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Title: O ensino de matemática na escola pública: uma (inter)invenção pedagógica no 7º ano com o conceito de fração
Authors: Silva, Welington Ribeiro da
Keywords: Matemática ensino fundamental;Números racionais;Fração;Estratégias cognitivas;Autoestima;Reconstrução de conceito;Mathematics fundamental schooling;Rational numbers;Fraction;Cognitive strategies;Self-esteem;Reconstruction of concept
Issue Date: 2-Jun-2011
Publisher: Universidade Federal do Espírito Santo
Citation: SILVA, Welington Ribeiro da. O ensino de matemática na escola pública: uma (inter)invenção pedagógica no 7º ano com o conceito de fração. 2011. 260 f. Dissertação (Mestrado em Educação) - Universidade Federal do Espírito Santo, Vitória, 2011.
Abstract: The present work investigates the acquisition of the concept of rational number in its fractional representation in a group of 36 seventh grade students of the fundamental schooling, in a public school of Guarapari/ES. The students developed activities about fraction for about one year. In the year 2009, it was realized a pilot study with the students from this class when they were in the sixth grade. In the year 2010 (in the second semester), the students were investigated by research activities and records developed in the lessons. It was planned and implemented a pedagogical intervention with thirty nine classrooms. These considered the cognitive, affective, social and moral development of the students. And, at the same time, they took advantage of their previous experiences with fractions. The pedagogical intervention let them look again to initial concepts of fraction already studied in previous school years. It searched to instigate the students, and to comprehend cognitive strategies used by them, while conducting them in the process of (re)discovering and (re)constructing the different meanings of fraction. This occurred while they were experimenting and manipulating with concrete materials and/or graphical representations. In the study we describe some cognitive strategies used by the students. We verified disconnection between students‟ comprehension about division and fraction. At the beginning, and during the research, the students` strategies were limited to emphasize the part-whole meaning of fraction. At the initial phases of the work, we observed a strong tendency from some students in associating the fraction idea in geometrical shapes as the relationship between the colored parts to the non-colored ones of a shape. In addition to that, they showed not to comprehend the other ideas and meanings of fraction as part-whole, ratio, division or quotient and of multiplicative operator. During the investigation path, it was taken into consideration the students` informal knowledge, and the different strategies used by them in both individual and group activities. This praised students` knowledge, actions, cognitive strategies and dialogues in classroom. And this promoted interactions among the students and with the teacher with respect to mathematics, and in particular, the fraction concept. This offered a view about the several meanings linked with fraction. In other words, it offered diversity of teaching and learning processes as well as reflections about students` strategies and teacher`s teaching methods. The work restored students` self-esteem who felt completely incapable of learning mathematics because they had remained previously in the same school year two or more time due to their several failure experiences with mathematics. The students felt able to learning mathematics, solving activities and problems and enjoying studying mathematics. The results display the importance of student`s action in the learning tasks through the reconstruction of fraction meanings in the school experience in order to occur a meaningful learning situation. The investigation points out the need to explore the acquisition of rational numbers in several situations and in different contexts, and in this way to rethink the teaching of fraction in school
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