Contribuições da resolução, exploração e proposição de problemas ao processo de ensino e aprendizagem da combinatória nos anos iniciais do Ensino Fundamental

Abstract

This research investigates the contributions of Problem Solving, Exploration and Posing to the teaching and learning process of Combinatorics in the early years of Elementary School, based on studies related to the Problem Solving methodology and Combinatorial Education. By means of bibliographical survey and studies discussed in the theoretical frame of reference, it is observed that, although the amount of research in the domain of Combinatory Education has increased progressively in recent years, there are still few studies specifically focused on pedagogical work in the early years of Elementary Education. Field research is characterized by a qualitative nature, as it has been endeavored to describing and analyzing in detail the data collected through observations, field notes, written record by the students and audio recordings (BOGDAN; BIKLEN, 1994; OLSEN, 2015). As subjects of the research, 16 students from a 5th grade class from Primary School of a municipal public institution in the State of Paraíba were adopted. Pedagogical activities carried out in classroom context were supported by the methodological perspective of Problem Solving, Exploration and Posing advocated by Andrade (1998; 2017), as well as by studies related to teaching and learning process of Combinatorics. On that occasion, the four types of combinatorial problems (combination, arrangement, permutation and Cartesian product [BORBA, 2010]) – which need to be approached in the early years of Elementary Education – were worked on, taking as basis combinatorial problems extracted from Pessoa's research (2009) and proposed by the students. The conclusion is that the methodological proposal of Problem Solving, Exploration and Posing contributes to promoting combinatorial learning for the benefit of students, making it possible to develop a reflective educational process. It was found that the discussions that arose during the process of Problem Solving, Exploration and Posing maximized reflection on the invariants of the combinatorial problems, which favored the development of logical generalizing combinatorial reasoning on the part of the students, while it made possible to explore different dimensions of the proposed problems dealing with these aspects.