Ensino e aprendizagem de fração via exploração-resolução-proposição de problemas

Abstract

The aim of this study is to identify how the Problem Exploration-Posing-Solving can boost the teaching and learning of fractions. Based on the problem solving perspective, the research explored conceptual ideas related to the teaching and learning of fraction, employing the Tangram as a manipulative material and the Exploration as a connecting thread. Such exploration is not just about the mathematical context, but is also about the social world; exploration that goes beyond inquiring, problematizing, investigating; a free, though not loose, exploration, such as described by Andrade (1988; 2017); a critic and creative exploration, which flows from the interaction and socialization of ideas between teacher-student and/or student-student; a reflexive exploration, that views, reviews, creates and recreates new perspectives, generating new problems, promoting new forms of exploration and so on. Therefore, this study was conducted through a qualitative approach, in the teacher Research modality, since it favors the survey data collection and, besides that, this kind of research enables a teaching upgrading in connection to mathematics teaching practices and, thus, the development of alternatives that might enrich the learning process. The locus of the research is a public school situated in Lagoa Seca-PB, and the participants are 25 students from the 5th grade A of the morning shift, with ages ranging from 10 to 15. The present study, 15 meetings were arranged in two phases: the first phase consisted of the diagnostic activity I and II and the second phase was based on the pedagogical intervention. The obtained results point to a potentiation in the teaching and learning of fractions through the Problem Exploration-Posing-Solving, since it gives the teachers the chance to evaluate their own practice and the chance to also evaluate, in the meantime, if and how the students are moving forward in the process of learning fractions and other inherent aspects of the subject. In this way, teachers will be able to articulate means and practices that might lead to a greater success in the mediation by giving the students the chance to solve and to come up with new problem sin an interactive, free, critic and creative way, while at the same time exploring, externalizing and getting their minds around fraction, converting and inverting, representing it graphically, numerically and in full. Therefore, through this research we conclude that the proposal, in a significant way, favored the reading and writing of fractions; the identification of the fractional portion configuration, indicating the difference between fraction and ratio; the identification of the essential meanings of a fraction, taking into account that regarding the fraction with numerical meaning and the fraction with operator meaning, the identification was accomplished. It was identified, however, a struggle with going deeper, especially when it comes to the fraction with numerical meaning, perhaps because it demands a higher abstract cognitive maturation.