master degree student with scholarship, the formative encounters developed and the result of tests made through this project showed the fragility of students and teachers to the comprehension and treatment of teaching fractions. In front of this scenery, the proposition of offering continuing formation to these teachers, besides the already done by the project, it was constituted as a possibility of intervention in this reality. So, the investigation is developed from a proposal of continuing formation that was organized in a movement that integrated nine encounters of formation; following-up of planning activities of the teachers and the development of the activities planned with the students in the classroom. The formative process had as foundation the Theory of Activity of Leontiev (1972) and Palma (2010), comprehending the continuing formation as a process that has to allow and promote the professional and personal development of the teachers. We had as research data source: semi-structured interview; observation; video-graphic record; teacher’s portfolio; record of the following-up meeting in the school and field diary of the trainer/researcher. For the analysis procedures, we later defined three categories: The motives: the mathematics and the fractions in the educational, academic and professional trajectories of teachers; The processes of appropriation and concept signification; The movement of reorganization of actions: the advances and difficulties. The results show that the teachers had few opportunities of access and attribution of meanings to the study of fractions in their educational, academic and professional trajectories. Among the learning manifested by the teachers, we point out, in relation to the specific knowledge, the attribution of other meanings to the fractions beside of part/whole and quotient. In relation to the pedagogic and curricular knowledge, our data point, among other, to the reorganization of the teaching of fraction: they considered in the planning other curricular references beyond the book and they contemplate in the development of this school content the origin of fraction as a fruit of human construction associated to the need for measuring. Among the difficulties in relation to the pedagogical, curricular and specific knowledge, showed in this order, the results indicated: handling the questions and answers of students; using and comprehending the proposals of the curricular references and representing geometrically the improper fractions. We understand that, to appropriate of the specific content to be taught and to know the how and also the meaning of teaching it, it is part of the process of humanize yourself and become a teacher.